@article {3486, title = {Average R{\'e}nyi Entanglement Entropy in Gaussian Boson Sampling}, year = {2024}, month = {3/27/2024}, abstract = {

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian Boson Sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this work, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various R{\'e}nyi-α entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for α=1 (i.e. the von Neumann entropy), and, more generally, for all positive integer α, in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the R{\'e}nyi-α variance for integers α\>1, and we are able to show that these entropies are weakly typical.

}, url = {https://arxiv.org/abs/2403.18890}, author = {Jason Youm and Joseph T. Iosue and Adam Ehrenberg and Yu-Xin Wang and Alexey V. Gorshkov} } @article {3490, title = {Efficiently verifiable quantum advantage on near-term analog quantum simulators}, year = {2024}, month = {3/13/2024}, abstract = {

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an O(λ2)-time classical computation, and the prover need only prepare O(1) samples of a history state and perform O(λ2) single-qubit measurements, for a security parameter λ. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

}, url = {https://arxiv.org/abs/2403.08195}, author = {Zhenning Liu and Dhruv Devulapalli and Dominik Hangleiter and Yi-Kai Liu and Alicia J. Koll{\'a}r and Alexey V. Gorshkov and Andrew M. Childs} } @article {3462, title = {Estimation of Hamiltonian parameters from thermal states}, year = {2024}, month = {1/18/2024}, abstract = {

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term\&$\#$39;s degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/n\−\−\√, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g. a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

}, url = {https://arxiv.org/abs/2401.10343}, author = {Luis Pedro Garc{\'\i}a-Pintos and Kishor Bharti and Jacob Bringewatt and Hossein Dehghani and Adam Ehrenberg and Nicole Yunger Halpern and Alexey V. Gorshkov} } @article {3498, title = {Experimental roadmap for optimal state transfer and entanglement generation in power-law systems}, year = {2024}, month = {2/12/2024}, abstract = {

Experimental systems with power-law interactions have recently garnered interest as promising platforms for quantum information processing. Such systems are capable of spreading entanglement superballistically and achieving an asymptotic speed-up over locally interacting systems. Recently, protocols developed by Eldredge et al. [Phys. Rev. Lett. 119, 170503 (2017)] and Tran et al. [Phys. Rev. X 11, 031016 (2021)] for the task of transferring a quantum state between distant particles quickly were shown to be optimal and saturate theoretical bounds. However, the implementation of these protocols in physical systems with long-range interactions remains to be fully realized. In this work, we provide an experimental roadmap towards realizing fast state-transfer protocols in three classes of atomic and molecular systems with dipolar interactions: polar molecules composed of alkali-metal dimers, neutral atoms in excited Rydberg states, and atoms with strong magnetic moments (e.g. dysprosium). As a guide to near-term experimental implementation, we numerically evaluate the tradeoffs between the two protocols for small system sizes and develop methods to address potential crosstalk errors that may arise during the execution of the protocols.

}, url = {https://arxiv.org/abs/2402.07974}, author = {Andrew Y. Guo and Jeremy T. Young and Ron Belyansky and Przemyslaw Bienias and Alexey V. Gorshkov} } @article {3488, title = {The Second Moment of Hafnians in Gaussian Boson Sampling}, year = {2024}, month = {3/20/2024}, abstract = {

Gaussian Boson Sampling is a popular method for experimental demonstrations of quantum advantage, but many subtleties remain in fully understanding its theoretical underpinnings. An important component in the theoretical arguments for approximate average-case hardness of sampling is anticoncentration, which is a second-moment property of the output probabilities. In Gaussian Boson Sampling these are given by hafnians of generalized circular orthogonal ensemble matrices. In a companion work [arXiv:2312.08433], we develop a graph-theoretic method to study these moments and use it to identify a transition in anticoncentration. In this work, we find a recursive expression for the second moment using these graph-theoretic techniques. While we have not been able to solve this recursion by hand, we are able to solve it numerically exactly, which we do up to Fock sector 2n=80. We further derive new analytical results about the second moment. These results allow us to pinpoint the transition in anticoncentration and furthermore yield the expected linear cross-entropy benchmarking score for an ideal (error-free) device.

}, url = {https://arxiv.org/abs/2403.13878}, author = {Adam Ehrenberg and Joseph T. Iosue and Abhinav Deshpande and Dominik Hangleiter and Alexey V. Gorshkov} } @article {3491, title = {Simulating Meson Scattering on Spin Quantum Simulators}, year = {2024}, month = {3/11/2024}, abstract = {

Studying high-energy collisions of composite particles, such as hadrons and nuclei, is an outstanding goal for quantum simulators. However, preparation of hadronic wave packets has posed a significant challenge, due to the complexity of hadrons and the precise structure of wave packets. This has limited demonstrations of hadron scattering on quantum simulators to date. Observations of confinement and composite excitations in quantum spin systems have opened up the possibility to explore scattering dynamics in spin models. In this article, we develop two methods to create entangled spin states corresponding to wave packets of composite particles in analog quantum simulators of Ising spin Hamiltonians. One wave-packet preparation method uses the blockade effect enabled by beyond-nearest-neighbor Ising spin interactions. The other method utilizes a quantum-bus-mediated exchange, such as the native spin-phonon coupling in trapped-ion arrays. With a focus on trapped-ion simulators, we numerically benchmark both methods and show that high-fidelity wave packets can be achieved in near-term experiments. We numerically study scattering of wave packets for experimentally realizable parameters in the Ising model and find inelastic-scattering regimes, corresponding to particle production in the scattering event, with prominent and distinct experimental signals. Our proposal, therefore, demonstrates the potential of observing inelastic scattering in near-term quantum simulators.

}, url = {https://arxiv.org/abs/2403.07061}, author = {Elizabeth R. Bennewitz and Brayden Ware and Alexander Schuckert and Alessio Lerose and Federica M. Surace and Ron Belyansky and William Morong and De Luo and Arinjoy De and Kate S. Collins and Or Katz and Christopher Monroe and Zohreh Davoudi and Alexey V. Gorshkov} } @article {3480, title = {Strong interactions between integrated microresonators and alkali atomic vapors: towards single-atom, single-photon operation}, year = {2024}, month = {4/5/2024}, abstract = {

Cavity quantum electrodynamics (cQED), the interaction of a two-level system with a high quality factor (Q) cavity, is a foundational building block in different architectures for quantum computation, communication, and metrology. The strong interaction between the atom and the cavity enables single photon operation which is required for quantum gates and sources. Cold atoms, quantum dots, and color centers in crystals are amongst the systems that have shown single photon operations, but they require significant physical infrastructure. Atomic vapors, on the other hand, require limited experimental infrastructure and are hence much easier to deploy outside a laboratory, but they produce an ensemble of moving atoms that results in short interaction times involving multiple atoms, which can hamper quantum operations. A solution to this issue can be found in nanophotonic cavities, where light-matter interaction is enhanced and the volume of operation is small, so that fast single-atom, single-photon operations are enabled. In this work, we study the interaction of an atomically-clad microring resonator (ACMRR) with different-sized ensembles of Rb atoms. We demonstrate strong coupling between an ensemble of ~50 atoms interacting with a high-quality factor (Q \> 4 x 10^5) ACMRR, yielding a many-atom cooperativity C ~ 5.5. We continue to observe signatures of atom-photon interaction for a few (\< 3) atoms, for which we observe saturation at the level of one intracavity photon. Further development of our platform, which includes integrated thermo-optic heaters to enable cavity tuning and stabilization, should enable the observation of interactions between single photons and single atoms.

}, url = {https://arxiv.org/abs/2404.04372}, author = {Roy Zektzer and Xiyuan Lu and Khoi Tuan Hoang and Rahul Shrestha and Sharoon Austin and Feng Zhou and Ashish Chanana and Glenn Holland and Daron Westly and Paul Lett and Alexey V. Gorshkov and Kartik Srinivasan} } @article {3505, title = {Ultrastrong light-matter interaction in a multimode photonic crystal}, year = {2024}, month = {2/21/2024}, abstract = {

Harnessing the interaction between light and matter at the quantum level has been a central theme in atomic physics and quantum optics, with applications from quantum computation to quantum metrology. Combining complex interactions with photonic synthetic materials provides an opportunity to investigate novel quantum phases and phenomena, establishing interesting connections to condensed matter physics. Here we explore many-body phenomena with a single artificial atom coupled to the many discrete modes of a photonic crystal. This experiment reaches the ultrastrong light-matter coupling regime using the circuit quantum electrodynamics paradigm, by galvanically coupling a highly nonlinear fluxonium qubit to a tight-binding lattice of microwave resonators. In this regime, the transport of a single photon becomes a many-body problem, owing to the strong participation of multi-photon bound states arising from interactions that break particle number conservation. Exploiting the effective photon-photon interactions mediated by the qubit, the transport of multiple photons leads to complex multimode dynamics that can be employed for generating a continuous reservoir of strongly-correlated photons, an important resource for quantum networks. This work opens exciting prospects for exploring nonlinear quantum optics at the single-photon level and stabilizing entangled many-body phases of light.

}, url = {https://arxiv.org/abs/2209.14972}, author = {Andrei Vrajitoarea and Ron Belyansky and Rex Lundgren and Seth Whitsitt and Alexey V. Gorshkov and Andrew A. Houck} } @article {3056, title = {Advantages and limitations of quantum routing}, journal = {PRX Quantum}, volume = {4}, year = {2023}, month = {2/1/2023}, abstract = {

The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (1) allowing arbitrary two-qubit unitaries, or (2) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constraints, and give a generalized upper bound for all simple connected n-vertex graphs. In particular, we give conditions for a superpolynomial classical-quantum routing separation, which exclude graphs with a small spectral gap and graphs of bounded degree. Finally, we provide examples of a quadratic separation between gate-based and Hamiltonian routing models with a constant number of local ancillas per qubit and of an Ω(n) speedup if we also allow fast local interactions.

}, keywords = {Data Structures and Algorithms (cs.DS), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1103/PRXQuantum.4.010313}, url = {https://arxiv.org/abs/2206.01766}, author = {Bapat, Aniruddha and Andrew M. Childs and Alexey V. Gorshkov and Schoute, Eddie} } @article {3360, title = {Bounds on Autonomous Quantum Error Correction}, year = {2023}, month = {8/30/2023}, abstract = {

Autonomous quantum memories are a way to passively protect quantum information using engineered dissipation that creates an \"always-on\&$\#$39;\&$\#$39; decoder. We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit and bosonic error-correcting codes, and derive several upper bounds and a lower bound on the logical error rate in terms of correction and noise rates. For many-body quantum codes, we show that, to achieve error suppression comparable to active error correction, autonomous decoders generally require correction rates that grow with code size. For codes with a threshold, we show that it is possible to achieve faster-than-polynomial decay of the logical error rate with code size by using superlogarithmic scaling of the correction rate. We illustrate our results with several examples. One example is an exactly solvable global dissipative toric code model that can achieve an effective logical error rate that decreases exponentially with the linear lattice size, provided that the recovery rate grows proportionally with the linear lattice size.

}, url = {https://arxiv.org/abs/2308.16233}, author = {Oles Shtanko and Yu-Jie Liu and Simon Lieu and Alexey V. Gorshkov and Victor V. Albert} } @article {3258, title = {Candidate for a passively protected quantum memory in two dimensions}, year = {2023}, month = {3/2/2023}, abstract = {

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a {\textquoteleft}{\textquoteleft}passively protected quantum memory,\&$\#$39;\&$\#$39; defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model, the photonic-Ising model, which appears to passively correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic {\textquoteleft}{\textquoteleft}cat qubits\&$\#$39;\&$\#$39; coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z2-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips. We also discuss possible ways to realize the photonic-Ising model.

}, url = {https://arxiv.org/abs/2205.09767}, author = {Simon Lieu and Yu-Jie Liu and Alexey V. Gorshkov} } @article {3359, title = {Fault-tolerant hyperbolic Floquet quantum error correcting codes}, year = {2023}, month = {9/18/2023}, abstract = {

A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call \"hyperbolic Floquet codes.\" These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for n qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate (1/8+2/n) and have a depth-3 syndrome extraction circuit. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in n. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1\% in a phenomenological noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a [[400,52,8]] code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.

}, url = {https://arxiv.org/abs/2309.10033}, author = {Ali Fahimniya and Hossein Dehghani and Kishor Bharti and Sheryl Mathew and Alicia J. Koll{\'a}r and Alexey V. Gorshkov and Michael Gullans} } @article {3305, title = {High-Energy Collision of Quarks and Hadrons in the Schwinger Model: From Tensor Networks to Circuit QED}, year = {2023}, month = {7/5/2023}, abstract = {

With the aim of studying nonperturbative out-of-equilibrium dynamics of high-energy particle collisions on quantum simulators, we investigate the scattering dynamics of lattice quantum electrodynamics in 1+1 dimensions. Working in the bosonized formulation of the model, we propose an analog circuit-QED implementation that is native to the platform, requires minimal ingredients and approximations, and enables practical schemes for particle wave-packet preparation and evolution. Furthermore, working in the thermodynamic limit, we use uniform-matrix-product-state tensor networks to construct multi-particle wave-packet states, evolve them in time, and detect outgoing particles post collision. This facilitates the numerical simulation of scattering experiments in both confined and deconfined regimes of the model at different energies, giving rise to rich phenomenology, including inelastic production of quark and meson states, meson disintegration, and dynamical string formation and breaking. We obtain elastic and inelastic scattering cross sections, together with time-resolved momentum and position distributions of the outgoing particles. This study highlights the role of classical and quantum simulation in enhancing our understanding of scattering processes in quantum field theories in real time.

}, url = {https://arxiv.org/abs/2307.02522}, author = {Ron Belyansky and Seth Whitsitt and Niklas Mueller and Ali Fahimniya and Elizabeth R. Bennewitz and Zohreh Davoudi and Alexey V. Gorshkov} } @article {3423, title = {Improved Digital Quantum Simulation by Non-Unitary Channels}, year = {2023}, month = {7/24/2023}, abstract = {

Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the randomization of Suzuki-Trotter product formulas have been shown to be a powerful approach to reducing the errors of quantum simulation and lowering the gate count. In this paper, we study the performance of non-unitary simulation channels and consider the error structure of channels constructed from a weighted average of unitary circuits. We show that averaging over just a few simulation circuits can significantly reduce the Trotterization error for both single-step short-time and multi-step long-time simulations. We focus our analysis on two approaches for constructing circuit ensembles for averaging: (i) permuting the order of the terms in the Hamiltonian and (ii) applying a set of global symmetry transformations. We compare our analytical error bounds to empirical performance and show that empirical error reduction surpasses our analytical estimates in most cases. Finally, we test our method on an IonQ trapped-ion quantum computer accessed via the Amazon Braket cloud platform, and benchmark the performance of the averaging approach.

}, url = {https://arxiv.org/abs/2307.13028}, author = {W. Gong and Yaroslav Kharkov and Minh C. Tran and Przemyslaw Bienias and Alexey V. Gorshkov} } @article {3369, title = {Minimum-entanglement protocols for function estimation}, journal = {Physical Review Research}, volume = {5}, year = {2023}, month = {9/29/2023}, abstract = {

We derive a family of optimal protocols, in the sense of saturating the quantum Cram{\'e}r-Rao bound, for measuring a linear combination of d field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor network applications. We demonstrate how to select different protocols from this family under various constraints. Focusing primarily on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality in many cases. Specifically, we prove necessary and sufficient conditions for the existence of optimal protocols using at most k-partite entanglement. We prove that the protocols which satisfy these conditions use the minimum amount of entanglement possible, even when given access to arbitrary controls and ancilla. Our protocols require some amount of time-dependent control, and we show that a related class of time-independent protocols fail to achieve optimal scaling for generic functions.

}, doi = {10.1103/physrevresearch.5.033228}, url = {https://arxiv.org/abs/2110.07613}, author = {Adam Ehrenberg and Jacob Bringewatt and Alexey V. Gorshkov} } @article {3358, title = {Non-equilibrium critical scaling and universality in a quantum simulator}, year = {2023}, month = {9/19/2023}, abstract = {

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-ion resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents. While a generic quench can lead to thermal critical behaviour, we find that a second quench from one critical state to another (i.e. a double quench) results in critical behaviour that does not have an equilibrium counterpart. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond the equilibrium paradigm.

}, url = {https://arxiv.org/abs/2309.10856}, author = {A. De and P. Cook and K. Collins and W. Morong and D. Paz and P. Titum and G. Pagano and Alexey V. Gorshkov and M. Maghrebi and C. Monroe} } @article {3413, title = {Observation of a finite-energy phase transition in a one-dimensional quantum simulator}, year = {2023}, month = {10/30/2023}, abstract = {

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition in 1D can occur in the presence of long-range interactions, but an experimental realization has so far not been achieved due to the requirement to both prepare equilibrium states and realize sufficiently long-range interactions. Here we report on the first experimental demonstration of a finite-energy phase transition in 1D. We use the simple observation that finite-energy states can be prepared by time-evolving product initial states and letting them thermalize under the dynamics of a many-body Hamiltonian. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system. We observe a ferromagnetic equilibrium phase transition as well as a crossover from a low-energy polarized paramagnet to a high-energy unpolarized paramagnet in a system of up to 23 spins, in excellent agreement with numerical simulations. Our work demonstrates the ability of quantum simulators to realize and study previously inaccessible phases at finite energy density.

}, url = {https://arxiv.org/abs/2310.19869}, author = {Alexander Schuckert and Or Katz and Lei Feng and Eleanor Crane and Arinjoy De and Mohammad Hafezi and Alexey V. Gorshkov and Christopher Monroe} } @article {3315, title = {Page curves and typical entanglement in linear optics}, journal = {Quantum}, volume = {7}, year = {2023}, month = {5/18/2023}, pages = {1017}, abstract = {

Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the R{\'e}nyi-2 Page curve (the average R{\'e}nyi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the R{\'e}nyi-2 entropy by studying its variance. Using the aforementioned results for the R{\'e}nyi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity.

}, doi = {10.22331/q-2023-05-23-1017}, url = {https://arxiv.org/abs/2209.06838}, author = {Joseph T. Iosue and Adam Ehrenberg and Dominik Hangleiter and Abhinav Deshpande and Alexey V. Gorshkov} } @article {3405, title = {Projective toric designs, difference sets, and quantum state designs}, year = {2023}, month = {11/22/2023}, abstract = {

Trigonometric cubature rules of degree t are sets of points on the torus over which sums reproduce integrals of degree t monomials over the full torus. They can be thought of as t-designs on the torus. Motivated by the projective structure of quantum mechanics, we develop the notion of t-designs on the projective torus, which, surprisingly, have a much more restricted structure than their counterparts on full tori. We provide various constructions of these projective toric designs and prove some bounds on their size and characterizations of their structure. We draw connections between projective toric designs and a diverse set of mathematical objects, including difference and Sidon sets from the field of additive combinatorics, symmetric, informationally complete positive operator valued measures (SIC-POVMs) and complete sets of mutually unbiased bases (MUBs) (which are conjectured to relate to finite projective geometry) from quantum information theory, and crystal ball sequences of certain root lattices. Using these connections, we prove bounds on the maximal size of dense Btmodm sets. We also use projective toric designs to construct families of quantum state designs. Finally, we discuss many open questions about the properties of these projective toric designs and how they relate to other questions in number theory, geometry, and quantum information.

}, url = {https://arxiv.org/abs/2311.13479}, author = {Joseph T. Iosue and T. C. Mooney and Adam Ehrenberg and Alexey V. Gorshkov} } @article {3400, title = {Quantum Algorithms for Simulating Nuclear Effective Field Theories}, year = {2023}, month = {12/8/2023}, abstract = {

Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources, we employ state-of-the-art Hamiltonian-simulation methods, and conduct a thorough algorithmic analysis, to estimate the qubit and gate costs to simulate low-energy effective field theories (EFTs) of nuclear physics. In particular, within the framework of nuclear lattice EFT, we obtain simulation costs for the leading-order pionless and pionful EFTs. We consider both static pions represented by a one-pion-exchange potential between the nucleons, and dynamical pions represented by relativistic bosonic fields coupled to non-relativistic nucleons. We examine the resource costs for the tasks of time evolution and energy estimation for physically relevant scales. We account for model errors associated with truncating either long-range interactions in the one-pion-exchange EFT or the pionic Hilbert space in the dynamical-pion EFT, and for algorithmic errors associated with product-formula approximations and quantum phase estimation. Our results show that the pionless EFT is the least costly to simulate and the dynamical-pion theory is the costliest. We demonstrate how symmetries of the low-energy nuclear Hamiltonians can be utilized to obtain tighter error bounds on the simulation algorithm. By retaining the locality of nucleonic interactions when mapped to qubits, we achieve reduced circuit depth and substantial parallelization. We further develop new methods to bound the algorithmic error for classes of fermionic Hamiltonians that preserve the number of fermions, and demonstrate that reasonably tight Trotter error bounds can be achieved by explicitly computing nested commutators of Hamiltonian terms. This work highlights the importance of combining physics insights and algorithmic advancement in reducing quantum-simulation costs.

}, url = {https://arxiv.org/abs/2312.05344}, author = {James D. Watson and Jacob Bringewatt and Alexander F. Shaw and Andrew M. Childs and Alexey V. Gorshkov and Zohreh Davoudi} } @article {3355, title = {Quantum Sensing with Erasure Qubits}, year = {2023}, month = {10/2/2023}, abstract = {

The dominant noise in an \"erasure qubit\" is an erasure -- a type of error whose occurrence and location can be detected. Erasure qubits have potential to reduce the overhead associated with fault tolerance. To date, research on erasure qubits has primarily focused on quantum computing and quantum networking applications. Here, we consider the applicability of erasure qubits to quantum sensing and metrology. We show theoretically that, for the same level of noise, an erasure qubit acts as a more precise sensor or clock compared to its non-erasure counterpart. We experimentally demonstrate this by artificially injecting either erasure errors (in the form of atom loss) or dephasing errors into a differential optical lattice clock comparison, and observe enhanced precision in the case of erasure errors for the same injected error rate. Similar benefits of erasure qubits to sensing can be realized in other quantum platforms like Rydberg atoms and superconducting qubits

}, url = {https://arxiv.org/abs/2310.01512}, author = {Pradeep Niroula and Jack Dolde and Xin Zheng and Jacob Bringewatt and Adam Ehrenberg and Kevin C. Cox and Jeff Thompson and Michael Gullans and Shimon Kolkowitz and Alexey V. Gorshkov} } @article {3309, title = {Realization of 1D Anyons with Arbitrary Statistical Phase}, year = {2023}, month = {6/2/2023}, abstract = {

Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the physics of anyons in one dimension (1D) remains largely unexplored. Here, we realize Abelian anyons in 1D with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase via a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks, and observe the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of 1D anyons.

}, url = {https://arxiv.org/abs/2306.01737}, author = {Joyce Kwan and Perrin Segura and Yanfei Li and Sooshin Kim and Alexey V. Gorshkov and Andr{\'e} Eckardt and Brice Bakkali-Hassani and Markus Greiner} } @article {3312, title = {A sharp phase transition in linear cross-entropy benchmarking}, year = {2023}, month = {5/8/2023}, abstract = {

Demonstrations of quantum computational advantage and benchmarks of quantum processors via quantum random circuit sampling are based on evaluating the linear cross-entropy benchmark (XEB). A key question in the theory of XEB is whether it approximates the fidelity of the quantum state preparation. Previous works have shown that the XEB generically approximates the fidelity in a regime where the noise rate per qudit ε satisfies εN<<1 for a system of N qudits and that this approximation breaks down at large noise rates. Here, we show that the breakdown of XEB as a fidelity proxy occurs as a sharp phase transition at a critical value of εN that depends on the circuit architecture and properties of the two-qubit gates, including in particular their entangling power. We study the phase transition using a mapping of average two-copy quantities to statistical mechanics models in random quantum circuit architectures with full or one-dimensional connectivity. We explain the phase transition behavior in terms of spectral properties of the transfer matrix of the statistical mechanics model and identify two-qubit gate sets that exhibit the largest noise robustness.

}, url = {https://arxiv.org/abs/2305.04954}, author = {Brayden Ware and Abhinav Deshpande and Dominik Hangleiter and Pradeep Niroula and Bill Fefferman and Alexey V. Gorshkov and Michael Gullans} } @article {3399, title = {Transition of Anticoncentration in Gaussian Boson Sampling}, year = {2023}, month = {12/13/2023}, abstract = {

Gaussian Boson Sampling is a promising method for experimental demonstrations of quantum advantage because it is easier to implement than other comparable schemes. While most of the properties of Gaussian Boson Sampling are understood to the same degree as for these other schemes, we understand relatively little about the statistical properties of its output distribution. The most relevant statistical property, from the perspective of demonstrating quantum advantage, is the anticoncentration of the output distribution as measured by its second moment. The degree of anticoncentration features in arguments for the complexity-theoretic hardness of Gaussian Boson Sampling, and it is also important to know when using cross-entropy benchmarking to verify experimental performance. In this work, we develop a graph-theoretic framework for analyzing the moments of the Gaussian Boson Sampling distribution. Using this framework, we show that Gaussian Boson Sampling undergoes a transition in anticoncentration as a function of the number of modes that are initially squeezed compared to the number of photons measured at the end of the circuit. When the number of initially squeezed modes scales sufficiently slowly with the number of photons, there is a lack of anticoncentration. However, if the number of initially squeezed modes scales quickly enough, the output probabilities anticoncentrate weakly.

}, url = {https://arxiv.org/abs/2312.08433}, author = {Adam Ehrenberg and Joseph T. Iosue and Abhinav Deshpande and Dominik Hangleiter and Alexey V. Gorshkov} } @article {3073, title = {Candidate for a self-correcting quantum memory in two dimensions}, year = {2022}, month = {5/19/2022}, abstract = {

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a \"self-correcting quantum memory,\" defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model which appears to self correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic \"cat qubits\" coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z2-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips.\ 

}, url = {https://arxiv.org/abs/2205.09767}, author = {Simon Lieu and Yu-Jie Liu and Alexey V. Gorshkov} } @article {3184, title = {Continuous Symmetry Breaking in a Trapped-Ion Spin Chain}, year = {2022}, month = {11/2/2022}, abstract = {

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.

}, keywords = {FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.01275}, url = {https://arxiv.org/abs/2211.01275}, author = {Feng, Lei and Katz, Or and Haack, Casey and Maghrebi, Mohammad and Alexey V. Gorshkov and Gong, Zhexuan and Cetina, Marko and Monroe, Christopher} } @article {3127, title = {Disordered Lieb-Robinson bounds in one dimension}, year = {2022}, month = {8/10/2022}, abstract = {

By tightening the conventional Lieb-Robinson bounds to better handle systems which lack translation invariance, we determine the extent to which \"weak links\" suppress operator growth in disordered one-dimensional spin chains. In particular, we prove that ballistic growth is impossible when the distribution of coupling strengths μ(J) has a sufficiently heavy tail at small J, and identify the correct dynamical exponent to use instead. Furthermore, through a detailed analysis of the special case in which the couplings are genuinely random and independent, we find that the standard formulation of Lieb-Robinson bounds is insufficient to capture the complexity of the dynamics -- we must distinguish between bounds which hold for all sites of the chain and bounds which hold for a subsequence of sites, and we show by explicit example that these two can have dramatically different behaviors. All the same, our result for the dynamical exponent is tight, in that we prove by counterexample that there cannot exist any Lieb-Robinson bound with a smaller exponent. We close by discussing the implications of our results, both major and minor, for numerous applications ranging from quench dynamics to the structure of ground states.

}, keywords = {Disordered Systems and Neural Networks (cond-mat.dis-nn), FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2208.05509}, url = {https://arxiv.org/abs/2208.05509}, author = {Baldwin, Christopher L. and Ehrenberg, Adam and Guo, Andrew Y. and Alexey V. Gorshkov} } @article {3153, title = {Error-correcting codes for fermionic quantum simulation}, year = {2022}, month = {10/16/2022}, abstract = {

We provide ways to simulate fermions by qubits on 2d lattices using Z2 gauge theories (stabilizer codes). By studying the symplectic automorphisms of the Pauli module over the Laurent polynomial ring, we develop a systematic way to increase the code distances of stabilizer codes. We identify a family of stabilizer codes that can be used to simulate fermions with code distances of d=2,3,4,5,6,7 such that any \⌊d\−12\⌋-qubit error can be corrected. In particular, we demonstrate three stabilizer codes with code distances of d=3, d=4, and d=5, respectively, with all stabilizers and logical operators shown explicitly. The syndromes for all Pauli errors are provided. Finally, we introduce a syndrome-matching method to compute code distances numerically.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2210.08411}, url = {https://arxiv.org/abs/2210.08411}, author = {Chen, Yu-An and Alexey V. Gorshkov and Xu, Yijia} } @article {2607, title = {Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions}, journal = {Phys. Rev. Research}, volume = {4}, year = {2022}, month = {10/27/2022}, abstract = {

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor\&$\#$39;s algorithm to be performed on a D-dimensional lattice in time logarithmic in the number of qubits for interactions with α\≤D. As a corollary, we show that power-law systems with α\≤D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques.\ 

}, doi = {https://doi.org/10.1103/PhysRevResearch.4.L042016}, url = {https://arxiv.org/abs/2007.00662}, author = {Andrew Y. Guo and Abhinav Deshpande and Su-Kuan Chu and Zachary Eldredge and Przemyslaw Bienias and Dhruv Devulapalli and Yuan Su and Andrew M. Childs and Alexey V. Gorshkov} } @article {3188, title = {Importance of the Spectral gap in Estimating Ground-State Energies}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {12/9/2022}, abstract = {

The field of quantum Hamiltonian complexity lies at the intersection of quantum many-body physics and computational complexity theory, with deep implications to both fields. The main object of study is the LocalHamiltonian problem, which is concerned with estimating the ground-state energy of a local Hamiltonian and is complete for the class QMA, a quantum generalization of the class NP. A major challenge in the field is to understand the complexity of the LocalHamiltonian problem in more physically natural parameter regimes. One crucial parameter in understanding the ground space of any Hamiltonian in many-body physics is the spectral gap, which is the difference between the smallest two eigenvalues. Despite its importance in quantum many-body physics, the role played by the spectral gap in the complexity of the LocalHamiltonian is less well-understood. In this work, we make progress on this question by considering the precise regime, in which one estimates the ground-state energy to within inverse exponential precision. Computing ground-state energies precisely is a task that is important for quantum chemistry and quantum many-body physics.
In the setting of inverse-exponential precision, there is a surprising result that the complexity of LocalHamiltonian is magnified from QMA to PSPACE, the class of problems solvable in polynomial space. We clarify the reason behind this boost in complexity. Specifically, we show that the full complexity of the high precision case only comes about when the spectral gap is exponentially small. As a consequence of the proof techniques developed to show our results, we uncover important implications for the representability and circuit complexity of ground states of local Hamiltonians, the theory of uniqueness of quantum witnesses, and techniques for the amplification of quantum witnesses in the presence of postselection.

}, doi = {10.1103/prxquantum.3.040327}, url = {https://arxiv.org/abs/2007.11582}, author = {Abhinav Deshpande and Alexey V. Gorshkov and Bill Fefferman} } @article {2814, title = {Kramers{\textquoteright} degeneracy for open systems in thermal equilibrium}, journal = {Phys. Rev. B}, volume = {105}, year = {2022}, month = {3/10/2022}, pages = {L121104}, doi = {https://doi.org/10.1103/PhysRevB.105.L121104}, url = {https://arxiv.org/abs/2105.02888}, author = {Simon Lieu and Max McGinley and Oles Shtanko and Nigel R. Cooper and Alexey V. Gorshkov} } @article {3024, title = {Monitoring-induced Entanglement Entropy and Sampling Complexity}, year = {2022}, month = {1/29/2022}, abstract = {

The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical interferometer induces entanglement in the trajectory states. Since this model consists of an array of single-photon emitters, we show a direct equivalence with Fock-state boson sampling and link the hardness of sampling the outcomes of the quantum jumps with the scaling of trajectory entanglement.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2201.12672}, url = {https://arxiv.org/abs/2201.12672}, author = {Van Regemortel, Mathias and Shtanko, Oles and Garc{\'\i}a-Pintos, Luis Pedro and Deshpande, Abhinav and Dehghani, Hossein and Alexey V. Gorshkov and Hafezi, Mohammad} } @article {3124, title = {Quantum Many-Body Scars from Einstein-Podolsky-Rosen States in Bilayer Systems}, year = {2022}, month = {9/12/2022}, abstract = {

Quantum many-body scar states are special eigenstates of nonintegrable models with distinctive entanglement features that give rise to infinitely long-lived coherent dynamics under quantum quenches from certain initial states. We elaborate on a construction of quantum many-body scar states in which they emerge from Einstein-Podolsky-Rosen (EPR) states in systems with two layers, wherein the two layers are maximally entangled. We apply this construction to spin systems as well as systems of itinerant fermions and bosons and demonstrate how symmetries can be harnessed to enhance its versatility. We show that several well-known examples of quantum many-body scars, including the tower of states in the spin-1 XY model and the η-pairing states in the Fermi-Hubbard model, can be understood within this formalism. We also demonstrate how an {\it infinite} tower of many-body scar states can emerge in bilayer Bose-Hubbard models with charge conservation.

}, keywords = {FOS: Physical sciences, Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2209.05527}, url = {https://arxiv.org/abs/2209.05527}, author = {Wildeboer, Julia and Langlett, Christopher M. and Yang, Zhi-Cheng and Alexey V. Gorshkov and Iadecola, Thomas and Xu, Shenglong} } @article {2996, title = {Quantum Routing with Teleportation}, year = {2022}, month = {4/8/2022}, abstract = {

We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of speedups over swap-based and more general unitary routing methods by distributing entanglement and using LOCC to perform quantum teleportation. We further describe an example of an interaction graph for which teleportation gives a logarithmic speedup in the worst-case routing time over swap-based routing. We also study limits on the speedup afforded by quantum teleportation - showing an O(NlogN\−\−\−\−\−\−\−\√) upper bound on the separation in routing time for any interaction graph - and give tighter bounds for some common classes of graphs.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2204.04185}, url = {https://arxiv.org/abs/2204.04185}, author = {Devulapalli, Dhruv and Schoute, Eddie and Bapat, Aniruddha and Andrew M. Childs and Alexey V. Gorshkov} } @article {3178, title = {Sharp complexity phase transitions generated by entanglement}, year = {2022}, month = {12/20/2022}, abstract = {

Entanglement is one of the physical properties of quantum systems responsible for the computational hardness of simulating quantum systems. But while the runtime of specific algorithms, notably tensor network algorithms, explicitly depends on the amount of entanglement in the system, it is unknown whether this connection runs deeper and entanglement can also cause inherent, algorithm-independent complexity. In this work, we quantitatively connect the entanglement present in certain quantum systems to the computational complexity of simulating those systems. Moreover, we completely characterize the entanglement and complexity as a function of a system parameter. Specifically, we consider the task of simulating single-qubit measurements of k--regular graph states on n qubits. We show that, as the regularity parameter is increased from 1 to n\−1, there is a sharp transition from an easy regime with low entanglement to a hard regime with high entanglement at k=3, and a transition back to easy and low entanglement at k=n\−3. As a key technical result, we prove a duality for the simulation complexity of regular graph states between low and high regularity.

}, keywords = {Computational Complexity (cs.CC), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2212.10582}, url = {https://arxiv.org/abs/2212.10582}, author = {Ghosh, Soumik and Deshpande, Abhinav and Dominik Hangleiter and Alexey V. Gorshkov and Fefferman, Bill} } @article {3071, title = {Simulation Complexity of Many-Body Localized Systems}, year = {2022}, month = {5/25/2022}, abstract = {

We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of motion (LIOMs), we demonstrate a transition in the classical complexity of simulating such systems as a function of evolution time. On one side, we construct a quasipolynomial-time tensor-network-inspired algorithm for strong simulation of 1D MBL systems (i.e., calculating the expectation value of arbitrary products of local observables) evolved for any time polynomial in the system size. On the other side, we prove that even weak simulation, i.e. sampling, becomes formally hard after an exponentially long evolution time, assuming widely believed conjectures in complexity theory. Finally, using the consequences of our classical simulation results, we also show that the quantum circuit complexity for MBL systems is sublinear in evolution time. This result is a counterpart to a recent proof that the complexity of random quantum circuits grows linearly in time.\ 

}, url = {https://arxiv.org/abs/2205.12967}, author = {Adam Ehrenberg and Abhinav Deshpande and Christopher L. Baldwin and Dmitry A. Abanin and Alexey V. Gorshkov} } @article {3120, title = {Ultrastrong light-matter interaction in a photonic crystal}, year = {2022}, month = {9/29/2022}, abstract = {

Harnessing the interaction between light and matter at the quantum level has been a central theme in the fields of atomic physics and quantum optics, with applications from quantum computation to quantum metrology. Combining complex interactions with photonic synthetic materials provides an opportunity to investigate novel quantum phases and phenomena, establishing interesting connections to condensed matter physics. Here we explore many-body phenomena with a single artificial atom coupled to the many discrete modes of a photonic crystal. This experiment reaches the ultrastrong light-matter coupling regime using the circuit QED paradigm, by galvanically coupling a highly nonlinear fluxonium qubit to a tight-binding lattice of microwave resonators. In this regime, the transport of a single photon is strongly modified by the presence of multi-photon bound states, owing to interactions that break particle number conservation. Exploiting the effective photon-photon interactions mediated by the qubit, the driven system can be configured as a continuous reservoir of strongly-correlated photons, a resource of interest for quantum networks. This work opens exciting prospects for exploring nonlinear quantum optics at the single-photon level and stabilizing entangled many-body phases of light.

}, keywords = {FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.14972}, url = {https://arxiv.org/abs/2209.14972}, author = {Vrajitoarea, Andrei and Belyansky, Ron and Lundgren, Rex and Whitsitt, Seth and Alexey V. Gorshkov and Houck, Andrew A.} } @article {3030, title = {Universal scattering with general dispersion relations}, journal = {Phys. Rev. Research}, volume = {4}, year = {2022}, month = {4/6/2022}, chapter = {023014}, abstract = {

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension D\≥1 when the density of states diverges at a specific energy. To illustrate the underlying principles in an experimentally relevant setting, we focus on waveguide quantum electrodynamics (QED) problems (i.e. D=1) with dispersion relation ϵ(k)=\±|d|km, where m\≥2 is an integer. For a large class of these problems for any positive integer m, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E\→0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson\&$\#$39;s theorem -- which relates the scattering phases to the number of bound states -- to waveguide QED scattering for these more general dispersion relations. We then extend these results to general integer dimensions D\≥1, dispersion relations ϵ(k)=|k|a for a D-dimensional momentum vector k with any real positive a, and separable potential scattering.

}, keywords = {FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1103/PhysRevResearch.4.023014}, url = {https://arxiv.org/abs/2103.09830}, author = {Wang, Yidan and Michael Gullans and Na, Xuesen and Whitsitt, Seth and Alexey V. Gorshkov} } @article {2760, title = {Universality in one-dimensional scattering with general dispersion relations}, journal = {Phys. Rev. Res.}, volume = {4}, year = {2022}, month = {3/17/2021}, chapter = {023014}, abstract = {

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in one dimension when the dispersion relation is ϵ(k)=\±|d|km, where m\≥2 is an integer. We study impurity scattering problems in which a single-particle in a one-dimensional waveguide scatters off of an inhomogeneous, discrete set of sites locally coupled to the waveguide. For a large class of these problems, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E\→0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson\&$\#$39;s theorem -- which relates the scattering phases to the number of bound states -- to impurity scattering for these more general dispersion relations.

}, doi = {https://doi.org/10.48550/arXiv.2103.09830}, url = {https://arxiv.org/abs/2103.09830}, author = {Yidan Wang and Michael Gullans and Xuesen Na and Alexey V. Gorshkov} } @article {2809, title = {Behavior of Analog Quantum Algorithms}, year = {2021}, month = {7/2/2021}, abstract = {

Analog quantum algorithms are formulated in terms of Hamiltonians rather than unitary gates and include quantum adiabatic computing, quantum annealing, and the quantum approximate optimization algorithm (QAOA). These algorithms are promising candidates for near-term quantum applications, but they often require fine tuning via the annealing schedule or variational parameters. In this work, we explore connections between these analog algorithms, as well as limits in which they become approximations of the optimal procedure.Notably, we explore how the optimal procedure approaches a smooth adiabatic procedure but with a superposed oscillatory pattern that can be explained in terms of the interactions between the ground state and first excited state that effect the coherent error cancellation of diabatic transitions. Furthermore, we provide numeric and analytic evidence that QAOA emulates this optimal procedure with the length of each QAOA layer equal to the period of the oscillatory pattern. Additionally, the ratios of the QAOA bangs are determined by the smooth, non-oscillatory part of the optimal procedure. We provide arguments for these phenomena in terms of the product formula expansion of the optimal procedure. With these arguments, we conclude that different analog algorithms can emulate the optimal protocol under different limits and approximations. Finally, we present a new algorithm for better approximating the optimal protocol using the analytic and numeric insights from the rest of the paper. In practice, numerically, we find that this algorithm outperforms standard QAOA and naive quantum annealing procedures.\ 

}, url = {https://arxiv.org/abs/2107.01218}, author = {Lucas T. Brady and Lucas Kocia and Przemyslaw Bienias and Aniruddha Bapat and Yaroslav Kharkov and Alexey V. Gorshkov} } @article {2813, title = {Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models}, year = {2021}, month = {5/13/2021}, abstract = {

Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincar{\'e} disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically-frustrated hyperbolic quantum spin models with finite-range or exponentially-decaying interaction.

}, url = {https://arxiv.org/abs/2105.06490}, author = {Przemyslaw Bienias and Igor Boettcher and Ron Belyansky and Alicia J. Koll{\'a}r and Alexey V. Gorshkov} } @article {2920, title = {Clustering of steady-state correlations in open systems with long-range interactions}, year = {2021}, month = {10/28/2021}, abstract = {

Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from \"reversibility\" -- naturally satisfied for thermal environments -- we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open directions regarding the application of Lieb-Robinson bounds to dissipative systems.

}, url = {https://arxiv.org/abs/2110.15368}, author = {Andrew Y. Guo and Simon Lieu and Minh C. Tran and Alexey V. Gorshkov} } @article {2867, title = {Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {9/17/2021}, abstract = {

Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter. We determine important classes of simulable and nonsimulable two-body dissipation. Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates.\ 

}, issn = {2691-3399}, doi = {10.1103/prxquantum.2.030350}, url = {http://dx.doi.org/10.1103/PRXQuantum.2.030350}, author = {Shtanko, Oles and Deshpande, Abhinav and Julienne, Paul S. and Alexey V. Gorshkov} } @article {2815, title = {Crystallography of Hyperbolic Lattices}, year = {2021}, month = {5/3/2021}, abstract = {

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch\&$\#$39;s theorem precludes a simple understanding of their band structure. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive, for the first time, a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. Our results find application for both finite and infinite hyperbolic lattices. We describe a method to efficiently generate finite hyperbolic lattices of arbitrary size and explain why the present crystallography is the first step towards a complete band theory of hyperbolic lattices and apply it to construct Bloch wave Hamiltonians. This work lays the foundation for generalizing some of the most powerful concepts of solid state physics, such as crystal momentum and Brillouin zone, to the emerging field of hyperbolic lattices and tabletop simulations of gravitational theories, and reveals the connections to concepts from topology and algebraic geometry.

}, url = {https://arxiv.org/abs/2105.01087}, author = {Igor Boettcher and Alexey V. Gorshkov and Alicia J. Koll{\'a}r and Joseph Maciejko and Steven Rayan and Ronny Thomale} } @article {2916, title = {Discovering hydrodynamic equations of many-body quantum systems}, year = {2021}, month = {11/3/2021}, abstract = {

Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum systems often admit a simplified description, which involves a small set of physical observables and requires only a few parameters such as sound velocity or viscosity. Unveiling the relationship between these hydrodynamic equations and the underlying microscopic theory usually requires a great effort by condensed matter theorists. In the present paper, we develop a new machine-learning framework for automated discovery of effective equations from a limited set of available data, thus bypassing complicated analytical derivations. The data can be generated from numerical simulations or come from experimental quantum simulator platforms. Using integrable models, where direct comparisons can be made, we reproduce previously known hydrodynamic equations, strikingly discover novel equations and provide their derivation whenever possible. We discover new hydrodynamic equations describing dynamics of interacting systems, for which the derivation remains an outstanding challenge. Our approach provides a new interpretable method to study properties of quantum materials and quantum simulators in non-perturbative regimes.

}, url = {https://arxiv.org/abs/2111.02385}, author = {Yaroslav Kharkov and Oles Shtanko and Alireza Seif and Przemyslaw Bienias and Mathias Van Regemortel and Mohammad Hafezi and Alexey V. Gorshkov} } @article {2811, title = {Feedback-stabilized dynamical steady states in the Bose-Hubbard model}, journal = {Phys. Rev. Research}, volume = {3}, year = {2021}, month = {12/15/2021}, pages = {043075 }, abstract = {

The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this work, we investigate the potential of this approach from three perspectives. First, we consider a double-well system in the classical large-atom-number limit, deriving the exact equations of motion in the presence of feedback. Second, we consider the same system in the limit of small atom number, revealing the effect that quantum fluctuations have on the feedback scheme. Finally, we explore the behavior of modest sized Hubbard chains using exact numerics, demonstrating the near-deterministic preparation of number states, a tradeoff between local and non-local feedback for state preparation, and evidence of a feedback-driven symmetry-breaking phase transition.

}, doi = {https://doi.org/10.1103/PhysRevResearch.3.043075}, url = {https://arxiv.org/abs/2106.09744}, author = {Jeremy T. Young and Alexey V. Gorshkov and I. B. Spielman} } @article {2762, title = {Frustration-induced anomalous transport and strong photon decay in waveguide QED}, journal = {Phys. Rev. Research}, volume = {3}, year = {2021}, month = {9/16/2021}, abstract = {

We study the propagation of photons in a one-dimensional environment consisting of two non-interacting species of photons frustratingly coupled to a single spin-1/2. The ultrastrong frustrated coupling leads to an extreme mixing of the light and matter degrees of freedom, resulting in the disintegration of the spin and a breakdown of the \"dressed-spin\", or polaron, description. Using a combination of numerical and analytical methods, we show that the elastic response becomes increasingly weak at the effective spin frequency, showing instead an increasingly strong and broadband response at higher energies. We also show that the photons can decay into multiple photons of smaller energies. The total probability of these inelastic processes can be as large as the total elastic scattering rate, or half of the total scattering rate, which is as large as it can be. The frustrated spin induces strong anisotropic photon-photon interactions that are dominated by inter-species interactions. Our results are relevant to state-of-the-art circuit and cavity quantum electrodynamics experiments.

}, doi = {https://doi.org/10.1103/PhysRevResearch.3.L032058}, url = {https://arxiv.org/abs/2007.03690}, author = {Ron Belyansky and Seth Whitsitt and Rex Lundgren and Yidan Wang and Andrei Vrajitoarea and Andrew A. Houck and Alexey V. Gorshkov} } @article {2759, title = {The Lieb-Robinson light cone for power-law interactions}, year = {2021}, month = {3/29/2021}, abstract = {

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α\>2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α\−2d} to propagate a distance~r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

}, url = {https://arxiv.org/abs/2103.15828}, author = {Minh C. Tran and Andrew Y. Guo and Christopher L. Baldwin and Adam Ehrenberg and Alexey V. Gorshkov and Andrew Lucas} } @article {2865, title = {Linear and continuous variable spin-wave processing using a cavity-coupled atomic ensemble}, year = {2021}, month = {9/30/2021}, abstract = {

Spin-wave excitations in ensembles of atoms are gaining attention as a quantum information resource. However, current techniques with atomic spin waves do not achieve universal quantum information processing. We conduct a theoretical analysis of methods to create a high-capacity universal quantum processor and network node using an ensemble of laser-cooled atoms, trapped in a one-dimensional periodic potential and coupled to a ring cavity. We describe how to establish linear quantum processing using a lambda-scheme in a rubidium-atom system, calculate the expected experimental operational fidelities. Second, we derive an efficient method to achieve linear controllability with a single ensemble of atoms, rather than two-ensembles as proposed in [K. C. Cox et al. Spin-Wave Quantum Computing with Atoms in a Single-Mode Cavity, preprint 2021]. Finally, we propose to use the spin-wave processor for continuous-variable quantum information processing and present a scheme to generate large dual-rail cluster states useful for deterministic computing.\ 

}, url = {https://arxiv.org/abs/2109.15246}, author = {Kevin C. Cox and Przemyslaw Bienias and David H. Meyer and Donald P. Fahey and Paul D. Kunz and Alexey V. Gorshkov} } @article {2805, title = {Observation of measurement-induced quantum phases in a trapped-ion quantum computer}, year = {2021}, month = {6/10/2021}, abstract = {

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the \"pure\" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the \"mixed\" or \"coding\" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

}, url = {https://arxiv.org/abs/2106.05881}, author = {Crystal Noel and Pradeep Niroula and Daiwei Zhu and Andrew Risinger and Laird Egan and Debopriyo Biswas and Marko Cetina and Alexey V. Gorshkov and Michael Gullans and David A. Huse and Christopher Monroe} } @article {2763, title = {Observation of Stark many-body localization without disorder}, year = {2021}, month = {2/14/2021}, abstract = {

Thermalization is a ubiquitous process of statistical physics, in which details of few-body observables are washed out in favor of a featureless steady state. Even in isolated quantum many-body systems, limited to reversible dynamics, thermalization typically prevails. However, in these systems, there is another possibility: many-body localization (MBL) can result in preservation of a non-thermal state. While disorder has long been considered an essential ingredient for this phenomenon, recent theoretical work has suggested that a quantum many-body system with a uniformly increasing field -- but no disorder -- can also exhibit MBL, resulting in {\textquoteleft}Stark MBL.\&$\#$39; Here we realize Stark MBL in a trapped-ion quantum simulator and demonstrate its key properties: halting of thermalization and slow propagation of correlations. Tailoring the interactions between ionic spins in an effective field gradient, we directly observe their microscopic equilibration for a variety of initial states, and we apply single-site control to measure correlations between separate regions of the spin chain. Further, by engineering a varying gradient, we create a disorder-free system with coexisting long-lived thermalized and nonthermal regions. The results demonstrate the unexpected generality of MBL, with implications about the fundamental requirements for thermalization and with potential uses in engineering long-lived non-equilibrium quantum matter.

}, url = {https://arxiv.org/abs/2102.07250}, author = {W. Morong and F. Liu and P. Becker and K. S. Collins and L. Feng and A. Kyprianidis and G. Pagano and T. You and Alexey V. Gorshkov and C. Monroe} } @article {2816, title = {Protocols for estimating multiple functions with quantum sensor networks: Geometry and performance}, journal = {Physical Review Research}, volume = {3}, year = {2021}, month = {5/3/2021}, abstract = {

We consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds of Rubio et. al. [J. Phys. A: Math. Theor. 53 344001 (2020)] and develop a new optimized sequential protocol for measuring such functions. We compare the performance of both approaches to one another and to local protocols that do not utilize quantum entanglement, emphasizing the geometric significance of the coefficient vectors of the measured functions in determining the best choice of measurement protocol. We show that, in many cases, especially for a large number of sensors, the optimized sequential protocol results in more accurate measurements than the other strategies. In addition, in contrast to the the sensor symmetric approach, the sequential protocol is known to always be explicitly implementable. The sequential protocol is very general and has a wide range of metrological applications.

}, issn = {2643-1564}, doi = {10.1103/physrevresearch.3.033011}, url = {https://arxiv.org/abs/2104.09540}, author = {Jacob Bringewatt and Boettcher, Igor and Niroula, Pradeep and Bienias, Przemyslaw and Alexey V. Gorshkov} } @article {2751, title = {Quantum routing with fast reversals}, journal = {Quantum}, volume = {5}, year = {2021}, month = {8/24/2021}, chapter = {533}, abstract = {

We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length n, we show that there exists a constant ϵ\≈0.034 such that the quantum routing time is at most (1\−ϵ)n, whereas any swap-based protocol needs at least time n\−1. This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of 2n/3 in expectation for uniformly random permutations, whereas swap-based protocols require time n asymptotically. Additionally, we consider sparse permutations that route k\≤n qubits and give algorithms with quantum routing time at most n/3+O(k2) on paths and at most 2r/3+O(k2) on general graphs with radius r.

}, doi = {https://doi.org/10.22331/q-2021-08-31-533}, url = {https://arxiv.org/abs/2103.03264}, author = {Aniruddha Bapat and Andrew M. Childs and Alexey V. Gorshkov and Samuel King and Eddie Schoute and Hrishee Shastri} } @article {2671, title = {Quench Dynamics of a Fermi Gas with Strong Long-Range Interactions}, journal = {Phys. Rev. X}, volume = {11}, year = {2021}, month = {5/24/2021}, abstract = {

We induce strong non-local interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a t\−V model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of non-local interactions with tunneling, we investigate the short-time relaxation dynamics of charge density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong non-local interactions such as extended Fermi-Hubbard models.

}, doi = {https://doi.org/10.1103/PhysRevX.11.021036}, url = {https://arxiv.org/abs/2010.05871}, author = {Elmer Guardado-Sanchez and Benjamin M. Spar and Peter Schauss and Ron Belyansky and Jeremy T. Young and Przemyslaw Bienias and Alexey V. Gorshkov and Thomas Iadecola and Waseem S. Bakr} } @article {2808, title = {Rainbow Scars: From Area to Volume Law}, year = {2021}, month = {7/12/2021}, abstract = {

Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in which rare \"scarred\" eigenstates mediate weak ergodicity breaking. One open question is to understand the most general setting in which these states arise. In this work, we develop a generic construction that embeds a new class of QMBS, rainbow scars, into the spectrum of an arbitrary Hamiltonian. Unlike other examples of QMBS, rainbow scars display extensive bipartite entanglement entropy while retaining a simple entanglement structure. Specifically, the entanglement scaling is volume-law for a random bipartition, while scaling for a fine-tuned bipartition is sub-extensive. When internal symmetries are present, the construction leads to multiple, and even towers of rainbow scars revealed through distinctive non-thermal dynamics. To this end, we provide an experimental road map for realizing rainbow scar states in a Rydberg-atom quantum simulator, leading to coherent oscillations distinct from the strictly sub-volume-law QMBS previously realized in the same system.\ 

}, url = {https://arxiv.org/abs/2107.03416}, author = {Christopher M. Langlett and Zhi-Cheng Yang and Julia Wildeboer and Alexey V. Gorshkov and Thomas Iadecola and Shenglong Xu} } @article {2761, title = {Singularities in nearly-uniform 1D condensates due to quantum diffusion}, year = {2021}, month = {3/10/2021}, abstract = {

Dissipative systems can often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically-induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to k2 (k being the wavevector) and vanishing at long wavelengths as k\→0. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly-uniform condensate -- a dispersive analogue to the Kardar-Parisi-Zhang (KPZ) equation -- which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

}, url = {https://arxiv.org/abs/2103.06293}, author = {Christopher L. Baldwin and P. Bienias and Alexey V. Gorshkov and Michael Gullans and M. Maghrebi} } @article {2864, title = {Spin-Wave Quantum Computing with Atoms in a Single-Mode Cavity}, year = {2021}, month = {9/30/2021}, abstract = {

We present a method for network-capable quantum computing that relies on holographic spin-wave excitations stored collectively in ensembles of qubits. We construct an orthogonal basis of spin waves in a one-dimensional array and show that high-fidelity universal linear controllability can be achieved using only phase shifts, applied in both momentum and position space. Neither single-site addressability nor high single-qubit cooperativity is required, and the spin waves can be read out with high efficiency into a single cavity mode for quantum computing and networking applications.\ 

}, url = {https://arxiv.org/abs/2109.15252}, author = {Kevin C. Cox and Przemyslaw Bienias and David H. Meyer and Paul D. Kunz and Donald P. Fahey and Alexey V. Gorshkov} } @article {2909, title = {Tight bounds on the convergence of noisy random circuits to uniform}, year = {2021}, month = {12/1/2021}, abstract = {

We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work.\ 

}, url = {https://arxiv.org/abs/2112.00716}, author = {Abhinav Deshpande and Bill Fefferman and Alexey V. Gorshkov and Michael Gullans and Pradeep Niroula and Oles Shtanko} } @article {2682, title = {Tunable three-body loss in a nonlinear Rydberg medium}, journal = {Phys. Rev. Lett., in press }, year = {2021}, month = {9/28/2020}, abstract = {

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential to generate novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study a three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wavefunction and analytical estimates based on Fermi\&$\#$39;s Golden Rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

}, url = {https://arxiv.org/abs/2009.13599}, author = {Dalia P. Ornelas Huerta and Przemyslaw Bienias and Alexander N. Craddock and Michael Gullans and Andrew J. Hachtel and Marcin Kalinowski and Mary E. Lyon and Alexey V. Gorshkov and Steven L. Rolston and J. V. Porto} } @article {2866, title = {Unifying Quantum and Classical Speed Limits on Observables}, year = {2021}, month = {8/9/2021}, abstract = {

The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit divides into Mandalestam and Tamm\&$\#$39;s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, generalizing both to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds to the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits, and that a preferred basis of \emph{speed operators} serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.

}, url = {https://arxiv.org/abs/2108.04261}, author = {Luis Pedro Garc{\'\i}a-Pintos and Schuyler Nicholson and Jason R. Green and Adolfo del Campo and Alexey V. Gorshkov} } @article {2594, title = {Asymmetric blockade and multi-qubit gates via dipole-dipole interactions}, year = {2020}, month = {6/3/2020}, abstract = {

Due to their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multi-qubit Rydberg-blockade gates which involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multi-qubit gates can drastically simplify both quantum algorithms and state preparation. To illustrate this, we show that a 25-atom GHZ state can be created using only three gates with an error of 7.8\%.

}, url = {https://arxiv.org/abs/2006.02486}, author = {Jeremy T. Young and Przemyslaw Bienias and Ron Belyansky and Adam M. Kaufman and Alexey V. Gorshkov} } @article {2364, title = {Circuit Complexity across a Topological Phase Transition}, journal = {Physical Review Research }, volume = {2}, year = {2020}, month = {03/16/2020}, pages = {013323}, abstract = {

We use Nielsen\&$\#$39;s approach to quantify the circuit complexity in the one-dimensional Kitaev model. In equilibrium, we find that the circuit complexity of ground states exhibits a divergent derivative at the critical point, signaling the presence of a topological phase transition. Out of equilibrium, we study the complexity dynamics after a sudden quench, and find that the steady-state complexity exhibits nonanalytical behavior when quenched across critical points. We generalize our results to the long-range interacting case, and demonstrate that the circuit complexity correctly predicts the critical point between regions with different semi-integer topological numbers. Our results establish a connection between circuit complexity and quantum phase transitions both in and out of equilibrium, and can be easily generalized to topological phase transitions in higher dimensions. Our study opens a new avenue to using circuit complexity as a novel quantity to understand many-body systems.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.013323}, url = {https://arxiv.org/abs/1902.10720}, author = {Fangli Liu and Rex Lundgren and Paraj Titum and James R. Garrison and Alexey V. Gorshkov} } @article {2565, title = {Classical Models of Entanglement in Monitored Random Circuits}, year = {2020}, month = {4/14/2020}, abstract = {

The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth R{\'e}nyi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-R{\'e}nyi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.

}, url = {https://arxiv.org/abs/2004.06736}, author = {Oles Shtanko and Yaroslav A. Kharkov and Luis Pedro Garc{\'\i}a-Pintos and Alexey V. Gorshkov} } @article {2637, title = {Critical Theory for the Breakdown of Photon Blockade}, year = {2020}, month = {6/9/2020}, abstract = {

Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons. We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes--Cummings model, in which case the photon blockade breaks down in a second order phase transition at a critical drive strength. We show that this transition is associated to the spontaneous breaking of an anti-unitary PT-symmetry. Within a semiclassical approximation we calculate the expectation values of observables in the steady state. We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve. The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power-law, allowing us to calculate the critical scaling of steady state observables without invoking mean-field theory. We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state. We list several experimental platforms where this phenomenon may be observed.

}, url = {https://arxiv.org/abs/2006.05593}, author = {Jonathan B. Curtis and Igor Boettcher and Jeremy T. Young and Mohammad F. Maghrebi and Howard Carmichael and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2514, title = {Destructive Error Interference in Product-Formula Lattice Simulation}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {6/4/2020}, abstract = {

Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt3/r2) when nt2/r is less than a small constant. Given an error tolerance ε, the error bound yields an estimate of max{O(n2t/ε),O(n2t3/2/ε1/2)} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.\ 

}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.220502}, url = {https://arxiv.org/abs/1912.11047}, author = {Minh C. Tran and Su-Kuan Chu and Yuan Su and Andrew M. Childs and Alexey V. Gorshkov} } @article {2457, title = {Entanglement Bounds on the Performance of Quantum Computing Architectures}, journal = {Phys. Rev. Research}, volume = {2}, year = {2020}, month = {9/22/2020}, abstract = {

There are many possible architectures for future quantum computers that designers will need to choose between. However, the process of evaluating a particular connectivity graph\&$\#$39;s performance as a quantum architecture can be difficult. In this paper, we establish a connection between a quantity known as the isoperimetric number and a lower bound on the time required to create highly entangled states. The metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We describe how these results can be applied to the evaluation of the hierarchical architecture proposed in Phys. Rev. A 98, 062328 (2018). We also show that the time-complexity bound we place on the creation of highly-entangled states can be saturated up to a multiplicative factor logarithmic in the number of qubits.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.033316}, url = {https://arxiv.org/abs/1908.04802}, author = {Zachary Eldredge and Leo Zhou and Aniruddha Bapat and James R. Garrison and Abhinav Deshpande and Frederic T. Chong and Alexey V. Gorshkov} } @article {2567, title = {Exotic photonic molecules via Lennard-Jones-like potentials}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {9/19/2020}, abstract = {

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a F{{\"o}}rster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters (\"molecules\") of photons. We demonstrate that for a few-body problem, the multi-body interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in 2D preferentially arrange themselves in a line-configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

}, doi = {https://doi.org/10.1103/PhysRevLett.125.093601}, url = {https://arxiv.org/abs/2003.07864}, author = {Przemyslaw Bienias and Michael Gullans and Marcin Kalinowski and Alexander N. Craddock and Dalia P. Ornelas-Huerta and Steven L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {2577, title = {Hierarchy of linear light cones with long-range interactions}, journal = {Physical Review X}, volume = {10}, year = {2020}, month = {5/29/2020}, abstract = {

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a \"linear light cone,\" which expands at an emergent velocity analogous to the speed of light. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance r interact with potential energy V(r)\∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same α, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, commutators of local operators \⟨ψ|[Ox(t),Oy]|ψ\⟩ are negligible in every state |ψ\⟩ when |x\−y|≳vt, where v is finite when α\>3 (Lieb-Robinson light cone); in a typical state |ψ\⟩ drawn from the infinite temperature ensemble, v is finite when α\>52 (Frobenius light cone); in non-interacting systems, v is finite in every state when α\>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones, and their tightness, also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that quantum state transfer and many-body quantum chaos are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

}, doi = {https://doi.org/10.1103/PhysRevX.10.031009}, url = {https://arxiv.org/abs/2001.11509}, author = {Minh C. Tran and Chi-Fang Chen and Adam Ehrenberg and Andrew Y. Guo and Abhinav Deshpande and Yifan Hong and Zhe-Xuan Gong and Alexey V. Gorshkov and Andrew Lucas} } @article {2498, title = {Hilbert-Space Fragmentation from Strict Confinement}, journal = {Phys. Rev. Lett.}, volume = {124}, year = {2020}, month = {5/22/2020}, abstract = {

We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most of the previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of Z2 gauge theory coupled to fermionic matter, leading to a hierarchy of time scales for motion of the fermions. This model can be realized experimentally in two complementary settings.

}, doi = {https://doi.org/10.1103/PhysRevLett.124.207602}, url = {https://arxiv.org/abs/1912.04300}, author = {Zhi-Cheng Yang and Fangli Liu and Alexey V. Gorshkov and Thomas Iadecola} } @article {2593, title = {Limits on Classical Simulation of Free Fermions with Dissipation}, year = {2020}, month = {5/21/2020}, abstract = {

Free-fermionic systems are a valuable, but limited, class of many-body problems efficiently simulable on a classical computer. We examine how classical simulability of noninteracting fermions is modified in the presence of Markovian dissipation described by quadratic Lindblad operators, including, for example, incoherent transitions or pair losses. On the one hand, we establish three broad classes of Markovian dynamics that are efficiently simulable classically, by devising efficient algorithms. On the other hand, we demonstrate that, in the worst case, simulating Markovian dynamics with quadratic Lindblad operators is at least as hard as simulating universal quantum circuits. This result is applicable to an experimentally relevant setting in cold atomic systems, where magnetic Feshbach resonances can be used to engineer the desired dissipation. For such systems, our hardness result provides a direct scheme for dissipation-assisted quantum computing with a potential significant advantage in the speed of two-qubit gates and, therefore, in error tolerance.

}, url = {https://arxiv.org/abs/2005.10840}, author = {Oles Shtanko and Abhinav Deshpande and Paul S. Julienne and Alexey V. Gorshkov} } @article {2720, title = {Localization and criticality in antiblockaded 2D Rydberg atom arrays}, year = {2020}, month = {12/7/2020}, abstract = {

Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime\&$\#$39;s existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.\ 

}, url = {https://arxiv.org/abs/2012.03946}, author = {Fangli Liu and Zhi-Cheng Yang and Przemyslaw Bienias and Thomas Iadecola and Alexey V. Gorshkov} } @article {2595, title = {Minimal model for fast scrambling}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {9/22/2020}, abstract = {

We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two exactly solvable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled non-linear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results can be verified with state-of-the-art quantum simulators.

}, doi = {https://doi.org/10.1103/PhysRevLett.125.130601}, url = {https://arxiv.org/abs/2005.05362}, author = {Ron Belyansky and Przemyslaw Bienias and Yaroslav A. Kharkov and Alexey V. Gorshkov and Brian Swingle} } @article {2556, title = {Nearly optimal time-independent reversal of a spin chain}, journal = {accepted for publication in Physical Review Research}, year = {2020}, month = {3/5/2020}, abstract = {

We propose a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of N spins. Our protocol has an easily implementable nearest-neighbor, transverse-field Ising model Hamiltonian with time-independent, non-uniform couplings. Under appropriate normalization, we implement this state reversal three times faster than a naive approach using SWAP gates, in time comparable to a protocol of Raussendorf [Phys. Rev. A 72, 052301 (2005)] that requires dynamical control. We also prove lower bounds on state reversal by using results on the entanglement capacity of Hamiltonians and show that we are within a factor 1.502(1+1/N) of the shortest time possible. Our lower bound holds for all nearest-neighbor qubit protocols with arbitrary finite ancilla spaces and local operations and classical communication. Finally, we extend our protocol to an infinite family of nearest-neighbor, time-independent Hamiltonian protocols for state reversal. This includes chains with nearly uniform coupling that may be especially feasible for experimental implementation.\ 

}, url = {https://arxiv.org/abs/2003.02843}, author = {Aniruddha Bapat and Eddie Schoute and Alexey V. Gorshkov and Andrew M. Childs} } @article {2363, title = {Non-equilibrium fixed points of coupled Ising models}, journal = {Phys. Rev. X }, volume = {10}, year = {2020}, month = {2/26/2020}, abstract = {

Driven-dissipative systems can exhibit non-equilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions present in these systems generically exhibit an effectively classical equilibrium behavior in spite of their quantum non-equilibrium origin. In this paper, we show that multicritical points in driven-dissipative systems can give rise to genuinely non-equilibrium behavior. We investigate a non-equilibrium driven-dissipative model of interacting bosons that exhibits two distinct phase transitions: one from a high- to a low-density phase---reminiscent of a liquid-gas transition---and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) Z2 symmetry. They, however, coalesce at a multicritical point giving rise to a non-equilibrium model of coupled Ising-like order parameters described by a Z2\×Z2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of non-equilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents, spiraling phase boundaries, and a complex Liouvillian gap even close to the phase transition. As direct evidence of the non-equilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes \"hotter\" and \"hotter\" at longer and longer wavelengths. Finally, we argue that this non-equilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.

}, doi = {https://doi.org/10.1103/PhysRevX.10.011039}, url = {https://arxiv.org/abs/1903.02569}, author = {Jeremy T. Young and Alexey V. Gorshkov and Michael Foss-Feig and Mohammad F. Maghrebi} } @article {2568, title = {On-demand indistinguishable single photons from an efficient and pure source based on a Rydberg ensemble}, year = {2020}, month = {3/4/2020}, abstract = {

Single photons coupled to atomic systems have shown to be a promising platform for developing quantum technologies. Yet a bright on-demand, highly pure and highly indistinguishable single-photon source compatible with atomic platforms is lacking. In this work, we demonstrate such a source based on a strongly interacting Rydberg system. The large optical nonlinearities in a blockaded Rydberg ensemble convert coherent light into a single-collective excitation that can be coherently retrieved as a quantum field. We observe a single-transverse-mode efficiency up to 0.18(2), g(2)=2.0(1.5)\×10\−4, and indistinguishability of 0.982(7), making this system promising for scalable quantum information applications. Accounting for losses, we infer a generation probability up to 0.40(4). Furthermore, we investigate the effects of contaminant Rydberg excitations on the source efficiency. Finally, we introduce metrics to benchmark the performance of on-demand single-photon sources.\ 

}, url = {https://arxiv.org/abs/2003.02202}, author = {Dalia P. Ornelas-Huerta and Alexander N. Craddock and Elizabeth A. Goldschmidt and Andrew J. Hachtel and Yidan Wang and P. Bienias and Alexey V. Gorshkov and Steve L. Rolston and James V. Porto} } @article {2635, title = {Optical quantum memory with optically inaccessible noble-gas spins}, year = {2020}, month = {7/17/2020}, abstract = {

Optical quantum memories, which store and preserve the quantum state of photons, rely on a coherent mapping of the photonic state onto matter states that are optically accessible. Here we outline a new physical mechanism to map the state of photons onto the long-lived but optically inaccessible collective state of noble-gas spins. The mapping employs the coherent spin-exchange interaction arising from random collisions with alkali vapor. We analyze optimal strategies for high-efficiency storage and retrieval of non-classical light at various parameter regimes. Based on these strategies, we identify feasible experimental conditions for realizing efficient quantum memories with noble-gas spins having hours-long coherence times at room temperature and above

}, url = {https://arxiv.org/abs/2007.08770}, author = {Or Katz and Eran Reches and Roy Shaham and Alexey V. Gorshkov and Ofer Firstenberg} } @article {2721, title = {Optimal Measurement of Field Properties with Quantum Sensor Networks}, year = {2020}, month = {11/2/2020}, abstract = {

We consider a quantum sensor network of qubit sensors coupled to a field f(x⃗ ;θ⃗ ) analytically parameterized by the vector of parameters θ⃗ . The qubit sensors are fixed at positions x⃗ 1,\…,x⃗ d. While the functional form of f(x⃗ ;θ⃗ ) is known, the parameters θ⃗\  are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function q(θ⃗ ) of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.

}, url = {https://arxiv.org/abs/2011.01259}, author = {Timothy Qian and Jacob Bringewatt and Igor Boettcher and Przemyslaw Bienias and Alexey V. Gorshkov} } @article {2564, title = {Optimal Protocols in Quantum Annealing and QAOA Problems}, year = {2020}, month = {3/19/2020}, abstract = {

Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or \"bang-bang\") structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. Through simulations of various transverse field Ising models, we demonstrate that bang-anneal-bang protocols are more common. The general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

}, url = {https://arxiv.org/abs/2003.08952}, author = {Lucas T. Brady and Christopher L. Baldwin and Aniruddha Bapat and Yaroslav Kharkov and Alexey V. Gorshkov} } @article {2689, title = {Optimal state transfer and entanglement generation in power-law interacting systems}, year = {2020}, month = {10/6/2020}, abstract = {

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/rα) interactions. For all power-law exponents α between d and 2d+1, where d is the dimension of the system, the protocol yields a polynomial speedup for α\>2d and a superpolynomial speedup for α\≤2d, compared to the state of the art. For all α\>d, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states.\ 

}, url = {https://arxiv.org/abs/2010.02930}, author = {Minh C. Tran and Abhinav Deshpande and Andrew Y. Guo and Andrew Lucas and Alexey V. Gorshkov} } @article {2497, title = {Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry}, journal = {Phys. Rev. A}, volume = {102}, year = {2020}, month = {9/11/2020}, abstract = {

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincar{\'e} disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Our analysis also reveals in which sense discrete hyperbolic lattices emulate the continuous geometry of negatively curved space and thus can be used to resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

}, doi = {https://doi.org/10.1103/PhysRevA.102.032208}, url = {https://arxiv.org/abs/1910.12318}, author = {Igor Boettcher and Przemyslaw Bienias and Ron Belyansky and Alicia J. Koll{\'a}r and Alexey V. Gorshkov} } @article {2636, title = {Realizing and Probing Baryonic Excitations in Rydberg Atom Arrays}, year = {2020}, month = {7/14/2020}, abstract = {

We propose a realization of mesonic and baryonic quasiparticle excitations in Rydberg atom arrays with programmable interactions. Recent experiments have shown that such systems possess a Z3-ordered crystalline phase whose low-energy quasiparticles are defects in the crystalline order. By engineering a Z3-translational-symmetry breaking field on top of the Rydberg-blockaded Hamiltonian, we show that different types of defects experience confinement, and as a consequence form mesonic or baryonic quasiparticle excitations. We illustrate the formation of these quasiparticles by studying a quantum chiral clock model related to the Rydberg Hamiltonian. We then propose an experimental protocol involving out-of-equilibrium dynamics to directly probe the spectrum of the confined excitations. We show that the confined quasiparticle spectrum can limit quantum information spreading in this system. This proposal is readily applicable to current Rydberg experiments, and the method can be easily generalized to more complex confined excitations (e.g. {\textquoteleft}tetraquarks\&$\#$39;, {\textquoteleft}pentaquarks\&$\#$39;) in phases with Zq order for q\>3.\ 

}, url = {https://arxiv.org/abs/2007.07258}, author = {Fangli Liu and Seth Whitsitt and Przemyslaw Bienias and Rex Lundgren and Alexey V. Gorshkov} } @article {2681, title = {Resonant enhancement of three-body loss between strongly interacting photons}, year = {2020}, month = {10/19/2020}, abstract = {

Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong or even stronger than two-body interactions. The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly-interacting, and topological phases of matter. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the three-body Schr{\"o}dinger equation, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiment

}, url = {https://arxiv.org/abs/2010.09772}, author = {Marcin Kalinowski and Yidan Wang and Przemyslaw Bienias and Michael Gullans and Dalia P. Ornelas-Huerta and Alexander N. Craddock and Steven L. Rolston and J. V. Porto and Hans Peter B{\"u}chler and Alexey V. Gorshkov} } @article {2403, title = {Signaling and Scrambling with Strongly Long-Range Interactions}, journal = {Physical Review A}, volume = {102}, year = {2020}, month = {7/8/2020}, abstract = {

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law 1/rα in the distance r on a D-dimensional lattice for α\≤D---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α\≤D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all α\<D. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.\ 

}, doi = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.010401}, url = {https://arxiv.org/abs/1906.02662}, author = {Andrew Y. Guo and Minh C. Tran and Andrew M. Childs and Alexey V. Gorshkov and Zhe-Xuan Gong} } @article {2690, title = {Symmetry breaking and error correction in open quantum systems}, journal = {Phys. Rev. Lett. }, volume = {125}, year = {2020}, month = {8/6/2020}, pages = {240405}, abstract = {

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system---a Lindbladian---a unitary symmetry can be imposed in a \"weak\" or a \"strong\" way. We characterize the possible Zn symmetry breaking transitions for both cases. In the case of Z2, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially-protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correctio

}, doi = {https://doi.org/10.1103/PhysRevLett.125.240405}, url = {https://arxiv.org/abs/2008.02816}, author = {Simon Lieu and Ron Belyansky and Jeremy T. Young and Rex Lundgren and Victor V. Albert and Alexey V. Gorshkov} } @article {2609, title = {Transport and dynamics in the frustrated two-bath spin-boson model}, year = {2020}, month = {7/7/2020}, abstract = {

We study the strong coupling dynamics as well as transport properties of photons in the two-bath spin-boson model, in which a spin-1/2 particle is frustratingly coupled to two independent Ohmic bosonic baths. Using a combination of numerical and analytical methods, we show that the frustration in this model gives rise to rich physics in a very wide range of energies. This is in contrast to the one-bath spin-boson model, where the non-trivial physics occurs at an energy scale close to the renormalized spin frequency. The renormalized spin frequency in the two-bath spin-boson model is still important, featuring in different observables, including the non-equiblirum dynamics of both the spin and the baths along with the elastic transport properties of a photon. The latter however reveals a much more complex structure. The elastic scattering displays non-monotonic behavior at high frequencies, and is very different in the two channels: intra- and inter-bath scattering. The photon can also be inelastically scattered, a process in which it is split into several photons of smaller energies. We show that such inelastic processes are highly anisotropic, with the outgoing particles being preferentially emitted into only one of the baths. Moreover, the inelastic scattering rate is parameterically larger than in the one-bath case, and can even exceed the total elastic rate. Our results can be verified with state-of-the-art circuit and cavity quantum electrodynamics experiments.\ 

}, url = {https://arxiv.org/abs/2007.03690}, author = {Ron Belyansky and Seth Whitsitt and Rex Lundgren and Yidan Wang and Andrei Vrajitoarea and Andrew A. Houck and Alexey V. Gorshkov} } @article {2406, title = {Complexity phase diagram for interacting and long-range bosonic Hamiltonians}, year = {2019}, month = {06/10/2019}, abstract = {

Recent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity theory aims to classify computational problems based on how the time required to solve the problem scales as the problem size becomes large. In this work, we use insights from complexity theory to classify phases in interacting many-body systems. Specifically, we demonstrate a \"complexity phase diagram\" for the Bose-Hubbard model with long-range hopping. This shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality. We find that classification of complexity phases is closely related to upper bounds on the spread of quantum correlations, and protocols to transfer quantum information in a controlled manner. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.\ 

}, url = {https://arxiv.org/abs/1906.04178}, author = {Nishad Maskara and Abhinav Deshpande and Minh C. Tran and Adam Ehrenberg and Bill Fefferman and Alexey V. Gorshkov} } @article {2264, title = {Confined Dynamics in Long-Range Interacting Quantum Spin Chains}, journal = {Phys. Rev. Lett.}, volume = {122 }, year = {2019}, month = {04/17/2019}, abstract = {

We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/rα) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these bound states have dramatic consequences for the non-equilibrium dynamics following a global quantum quench, such as suppressed spreading of quantum information and oscillations of order parameters. The masses of these bound states can be read out from the Fourier spectrum of these oscillating order parameters. We then use a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement. The masses of the bound states predicted by this model are in good quantitative agreement with exact diagonalization results. Moreover, we illustrate that these bound states lead to weak thermalization of local observables for initial states with energy near the bottom of the many-body energy spectrum. Our work is readily applicable to current trapped-ion experiments.

}, doi = {https://doi.org/10.1103/PhysRevLett.122.150601}, url = {https://arxiv.org/abs/1810.02365}, author = {Fangli Liu and Rex Lundgren and Paraj Titum and Guido Pagano and Jiehang Zhang and Christopher Monroe and Alexey V. Gorshkov} } @article {2409, title = {Floquet engineering of optical lattices with spatial features and periodicity below the diffraction limit}, year = {2019}, month = {06/18/2019}, abstract = {

Floquet engineering or coherent time periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological band structures, and observation of dynamical localization, to name just a few. Here we present a Floquet-based framework to stroboscopically engineer Hamiltonians with spatial features and periodicity below the diffraction limit of light used to create them by time-averaging over various configurations of a 1D optical Kronig-Penney (KP) lattice. The KP potential is a lattice of narrow subwavelength barriers spaced by half the optical wavelength (λ/2) and arises from the non-linear optical response of the atomic dark state. Stroboscopic control over the strength and position of this lattice requires time-dependent adiabatic manipulation of the dark state spin composition. We investigate adiabaticity requirements and shape our time-dependent light fields to respect the requirements. We apply this framework to show that a λ/4-spaced lattice can be synthesized using realistic experimental parameters as an example, discuss mechanisms that limit lifetimes in these lattices, explore candidate systems and their limitations, and treat adiabatic loading into the ground band of these lattices.

}, url = {https://arxiv.org/abs/1906.07646}, author = {S. Subhankar and P. Bienias and P. Titum and T-C. Tsui and Y. Wang and Alexey V. Gorshkov and S. L. Rolston and J. V. Porto} } @article {2276, title = {Fluctuation-induced torque on a topological insulator out of thermal equilibrium}, journal = {Phys. Rev. Lett.}, volume = {123}, year = {2019}, month = {8/1/2019}, abstract = {

Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well-understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. Utilizing the Keldysh framework, we investigate the universal nonequilibrium response of the TI to the temperature difference with the environment. Finally, we argue that experimental observation of this effect is within reach.

}, doi = {https://doi.org/10.1103/PhysRevLett.123.055901}, url = {https://arxiv.org/abs/1811.06080}, author = {M. F. Maghrebi and Alexey V. Gorshkov and J. D. Sau} } @article {2365, title = {Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks}, journal = {Phys. Rev. A}, volume = {100}, year = {2019}, month = {10/7/2019}, abstract = {

We generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

}, doi = {https://doi.org/10.1103/PhysRevA.100.042304}, url = {https://arxiv.org/abs/1901.09042}, author = {Kevin Qian and Zachary Eldredge and Wenchao Ge and Guido Pagano and Christopher Monroe and James V. Porto and Alexey V. Gorshkov} } @article {2143, title = {Interacting Qubit-Photon Bound States with Superconducting Circuits}, journal = {Phys. Rev. }, volume = {X 9}, year = {2019}, month = {2018/01/30}, abstract = {

Qubits strongly coupled to a photonic crystal give rise to many exotic physical scenarios, beginning with single and multi-excitation qubit-photon dressed bound states comprising induced spatially localized photonic modes, centered around the qubits, and the qubits themselves. The localization of these states changes with qubit detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Here, we present experimental results from a device with two qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and inter-bound state interactions. We observe a fourth-order two photon virtual process between bound states indicating strong coupling between the photonic crystal and qubits. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits\&$\#$39; spatial organization, a key criterion for realization of certain quantum many-body models. The widely tunable, strong and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems of bound states.

}, doi = {https://doi.org/10.1103/PhysRevX.9.011021}, url = {http://arxiv.org/abs/1801.10167}, author = {Neereja M. Sundaresan and Rex Lundgren and Guanyu Zhu and Alexey V. Gorshkov and Andrew A. Houck} } @article {2366, title = {Interaction-induced transition in the quantum chaotic dynamics of a disordered metal}, journal = {Ann. Phys. }, volume = {405}, year = {2019}, month = {03/25/2019}, abstract = {

We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.

}, doi = {https://doi.org/10.1016/j.aop.2019.03.008}, url = {https://arxiv.org/abs/1709.09296}, author = {S. V. Syzranov and Alexey V. Gorshkov and V. M. Galitski} } @article {2459, title = {Interference of Temporally Distinguishable Photons Using Frequency-Resolved Detection}, journal = {Phys. Rev. Lett. }, volume = {123}, year = {2019}, month = {9/24/2019}, abstract = {

We demonstrate quantum interference of three photons that are distinguishable in time, by resolving them in the conjugate parameter, frequency. We show that the multiphoton interference pattern in our setup can be manipulated by tuning the relative delays between the photons, without the need for reconfiguring the optical network. Furthermore, we observe that the symmetries of our optical network and the spectral amplitude of the input photons are manifested in the interference pattern. Moreover, we demonstrate time-reversed HOM-like interference in the spectral correlations using time-bin entangled photon pairs. By adding a time-varying dispersion using a phase modulator, our setup can be used to realize dynamically reconfigurable and scalable boson sampling in the time domain as well as frequency-resolved multiboson correlation sampling.

}, doi = {https://doi.org/10.1103/PhysRevLett.123.123603}, url = {https://arxiv.org/abs/1904.03222}, author = {Venkata Vikram Orre and Elizabeth A. Goldschmidt and Abhinav Deshpande and Alexey V. Gorshkov and Vincenzo Tamma and Mohammad Hafezi and Sunil Mittal} } @article {2195, title = {Locality and digital quantum simulation of power-law interactions}, journal = {Phys. Rev. X 9, 031006}, volume = {9}, year = {2019}, month = {07/10/2019}, abstract = {

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α\>3D (where D is the number of dimensions).

}, doi = {https://doi.org/10.1103/PhysRevX.9.031006}, url = {https://arxiv.org/abs/1808.05225}, author = {Minh C. Tran and Andrew Y. Guo and Yuan Su and James R. Garrison and Zachary Eldredge and Michael Foss-Feig and Andrew M. Childs and Alexey V. Gorshkov} } @article {2458, title = {Locality and Heating in Periodically Driven, Power-law Interacting Systems}, journal = {Phys. Rev. A }, volume = {100}, year = {2019}, month = {2019/11/12}, abstract = {

We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/rα. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α\>D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for α\>2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.\ 

}, doi = {https://doi.org/10.1103/PhysRevA.100.052103}, url = {https://arxiv.org/abs/1908.02773}, author = {Minh C. Tran and Adam Ehrenberg and Andrew Y. Guo and Paraj Titum and Dmitry A. Abanin and Alexey V. Gorshkov} } @article {2496, title = {On the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model}, year = {2019}, month = {2019/10/9}, abstract = {

The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this work, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents, including those, such as the dynamical critical exponent, that have not been previously considered. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely non-equilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that capture the system\&$\#$39;s long-time memory as well as its non-equilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.

}, url = {https://arxiv.org/abs/1910.04319}, author = {Rex Lundgren and Alexey V. Gorshkov and Mohammad F. Maghrebi} } @article {2460, title = {Nondestructive cooling of an atomic quantum register via state-insensitive Rydberg interactions}, year = {2019}, month = {7/28/2019}, abstract = {

We propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing state-insensitive Rydberg interactions between the data-carrying atoms and cold auxiliary atoms. The resulting interactions give rise to an effective phonon coupling, which leads to the transfer of heat from the data atoms to the auxiliary atoms, where the latter can be cooled by conventional methods. This can be used to extend the lifetime of quantum storage based on neutral atoms and can have applications for long quantum computations. The protocol can also be modified to realize state-insensitive interactions between the data and the auxiliary atoms but tunable and non-trivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spin-model.\ 

}, url = {https://arxiv.org/abs/1907.11156}, author = {Ron Belyansky and Jeremy T. Young and Przemyslaw Bienias and Zachary Eldredge and Adam M. Kaufman and Peter Zoller and Alexey V. Gorshkov} } @article {2520, title = {Observation of Domain Wall Confinement and Dynamics in a Quantum Simulator}, year = {2019}, month = {12/23/2019}, abstract = {

Confinement is a ubiquitous mechanism in nature, whereby particles feel an attractive force that increases without bound as they separate. A prominent example is color confinement in particle physics, in which baryons and mesons are produced by quark confinement. Analogously, confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here, we report the first observation of magnetic domain wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can dramatically suppress information propagation and thermalization in such many-body systems. We are able to quantitatively determine the excitation energy of domain wall bound states from non-equilibrium quench dynamics. Furthermore, we study the number of domain wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers. This work demonstrates the capability of quantum simulators for investigating exotic high-energy physics phenomena, such as quark collision and string breaking

}, url = {https://arxiv.org/abs/1912.11117}, author = {W. L. Tan and P. Becker and F. Liu and G. Pagano and K. S. Collins and A. De and L. Feng and H. B. Kaplan and A. Kyprianidis and R. Lundgren and W. Morong and S. Whitsitt and Alexey V. Gorshkov and C. Monroe} } @article {2362, title = {Opportunities for Nuclear Physics \& Quantum Information Science}, year = {2019}, month = {03/13/2019}, abstract = {

his whitepaper is an outcome of the workshop Intersections between Nuclear Physics and Quantum Information held at Argonne National Laboratory on 28-30 March 2018 [www.phy.anl.gov/npqi2018/]. The workshop brought together 116 national and international experts in nuclear physics and quantum information science to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department of Energy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. The workshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topics discussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors, nuclear many-body problem, entanglement at collider energies, and lattice gauge theories.

}, url = {https://arxiv.org/abs/1903.05453}, author = {I. C. Clo{\"e}t and Matthew R. Dietrich and John Arrington and Alexei Bazavov and Michael Bishof and Adam Freese and Alexey V. Gorshkov and Anna Grassellino and Kawtar Hafidi and Zubin Jacob and Michael McGuigan and Yannick Meurice and Zein-Eddine Meziani and Peter Mueller and Christine Muschik and James Osborn and Matthew Otten and Peter Petreczky and Tomas Polakovic and Alan Poon and Raphael Pooser and Alessandro Roggero and Mark Saffman and Brent VanDevender and Jiehang Zhang and Erez Zohar} } @article {2265, title = {Probing ground-state phase transitions through quench dynamics}, journal = {Phys. Rev. Lett.}, volume = {123}, year = {2019}, month = {9/11/2019}, abstract = {

The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a non-analytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal time scales. Therefore, our method can be used to approximately locate the quantum critical point. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.

}, doi = {https://doi.org/10.1103/PhysRevLett.123.115701}, url = {https://arxiv.org/abs/1809.06377}, author = {Paraj Titum and Joseph T. Iosue and James R. Garrison and Alexey V. Gorshkov and Zhe-Xuan Gong} } @article {2529, title = {Programmable Quantum Simulations of Spin Systems with Trapped Ions}, year = {2019}, month = {12/17/2019}, abstract = {

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated in ways that give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theoretical mapping of atomic ions to interacting spin systems, the experimental preparation of complex equilibrium states, and the study of dynamical processes of this many-body interacting quantum system. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on interacting quantum systems that cannot be modeled with conventional computers.\ 

}, url = {https://arxiv.org/abs/1912.07845}, author = {C. Monroe and W. C. Campbell and L. -M. Duan and Z. -X. Gong and Alexey V. Gorshkov and P. Hess and R. Islam and K. Kim and G. Pagano and P. Richerme and C. Senko and N. Y. Yao} } @article {2410, title = {Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator}, year = {2019}, month = {06/06/2019}, abstract = {

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit.\ 

}, url = {https://arxiv.org/abs/1906.02700}, author = {G. Pagano and A. Bapat and P. Becker and K. S. Collins and A. De and P. W. Hess and H. B. Kaplan and A. Kyprianidis and W. L. Tan and Christopher L. Baldwin and L. T. Brady and A. Deshpande and F. Liu and S. Jordan and Alexey V. Gorshkov and C. Monroe} } @article {2530, title = {Quantum Computer Systems for Scientific Discovery}, year = {2019}, month = {12/16/2019}, abstract = {

The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, and significant challenges for the development of quantum computers for science over the next 2-10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21-22, 2019 in Alexandria, VA.

}, url = {https://arxiv.org/abs/1912.07577}, author = {Yuri Alexeev and Dave Bacon and Kenneth R. Brown and Robert Calderbank and Lincoln D. Carr and Frederic T. Chong and Brian DeMarco and Dirk Englund and Edward Farhi and Bill Fefferman and Alexey V. Gorshkov and Andrew Houck and Jungsang Kim and Shelby Kimmel and Michael Lange and Seth Lloyd and Mikhail D. Lukin and Dmitri Maslov and Peter Maunz and Christopher Monroe and John Preskill and Martin Roetteler and Martin Savage and Jeff Thompson and Umesh Vazirani} } @article {2487, title = {Real-time dynamics of string breaking in quantum spin chains}, year = {2019}, month = {2019/11/26}, abstract = {

String breaking is a central dynamical process in theories featuring confinement, where a string connecting two charges decays at the expense of the creation of new particle-antiparticle pairs. Here, we show that this process can also be observed in quantum Ising chains where domain walls get confined either by a symmetry-breaking field or by long-range interactions. We find that string breaking occurs, in general, as a two-stage process: First, the initial charges remain essentially static and stable. The connecting string, however, can become a dynamical object. We develop an effective description of this motion, which we find is strongly constrained. In the second stage, which can be severely delayed due to these dynamical constraints, the string finally breaks. We observe that the associated time scale can depend crucially on the initial separation between domain walls and can grow by orders of magnitude by changing the distance by just a few lattice sites. We discuss how our results generalize to one-dimensional confining gauge theories and how they can be made accessible in quantum simulator experiments such as Rydberg atoms or trapped ions.

}, url = {https://arxiv.org/abs/1911.11382}, author = {Roberto Verdel and Fangli Liu and Seth Whitsitt and Alexey V. Gorshkov and Markus Heyl} } @article {2217, title = {Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator}, journal = {Phys. Rev. Lett}, volume = {122}, year = {2019}, month = {03/27/2019}, abstract = {

The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.122.120502}, url = {https://arxiv.org/abs/1807.11486}, author = {Su-Kuan Chu and Guanyu Zhu and James R. Garrison and Zachary Eldredge and Ana Vald{\'e}s Curiel and Przemyslaw Bienias and I. B. Spielman and Alexey V. Gorshkov} } @article {2211, title = {Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics}, journal = {Phys. Rev. Lett}, volume = {121}, year = {2018}, month = {2018/12/20}, abstract = {

We study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast with the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through non-equilibrium dynamics.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.250404}, url = {https://arxiv.org/abs/1809.02614}, author = {Fangli Liu and James R. Garrison and Dong-Ling Deng and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {2216, title = {Coherent optical nano-tweezers for ultra-cold atoms}, year = {2018}, abstract = {

There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultra-cold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work opens a new frontier for the subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.

}, url = {https://arxiv.org/abs/1808.02487}, author = {P. Bienias and S. Subhankar and Y. Wang and T-C Tsui and F. Jendrzejewski and T. Tiecke and G. Juzeliunas and L. Jiang and S. L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {2141, title = {Dark state optical lattice with sub-wavelength spatial structure}, journal = {Phys. Rev. Lett.}, volume = {120}, year = {2018}, month = {2018/02/20}, pages = {083601}, abstract = {

We report on the experimental realization of a conservative optical lattice for cold atoms with a subwavelength spatial structure. The potential is based on the nonlinear optical response of three-level atoms in laser-dressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The lattice consists of a one-dimensional array of ultranarrow barriers with widths less than 10\ nm, well below the wavelength of the lattice light, physically realizing a Kronig-Penney potential. We study the band structure and dissipation of this lattice and find good agreement with theoretical predictions. Even on resonance, the observed lifetimes of atoms trapped in the lattice are as long as 44\ ms, nearly\ 105times the excited state lifetime, and could be further improved with more laser intensity. The potential is readily generalizable to higher dimensions and different geometries, allowing, for example, nearly perfect box traps, narrow tunnel junctions for atomtronics applications, and dynamically generated lattices with subwavelength spacings.

}, doi = {10.1103/PhysRevLett.120.083601}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.120.083601}, author = {Yang Wang and Sarthak Subhankar and Przemyslaw Bienias and Mateusz Lacki and Tsz-Chun Tsui and Mikhail A. Baranov and Alexey V. Gorshkov and Peter Zoller and James V. Porto and Steven L. Rolston} } @article {2142, title = {Dissipation induced dipole blockade and anti-blockade in driven Rydberg systems}, journal = {Phys. Rev. A}, volume = {97}, year = {2018}, month = {2018/02/28}, pages = {023424}, abstract = {

We study theoretically and experimentally the competing blockade and antiblockade effects induced by spontaneously generated contaminant Rydberg atoms in driven Rydberg systems. These contaminant atoms provide a source of strong dipole-dipole interactions and play a crucial role in the system\&$\#$39;s behavior. We study this problem theoretically using two different approaches. The first is a cumulant expansion approximation, in which we ignore third-order and higher connected correlations. Using this approach for the case of resonant drive, a many-body blockade radius picture arises, and we find qualitative agreement with previous experimental results. We further predict that as the atomic density is increased, the Rydberg population\&$\#$39;s dependence on Rabi frequency will transition from quadratic to linear dependence at lower Rabi frequencies. We study this behavior experimentally by observing this crossover at two different atomic densities. We confirm that the larger density system has a smaller crossover Rabi frequency than the smaller density system. The second theoretical approach is a set of phenomenological inhomogeneous rate equations. We compare the results of our rate-equation model to the experimental observations [E. A. Goldschmidt\ et al.,\ Phys. Rev. Lett.116, 113001 (2016)] and find that these rate equations provide quantitatively good scaling behavior of the steady-state Rydberg population for both resonant and off-resonant drives.

}, doi = {10.1103/PhysRevA.97.023424}, url = {https://link.aps.org/doi/10.1103/PhysRevA.97.023424}, author = {Jeremy T. Young and Thomas Boulier and Eric Magnan and Elizabeth A. Goldschmidt and Ryan M. Wilson and Steven L. Rolston and James V. Porto and Alexey V. Gorshkov} } @article {2278, title = {Distributed Quantum Metrology and the Entangling Power of Linear Networks}, journal = {Phys. Rev. Lett. 121, 043604}, year = {2018}, month = {2018/07/25}, abstract = {

We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.121.043604}, url = {https://arxiv.org/abs/1707.06655}, author = {Wenchao Ge and Kurt Jacobs and Zachary Eldredge and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2137, title = {Distributed Quantum Metrology and the Entangling Power of Linear Networks}, year = {2018}, month = {2018/07/25}, abstract = {

We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.043604}, url = {https://arxiv.org/abs/1707.06655}, author = {Wenchao Ge and Kurt Jacobs and Zachary Eldredge and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2210, title = {Dynamical phase transitions in sampling complexity}, journal = {Phys. Rev. Lett.}, volume = {121}, year = {2018}, pages = {12 pages, 4 figures. v3: published version}, abstract = {

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time\ t\ due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of\ t\ with the number of bosons\ n\ for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of\ t\ with\ n\ for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC \&$\#$39;11]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular and optical systems.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.030501}, url = {https://arxiv.org/abs/1703.05332}, author = {Abhinav Deshpande and Bill Fefferman and Minh C. Tran and Michael Foss-Feig and Alexey V. Gorshkov} } @article {2256, title = {Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal}, year = {2018}, abstract = {

Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems, and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half-filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal phase, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

}, url = {https://arxiv.org/abs/1809.04493}, author = {Tobias Gra{\ss} and Przemyslaw Bienias and Michael Gullans and Rex Lundgren and Joseph Maciejko and Alexey V. Gorshkov} } @article {2060, title = {Observation of three-photon bound states in a quantum nonlinear medium}, journal = {Science}, volume = {359}, year = {2018}, month = {2018/02/16}, pages = {783-786}, abstract = {

Bound states of massive particles, such as nuclei, atoms or molecules, are ubiquitous in nature and constitute the bulk of the visible world around us. In contrast, photons typically only weakly influence each other due to their very weak interactions and vanishing mass. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. In particular, photon correlation and conditional phase measurements reveal the distinct features associated with three-photon and two-photon bound states. Such photonic trimers and dimers can be viewed as quantum solitons with shape-preserving wavefunctions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are quantitatively described by an effective field theory (EFT) of Rydberg-induced photon-photon interactions, which demonstrates the presence of a substantial effective three-body force between the photons. These observations pave the way towards the realization, studies, and control of strongly interacting quantum many-body states of light.

}, doi = {10.1126/science.aao7293}, url = {http://science.sciencemag.org/content/359/6377/783}, author = {Qi-Yu Liang and Aditya V. Venkatramani and Sergio H. Cantu and Travis L. Nicholson and Michael Gullans and Alexey V. Gorshkov and Jeff D. Thompson and Cheng Chin and Mikhail D. Lukin and Vladan Vuletic} } @article {1836, title = {Optimal and Secure Measurement Protocols for Quantum Sensor Networks}, year = {2018}, month = {2018/03/23}, abstract = {

Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting where the quantity to be measured is a linear function of parameters coupled to each qubit individually. We first generalize the Heisenberg limit to the measurement of non-local observables in a quantum network, deriving a bound based on the multi-parameter quantum Fisher information. We then propose a protocol that can make use of GHZ states or spin-squeezed states, and show that in the case of GHZ states the procedure is optimal, i.e., it saturates our bound.

}, doi = {https://doi.org/10.1103/PhysRevA.97.042337}, url = {http://arxiv.org/abs/1607.04646}, author = {Zachary Eldredge and Michael Foss-Feig and Steven L. Rolston and Alexey V. Gorshkov} } @article {2209, title = {Optimization of photon storage fidelity in ordered atomic arrays}, journal = {New Journal of Physics}, volume = {20}, year = {2018}, month = {2018/08/31}, abstract = {

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. The validity of this model can break down, however, in systems such as dense, ordered atomic arrays, where strong interference in emission can give rise to phenomena such as subradiance and \"selective\" radiance. Here, we develop a general formalism that finds the maximum storage efficiency for a collection of atoms with discrete, known positions, and a given spatial mode in which an optical field is sent. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number Na like \∼(logNa)2/N2a, and that, remarkably, an array of just 4\×4 atoms in principle allows for an efficiency comparable to a disordered ensemble with optical depth of around 600.

}, doi = {https://doi.org/10.1088/1367-2630/aadb74}, url = {https://arxiv.org/abs/1710.06312}, author = {M. T. Manzoni and M. Moreno-Cardoner and A. Asenjo-Garcia and J. V. Porto and Alexey V. Gorshkov and D. E. Chang} } @article {2218, title = {Photon propagation through dissipative Rydberg media at large input rates}, year = {2018}, abstract = {

We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency (EIT). Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail for the first time the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly-stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.\ 

}, url = {https://arxiv.org/abs/1807.07586}, author = {Przemyslaw Bienias and James Douglas and Asaf Paris-Mandoki and Paraj Titum and Ivan Mirgorodskiy and Christoph Tresp and Emil Zeuthen and Michael Gullans and Marco Manzoni and Sebastian Hofferberth and Darrick Chang and Alexey V. Gorshkov} } @article {2144, title = {Photon Subtraction by Many-Body Decoherence}, year = {2018}, month = {2018/03/13}, abstract = {

We present an experimental and theoretical investigation of the scattering-induced decoherence of multiple photons stored in a strongly interacting atomic ensemble. We derive an exact solution to this many-body problem, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis demonstrates a correlated coherence-protection process, in which the induced decoherence of one photon can preserve the spatial coherence of all others. We discuss how this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability.

}, doi = {https://doi.org/10.1103/PhysRevLett.120.113601}, url = {https://arxiv.org/abs/1710.10047}, author = {Callum R. Murray and Ivan Mirgorodskiy and Christoph Tresp and Christoph Braun and Asaf Paris-Mandoki and Alexey V. Gorshkov and Sebastian Hofferberth and Thomas Pohl} } @article {2213, title = {Single-photon bound states in atomic ensembles}, year = {2018}, abstract = {

We illustrate the existence of single-excitation bound states for propagating photons interacting with N two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson\&$\#$39;s theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

}, url = {https://arxiv.org/abs/1809.01147}, author = {Yidan Wang and Michael Gullans and Antoine Browaeys and J. V. Porto and Darrick E. Chang and Alexey V. Gorshkov} } @article {1837, title = {Spectrum estimation of density operators with alkaline-earth atoms}, volume = {120}, year = {2018}, month = {2018/01/09}, abstract = {

We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkalineearth atoms are discussed.

}, doi = {https://doi.org/10.1103/PhysRevLett.120.025301}, url = {http://arxiv.org/abs/1608.02045}, author = {Michael E. Beverland and Jeongwan Haah and Gorjan Alagic and Gretchen K. Campbell and Ana Maria Rey and Alexey V. Gorshkov} } @article {2215, title = {Unitary Entanglement Construction in Hierarchical Networks}, year = {2018}, abstract = {

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

}, url = {https://arxiv.org/abs/1808.07876}, author = {Aniruddha Bapat and Zachary Eldredge and James R. Garrison and Abhinav Desphande and Frederic T. Chong and Alexey V. Gorshkov} } @article {1952, title = {Complexity of sampling as an order parameter}, year = {2017}, month = {2017/03/15}, abstract = {

We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time\ t. We obtain upper and lower bounds on the scaling of\ twith the number of bosons,\ n, for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian and conjecture a link to dynamical phase transitions. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter systems.

}, url = {https://arxiv.org/abs/1703.05332}, author = {Abhinav Deshpande and Bill Fefferman and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1814, title = {Correlated Photon Dynamics in Dissipative Rydberg Media}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/07/26}, pages = {043602}, abstract = {

Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative interactions relevant to current experiments. Our model is in good agreement with experimental data. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

}, doi = {10.1103/PhysRevLett.119.043602}, url = {https://arxiv.org/abs/1608.06068}, author = {Emil Zeuthen and Michael Gullans and Mohammad F. Maghrebi and Alexey V. Gorshkov} } @article {2001, title = {{E}ntanglement area laws for long-range interacting systems}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/07/31}, pages = {050501}, abstract = {

We prove that the entanglement entropy of any state evolved under an arbitrary 1/rα long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any α \> D + 1. We also prove that for any α \> 2D + 2, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.

}, doi = {10.1103/PhysRevLett.119.050501}, url = {https://arxiv.org/abs/1702.05368}, author = {Zhe-Xuan Gong and Michael Foss-Feig and Fernando G. S. L. Brand{\~a}o and Alexey V. Gorshkov} } @article {2059, title = {Efimov States of Strongly Interacting Photons}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/12/04}, pages = {233601}, abstract = {

We demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity, but with spatially anisotropic wavefunctions in the original coordinates. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the non-equilbrium, many-body regime.

}, doi = {10.1103/PhysRevLett.119.233601}, url = {https://arxiv.org/abs/1709.01955}, author = {Michael Gullans and S. Diehl and S. T. Rittenhouse and B. P. Ruzic and J. P. D{\textquoteright}Incao and P. Julienne and Alexey V. Gorshkov and J. M. Taylor} } @article {1906, title = {Emergent equilibrium in many-body optical bistability}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/04/17}, pages = {043826}, abstract = {

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

}, doi = {doi.org/10.1103/PhysRevA.95.043826}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826}, author = {Michael Foss-Feig and Pradeep Niroula and Jeremy T. Young and Mohammad Hafezi and Alexey V. Gorshkov and Ryan M. Wilson and Mohammad F. Maghrebi} } @article {1921, title = {Exact sampling hardness of Ising spin models}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/09/14}, pages = {032324}, abstract = {

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of\ exact\ classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in\ Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl\–Leibniz-Zentrum f{\"u}r Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

}, doi = {10.1103/PhysRevA.96.032324}, url = {https://arxiv.org/abs/1701.03167}, author = {Bill Fefferman and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1780, title = {Exactly soluble model of boundary degeneracy}, journal = {Physical Review B}, volume = {95}, year = {2017}, month = {2017/01/25}, chapter = {045309}, abstract = {

We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as \"boundary degeneracy\") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

}, doi = {10.1103/PhysRevB.95.045309}, url = {http://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.045309}, author = {Sriram Ganeshan and Alexey V. Gorshkov and Victor Gurarie and Victor M. Galitski} } @article {1908, title = {Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/10/25}, pages = {170503}, abstract = {

In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance\ L\ in\ d\ dimensions using long-range interactions with strength bounded by\ 1/rα. If\ α\<d, the state transfer time is asymptotically independent of\ L; if\ α=d, the time is logarithmic in distance\ L; if\ d\<α\<d+1, transfer occurs in time proportional to\ Lα\−d; and if\ α\≥d+1, it occurs in time proportional to\ L. We then use this protocol to upper bound the time required to create a state specified by a MERA (multiscale entanglement renormalization ansatz) tensor network, and show that, if the linear size of the MERA state is\ L, then it can be created in time that scales with\ L\ identically to state transfer up to multiplicative logarithmic corrections.

}, doi = {10.1103/PhysRevLett.119.170503}, url = {https://arxiv.org/abs/1612.02442}, author = {Zachary Eldredge and Zhe-Xuan Gong and Ali Hamed Moosavian and Michael Foss-Feig and Alexey V. Gorshkov} } @article {2277, title = {Lieb-Robinson bounds on n-partite connected correlation functions}, journal = {Phys. Rev. A 96, 052334}, year = {2017}, abstract = {

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

}, doi = {https://doi.org/10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1987, title = {Lieb-Robinson bounds on n-partite connected correlations}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/11/27}, abstract = {

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an\ n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an\ n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

}, doi = {10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1835, title = {Multicritical behavior in dissipative {I}sing models}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/04/26}, pages = {042133}, abstract = {

We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

}, doi = {doi.org/10.1103/PhysRevA.95.042133}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.042133}, author = {Vincent R. Overbeck and Mohammad F. Maghrebi and Alexey V. Gorshkov and Hendrik Weimer} } @article {2053, title = {Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator}, journal = {Nature}, volume = {551}, year = {2017}, month = {2017/11/29}, pages = {601-604}, abstract = {

A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99\% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.

}, doi = {10.1038/nature24654}, url = {https://www.nature.com/articles/nature24654}, author = {J. Zhang and G. Pagano and P. W. Hess and A. Kyprianidis and P. Becker and H. Kaplan and Alexey V. Gorshkov and Z. -X. Gong and C. Monroe} } @article {2002, title = {Out-of-time-order correlators in finite open systems}, year = {2017}, month = {2017/04/27}, abstract = {

We study out-of-time order correlators (OTOCs) of the form hA\ˆ(t)B\ˆ(0)C\ˆ(t)D\ˆ(0)i for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially \∝ Paie \−t/τi + const to a constant value at t \→ \∞, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focussing on the case of a two-level system, we calculate microscopically the decay times τi and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.

}, doi = {https://doi.org/10.1103/PhysRevB.97.161114}, url = {https://arxiv.org/abs/1704.08442}, author = {S. V. Syzranov and Alexey V. Gorshkov and V. Galitski} } @article {2003, title = {A solvable family of driven-dissipative many-body systems}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/11/10}, abstract = {

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. And conversely, the relative scarcity of solutions for non-equilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently in any number of spatial dimensions. We leverage these solutions to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions, and to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture.

}, doi = {10.1103/PhysRevLett.119.190402}, url = {https://arxiv.org/abs/1703.04626}, author = {Michael Foss-Feig and Jeremy T. Young and Victor V. Albert and Alexey V. Gorshkov and Mohammad F. Maghrebi} } @article {1678, title = {Anomalous broadening in driven dissipative Rydberg systems}, journal = {Physical Review Letters}, volume = {116}, year = {2016}, month = {2016/03/16}, pages = {113001}, abstract = {We observe interaction-induced broadening of the two-photon 5s-18s transition in 87Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly two orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with spontaneously created populations of nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms.}, doi = {10.1103/PhysRevLett.116.113001}, url = {http://arxiv.org/abs/1510.08710}, author = {E. A. Goldschmidt and T. Boulier and R. C. Brown and S. B. Koller and J. T. Young and Alexey V. Gorshkov and S. L. Rolston and J. V. Porto} } @article {1960, title = {Causality and quantum criticality in long-range lattice models}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/03/17}, pages = {125128}, doi = {10.1103/PhysRevB.93.125128}, url = {http://link.aps.org/doi/10.1103/PhysRevB.93.125128}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1179, title = {Causality and quantum criticality with long-range interactions}, journal = {Physical Review B}, volume = {92}, year = {2016}, month = {2016/03/17}, pages = {125128}, abstract = { Quantum lattice systems with long-range interactions often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model and a fermionic model with long-range interactions, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of long-range interactions, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent. }, doi = {10.1103/PhysRevB.93.125128}, url = {http://arxiv.org/abs/1508.00906}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1737, title = {Collective phases of strongly interacting cavity photons}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/09/01}, pages = {033801}, abstract = {

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-12 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

}, doi = {http://dx.doi.org/10.1103/PhysRevA.94.033801}, url = {http://arxiv.org/abs/1601.06857}, author = {Ryan M. Wilson and Khan W. Mahmud and Anzi Hu and Alexey V. Gorshkov and Mohammad Hafezi and Michael Foss-Feig} } @article {1784, title = {Effective Field Theory for Rydberg Polaritons}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/09/09}, pages = {113601}, abstract = {

We study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.

}, doi = {http://dx.doi.org/10.1103/PhysRevLett.117.113601}, url = {http://arxiv.org/abs/1605.05651}, author = {Michael Gullans and J. D. Thompson and Y. Wang and Q. -Y. Liang and V. Vuletic and M. D. Lukin and Alexey V. Gorshkov} } @article {2004, title = {Entanglement and spin-squeezing without infinite-range interactions}, year = {2016}, month = {2016/12/22}, abstract = {

Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.

}, url = {https://arxiv.org/abs/1612.07805}, author = {Michael Foss-Feig and Zhe-Xuan Gong and Alexey V. Gorshkov and Charles W. Clark} } @article {1695, title = {Kaleidoscope of quantum phases in a long-range interacting spin-1 chain}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/05/11}, pages = {205115}, abstract = {Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α≲3, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future. }, doi = {http://dx.doi.org/10.1103/PhysRevB.93.205115}, url = {http://arxiv.org/abs/1510.02108}, author = {Zhe-Xuan Gong and Mohammad F. Maghrebi and Anzi Hu and Michael Foss-Feig and Philip Richerme and Christopher Monroe and Alexey V. Gorshkov} } @article {1834, title = {Many-body decoherence dynamics and optimised operation of a single-photon switch}, journal = {New Journal of Physics}, volume = {18}, year = {2016}, month = {2016/09/13}, pages = {092001}, abstract = {

We develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimised switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments [arXiv:1511.09445] and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media.\ 

}, doi = {10.1088/1367-2630/18/9/092001}, url = {http://iopscience.iop.org/article/10.1088/1367-2630/18/9/092001}, author = {Callum R. Murray and Alexey V. Gorshkov and Thomas Pohl} } @article {1162, title = {Nonequilibrium many-body steady states via Keldysh formalism}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/01/27}, pages = {014307}, abstract = { Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. While these states and their phase transitions have been studied extensively with mean field theory, the validity of the mean field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class. }, doi = {10.1103/PhysRevB.93.014307}, url = {http://arxiv.org/abs/1507.01939}, author = {Mohammad F. Maghrebi and Alexey V. Gorshkov} } @article {2005, title = {{O}bservation of {P}rethermalization in {L}ong-{R}ange {I}nteracting {S}pin {C}hains}, year = {2016}, month = {2016/08/02}, abstract = {

Statistical mechanics can predict thermal equilibrium states for most classical systems, but for an isolated quantum system there is no general understanding on how equilibrium states dynamically emerge from the microscopic Hamiltonian. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale and, instead, relax to quasi-stationary prethermal states that can be described by statistical mechanics when approximately conserved quantities are appropriately included in a generalized Gibbs ensemble (GGE). Here we experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse field Ising Hamiltonian following a sudden quench. For sufficiently long-ranged interactions the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. In this case, the prethermal state cannot be described by a GGE, but rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a significantly broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.

}, url = {https://arxiv.org/abs/1608.00681}, author = {B. Neyenhuis and J. Smith and A. C. Lee and J. Zhang and P. Richerme and P. W. Hess and Z. -X. Gong and Alexey V. Gorshkov and C. Monroe} } @article {1187, title = {Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/05/06}, abstract = {

We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the Sn symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.

}, doi = {10.1103/PhysRevA.93.051601}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.051601}, author = {Michael E. Beverland and Gorjan Alagic and Michael J. Martin and Andrew P. Koller and Ana M. Rey and Alexey V. Gorshkov} } @article {1772, title = {Self-organization of atoms coupled to a chiral reservoir}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/11/29}, pages = {053855}, abstract = {

Tightly confined modes of light, as in optical nanofibers or photonic crystal waveguides, can lead to large optical coupling in atomic systems, which mediates long-range interactions between atoms. These one-dimensional systems can naturally possess couplings that are asymmetric between modes propagating in different directions. Strong long-range interaction among atoms via these modes can drive them to a self-organized periodic distribution. In this paper, we examine the self-organizing behavior of atoms in one dimension coupled to a chiral reservoir. We determine the solution to the equations of motion in different parameter regimes, relative to both the detuning of the pump laser that initializes the atomic dipole-dipole interactions and the degree of reservoir chirality. In addition, we calculate possible experimental signatures such as reflectivity from self-organized atoms and motional sidebands.

}, doi = {10.1103/PhysRevA.94.053855}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.053855}, author = {Zachary Eldredge and Pablo Solano and Darrick Chang and Alexey V. Gorshkov} } @article {1907, title = {Steady-state superradiance with Rydberg polaritons}, journal = {arXiv:1611.00797}, year = {2016}, month = {2016/11/02}, abstract = {

A steady-state superradiant laser can be used to generate ultranarrow-linewidth light, and thus has important applications in the fields of quantum information and precision metrology. However, the light produced by such a laser is still essentially classical. Here, we show that the introduction of a Rydberg medium into a cavity containing atoms with a narrow optical transition can lead to the steady-state superradiant emission of ultranarrow-linewidth\ nonclassical\ light. The cavity nonlinearity induced by the Rydberg medium strongly modifies the superradiance threshold, and leads to a Mollow triplet in the cavity output spectrum\−this behavior can be understood as an unusual analogue of resonance fluorescence. The cavity output spectrum has an extremely sharp central peak, with a linewidth that can be far narrower than that of a classical superradiant laser. This unprecedented spectral sharpness, together with the nonclassical nature of the light, could lead to new applications in which spectrally pure\ quantum\ light is desired.

}, url = {https://arxiv.org/abs/1611.00797}, author = {Zhe-Xuan Gong and Minghui Xu and Michael Foss-Feig and James K. Thompson and Ana Maria Rey and Murray Holland and Alexey V. Gorshkov} } @article {2006, title = {Subwavelength-width optical tunnel junctions for ultracold atoms}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/12/27}, pages = {063422}, abstract = {

We propose a method for creating far-field optical barrier potentials for ultracold atoms with widths that are narrower than the diffraction limit and can approach tens of nanometers. The reduced widths stem from the nonlinear atomic response to control fields that create spatially varying dark resonances. The subwavelength barrier is the result of the geometric scalar potential experienced by an atom prepared in such a spatially varying dark state. The performance of this technique, as well as its applications to the study of many-body physics and to the implementation of quantum-information protocols with ultracold atoms, are discussed, with a focus on the implementation of tunnel junctions.

}, doi = {10.1103/PhysRevA.94.063422}, url = {http://link.aps.org/doi/10.1103/PhysRevA.94.063422}, author = {Jendrzejewski, F. and Eckel, S. and Tiecke, T. G. and G. Juzeliunas and Campbell, G. K. and Jiang, Liang and Alexey V. Gorshkov} } @article {1191, title = {Topological phases with long-range interactions}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/01/08}, pages = {041102}, abstract = { Topological phases of matter are primarily studied in quantum many-body systems with short-range interactions. Whether various topological phases can survive in the presence of long-range interactions, however, is largely unknown. Here we show that a paradigmatic example of a symmetry-protected topological phase, the Haldane phase of an antiferromagnetic spin-1 chain, surprisingly remains intact in the presence of arbitrarily slowly decaying power-law interactions. The influence of long-range interactions on the topological order is largely quantitative, and we expect similar results for more general systems. Our conclusions are based on large-scale matrix-product-state simulations and two complementary effective-field-theory calculations. The striking agreement between the numerical and analytical results rules out finite-size effects. The topological phase considered here should be experimentally observable in a recently developed trapped-ion quantum simulator. }, doi = {10.1103/PhysRevB.93.041102}, url = {http://arxiv.org/abs/1505.03146}, author = {Zhe-Xuan Gong and Mohammad F. Maghrebi and Anzi Hu and Michael L. Wall and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1838, title = {Atom induced cavities and tunable long-range interactions between atoms trapped near photonic crystals}, journal = {Nature Photon. 9, 326 (2015)}, year = {2015}, month = {2015/03/03}, abstract = {

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, achieving tunable, coherent long-range interactions between atoms is an outstanding challenge, which currently leaves a large class of models inaccessible to quantum simulation. Here, we propose a solution exploiting the powerful new platform of cold atoms trapped near nano-photonic systems. We show that the dielectric contrast of an atom trapped near a photonic crystal can seed a localized cavity mode around the atomic position. In a dynamic form of \“all-atomic\” cavity QED, the length of these cavity modes can be tuned, and atoms separated by the order of the e\↵ective cavity length can interact coherently with each other. Considering realistic conditions such as fabrication disorder and photon losses, coherent long-range potentials or spin interactions can be dominant in the system over length scales up to hundreds of wavelengths.

}, doi = {doi:10.1038/nphoton.2015.57}, url = {http://www.nature.com/nphoton/journal/v9/n5/full/nphoton.2015.57.html}, author = {J S Douglas and H Habibian and Alexey V. Gorshkov and H J Kimble and D E Chang} } @article {1190, title = {Bilayer fractional quantum Hall states with ultracold dysprosium}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/09/10}, pages = {033609}, abstract = { We show how dipolar interactions between dysprosium atoms in an optical lattice can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-1/2 or spin-1 degree of freedom in each atom. Thinking of spin-1/2 particles as hardcore bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the \nu = 1/2 Laughlin state. Thinking of spin-1 particles as two-component hardcore bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed. }, doi = {10.1103/PhysRevA.92.033609}, url = {http://arxiv.org/abs/1505.03099v1}, author = {Norman Y. Yao and Steven D. Bennett and Chris R. Laumann and Benjamin L. Lev and Alexey V. Gorshkov} } @article {1696, title = {Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems}, year = {2015}, month = {2015/10/05}, abstract = {Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)\~{}1/rα, directly relevant to ion-trap experiments. Using bosonization and renormalization group theory, we find CSB for α smaller than a critical exponent αc(<=3) depending on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal symmetry due to long-range interactions, and is described by a new universality class akin to the Berezinskii-Kosterlitz-Thouless transition. Our analytical findings are in good agreement with a numerical calculation. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.}, url = {http://arxiv.org/abs/1510.01325}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1507, title = {Coulomb bound states of strongly interacting photons}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/09/16}, pages = {123601}, abstract = { We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. }, doi = {10.1103/PhysRevLett.115.123601}, url = {http://arxiv.org/abs/1505.03859v1}, author = {Mohammad F. Maghrebi and Michael Gullans and P. Bienias and S. Choi and I. Martin and O. Firstenberg and M. D. Lukin and H. P. B{\"u}chler and Alexey V. Gorshkov} } @article {1188, title = {Fractional Quantum Hall States of Rydberg Polaritons}, journal = {Physical Review A}, volume = {91}, year = {2015}, month = {2015/03/31}, pages = {033838}, abstract = { We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator -- a lattice-based, fractional quantum Hall state of light. }, doi = {10.1103/PhysRevA.91.033838}, url = {http://arxiv.org/abs/1411.6624v1}, author = {Mohammad F. Maghrebi and Norman Y. Yao and Mohammad Hafezi and Thomas Pohl and Ofer Firstenberg and Alexey V. Gorshkov} } @article {1178, title = {Nearly-linear light cones in long-range interacting quantum systems}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/04/13}, pages = {157201}, abstract = { In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems. }, doi = {10.1103/PhysRevLett.114.157201}, url = {http://arxiv.org/abs/1410.3466v1}, author = {Michael Foss-Feig and Zhe-Xuan Gong and Charles W. Clark and Alexey V. Gorshkov} } @article {1189, title = {Parafermionic zero modes in ultracold bosonic systems}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/08/06}, pages = {065301}, abstract = { Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The fractionalized statistics of these modes takes them an important step beyond the simplest non-Abelian anyons, Majorana fermions. Building on recent advances towards the realization of fractional quantum Hall states of bosonic ultracold atoms, we propose a realization of parafermions in a system consisting of Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trenches and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes. }, doi = {10.1103/PhysRevLett.115.065301}, url = {http://arxiv.org/abs/1504.04012v2}, author = {Mohammad F. Maghrebi and Sriram Ganeshan and David J. Clarke and Alexey V. Gorshkov and Jay D. Sau} } @article {1675, title = {Quantum many-body models with cold atoms coupled to photonic crystals}, journal = {Nature Photonics}, volume = {9}, year = {2015}, month = {2015/04/04}, pages = {326 - 331}, issn = {1749-4885}, doi = {10.1038/nphoton.2015.57}, url = {http://www.nature.com/doifinder/10.1038/nphoton.2015.57}, author = {Douglas, J. S. and Habibian, H. and Hung, C.-L. and Alexey V. Gorshkov and Kimble, H. J. and Chang, D. E.} } @article {1839, title = {Beyond the spin model approximation for Ramsey spectroscopy}, journal = {Phys. Rev. Lett.}, volume = {112}, year = {2014}, pages = {123001}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.123001}, author = {A P Koller and M Beverland and Alexey V. Gorshkov and A M Rey} } @article {1177, title = {Kitaev chains with long-range pairing}, journal = {Physical Review Letters}, volume = {113}, year = {2014}, month = {2014/10/9}, abstract = { We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($\alpha > 1$) or purely algebraically ($\alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $\alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions. }, doi = {10.1103/PhysRevLett.113.156402}, url = {http://arxiv.org/abs/1405.5440v2}, author = {Davide Vodola and Luca Lepori and Elisa Ercolessi and Alexey V. Gorshkov and Guido Pupillo} } @article {1202, title = {Non-local propagation of correlations in long-range interacting quantum systems }, journal = {Nature}, volume = {511}, year = {2014}, month = {2014/7/9}, pages = {198 - 201}, abstract = { The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated and how difficult the system will be to describe numerically. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective light cone. However, little is known about the propagation speed in systems with long-range interactions, since the best long-range bound is too loose to give the correct light-cone shape for any known spin model and since analytic solutions rarely exist. In this work, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Ising- or XY-model Hamiltonian. For several different interaction ranges, we extract the shape of the light cone and measure the velocity with which correlations propagate through the system. In many cases we find increasing propagation velocities, which violate the Lieb-Robinson prediction, and in one instance cannot be explained by any existing theory. Our results demonstrate that even modestly-sized quantum simulators are well-poised for studying complicated many-body systems that are intractable to classical computation. }, doi = {10.1038/nature13450}, url = {http://arxiv.org/abs/1401.5088v1}, author = {Philip Richerme and Zhe-Xuan Gong and Aaron Lee and Crystal Senko and Jacob Smith and Michael Foss-Feig and Spyridon Michalakis and Alexey V. Gorshkov and Christopher Monroe} } @article {1176, title = {Persistence of locality in systems with power-law interactions}, journal = {Physical Review Letters}, volume = {113}, year = {2014}, month = {2014/7/16}, abstract = { Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, \emph{qualitatively reproduce} the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems. }, doi = {10.1103/PhysRevLett.113.030602}, url = {http://arxiv.org/abs/1401.6174v2}, author = {Zhe-Xuan Gong and Michael Foss-Feig and Spyridon Michalakis and Alexey V. Gorshkov} } @article {1840, title = {Probing many-body interactions in an optical lattice clock}, journal = {Ann. Phys.}, volume = {340}, year = {2014}, pages = {311}, url = {http://www.sciencedirect.com/science/article/pii/S0003491613002546}, author = {Rey, A M and Alexey V. Gorshkov and Kraus, C V and Martin, M J and Bishof, M and Swallows, M D and Zhang, X and Benko, C and Ye, J and Lemke, N D and Ludlow, A D} } @article {1506, title = {Scattering resonances and bound states for strongly interacting Rydberg polaritons }, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/11/3}, abstract = { We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. }, doi = {10.1103/PhysRevA.90.053804}, url = {http://arxiv.org/abs/1402.7333v1}, author = {P. Bienias and S. Choi and O. Firstenberg and Mohammad F. Maghrebi and Michael Gullans and M. D. Lukin and Alexey V. Gorshkov and H. P. B{\"u}chler} } @article {1841, title = {Attractive Photons in a Quantum Nonlinear Medium}, journal = {Nature (London)}, volume = {502}, year = {2013}, pages = {71}, url = {http://dx.doi.org/10.1038/nature12512}, author = {Ofer Firstenberg and Thibault Peyronel and Qi-Yu Liang and Alexey V. Gorshkov and Mikhail D. Lukin and Vladan Vuletic} } @article {1186, title = {Controllable quantum spin glasses with magnetic impurities embedded in quantum solids }, journal = {Physical Review B}, volume = {88}, year = {2013}, month = {2013/7/24}, abstract = { Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo$_x$Y$_{1-x}$F$_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases. }, doi = {10.1103/PhysRevB.88.014426}, url = {http://arxiv.org/abs/1307.1130v1}, author = {Mikhail Lemeshko and Norman Y. Yao and Alexey V. Gorshkov and Hendrik Weimer and Steven D. Bennett and Takamasa Momose and Sarang Gopalakrishnan} } @article {1161, title = {Dissipative Many-body Quantum Optics in Rydberg Media}, journal = {Physical Review Letters}, volume = {110}, year = {2013}, month = {2013/4/9}, abstract = { We develop a theoretical framework for the dissipative propagation of quantized light in interacting optical media under conditions of electromagnetically induced transparency (EIT). The theory allows us to determine the peculiar spatiotemporal structure of the output of two complementary Rydberg-EIT-based light-processing modules: the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. In addition to being crucial for applications of these and other optical quantum devices, the theory opens the door to the study of exotic dissipative many-body dynamics of strongly interacting photons in nonlinear nonlocal media. }, doi = {10.1103/PhysRevLett.110.153601}, url = {http://arxiv.org/abs/1211.7060v1}, author = {Alexey V. Gorshkov and Rejish Nath and Thomas Pohl} } @article {1175, title = {Kitaev honeycomb and other exotic spin models with polar molecules}, journal = {Molecular Physics}, volume = {111}, year = {2013}, month = {2013/01/01}, pages = {1908 - 1916}, abstract = { We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry. }, doi = {10.1080/00268976.2013.800604}, url = {http://arxiv.org/abs/1301.5636v1}, author = {Alexey V. Gorshkov and Kaden R. A. Hazzard and Ana Maria Rey} } @article {1199, title = {Quantum Logic between Remote Quantum Registers}, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/2/6}, abstract = { We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder. }, doi = {10.1103/PhysRevA.87.022306}, url = {http://arxiv.org/abs/1206.0014v1}, author = {Norman Y. Yao and Zhe-Xuan Gong and Chris R. Laumann and Steven D. Bennett and L. -M. Duan and Mikhail D. Lukin and Liang Jiang and Alexey V. Gorshkov} } @article {1842, title = {A quantum many-body spin system in an optical lattice clock}, journal = {Science}, volume = {341}, year = {2013}, pages = {632}, url = {http://www.sciencemag.org/content/341/6146/632.abstract}, author = {M J Martin and Bishof, M and Swallows, M D and X Zhang and C Benko and J von-Stecher and Alexey V. Gorshkov and Rey, A M and Jun Ye} } @article {1843, title = {Quantum Nonlinear Optics: Strongly Interacting Photons}, journal = {Opt. Photonics News}, volume = {24}, year = {2013}, pages = {48}, url = {http://www.osa-opn.org/abstract.cfm?URI=opn-24-12-48}, author = {Firstenberg, O and Lukin, M D and Peyronel, T and Liang, Q -Y and Vuletic, V and Alexey V. Gorshkov and Hofferberth, S and Pohl, T} } @article {1185, title = {Realizing Fractional Chern Insulators with Dipolar Spins}, journal = {Physical Review Letters}, volume = {110}, year = {2013}, month = {2013/4/29}, abstract = { Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultra-cold polar molecules trapped in a deep optical lattice. While the orbital motion of the molecules is pinned, at finite densities, the rotational excitations form a fractional Chern insulator. We present a detailed experimental blueprint for KRb, and demonstrate that the energetics are consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications. }, doi = {10.1103/PhysRevLett.110.185302}, url = {http://arxiv.org/abs/1212.4839v1}, author = {Norman Y. Yao and Alexey V. Gorshkov and Chris R. Laumann and Andreas M. L{\"a}uchli and Jun Ye and Mikhail D. Lukin} } @article {1184, title = {Topological phases in ultracold polar-molecule quantum magnets}, journal = {Physical Review B}, volume = {87}, year = {2013}, month = {2013/2/26}, abstract = { We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S >= 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases -- previously studied only in the nearest-neighbor case -- survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed. }, doi = {10.1103/PhysRevB.87.081106}, url = {http://arxiv.org/abs/1210.5518v2}, author = {Salvatore R. Manmana and E. M. Stoudenmire and Kaden R. A. Hazzard and Ana Maria Rey and Alexey V. Gorshkov} } @article {1197, title = {Topologically Protected Quantum State Transfer in a Chiral Spin Liquid}, journal = {Nature Communications}, volume = {4}, year = {2013}, month = {2013/3/12}, pages = {1585}, abstract = { Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed. }, doi = {10.1038/ncomms2531}, url = {http://arxiv.org/abs/1110.3788v1}, author = {Norman Y. Yao and Chris R. Laumann and Alexey V. Gorshkov and Hendrik Weimer and Liang Jiang and J. Ignacio Cirac and Peter Zoller and Mikhail D. Lukin} } @article {1844, title = {Cavity QED with atomic mirrors}, journal = {New J. Phys.}, volume = {14}, year = {2012}, pages = {063003}, url = {http://iopscience.iop.org/1367-2630/14/6/063003/}, author = {D E Chang and Jiang, L and Alexey V. Gorshkov and H J Kimble} } @article {1845, title = {Quantum nonlinear optics with single photons enabled by strongly interacting atoms}, journal = {Nature (London)}, volume = {488}, year = {2012}, pages = {57}, url = {http://www.nature.com/nature/journal/v488/n7409/full/nature11361.html}, author = {Peyronel, Thibault and Firstenberg, Ofer and Liang, Qi-Yu and Hofferberth, Sebastian and Alexey V. Gorshkov and Pohl, Thomas and Lukin, Mikhail D. and Vuletic, Vladan} } @article {1200, title = {Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor }, journal = {Nature Communications}, volume = {3}, year = {2012}, month = {2012/4/24}, pages = {800}, abstract = { The realization of a scalable quantum information processor has emerged over the past decade as one of the central challenges at the interface of fundamental science and engineering. Much progress has been made towards this goal. Indeed, quantum operations have been demonstrated on several trapped ion qubits, and other solid-state systems are approaching similar levels of control. Extending these techniques to achieve fault-tolerant operations in larger systems with more qubits remains an extremely challenging goal, in part, due to the substantial technical complexity of current implementations. Here, we propose and analyze an architecture for a scalable, solid-state quantum information processor capable of operating at or near room temperature. The architecture is applicable to realistic conditions, which include disorder and relevant decoherence mechanisms, and includes a hierarchy of control at successive length scales. Our approach is based upon recent experimental advances involving Nitrogen-Vacancy color centers in diamond and will provide fundamental insights into the physics of non-equilibrium many-body quantum systems. Additionally, the proposed architecture may greatly alleviate the stringent constraints, currently limiting the realization of scalable quantum processors. }, doi = {10.1038/ncomms1788}, url = {http://arxiv.org/abs/1012.2864v1}, author = {Norman Y. Yao and Liang Jiang and Alexey V. Gorshkov and Peter C. Maurer and Geza Giedke and J. Ignacio Cirac and Mikhail D. Lukin} } @article {1201, title = {Topological Flat Bands from Dipolar Spin Systems}, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/12/26}, abstract = { We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultra-cold polar molecules or spins in the solid state is considered. }, doi = {10.1103/PhysRevLett.109.266804}, url = {http://arxiv.org/abs/1207.4479v3}, author = {Norman Y. Yao and Chris R. Laumann and Alexey V. Gorshkov and Steven D. Bennett and Eugene Demler and Peter Zoller and Mikhail D. Lukin} } @article {1171, title = {d-Wave Superfluidity in Optical Lattices of Ultracold Polar Molecules}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/12/29}, abstract = { Recent work on ultracold polar molecules, governed by a generalization of the t-J Hamiltonian, suggests that molecules may be better suited than atoms for studying d-wave superfluidity due to stronger interactions and larger tunability of the system. We compute the phase diagram for polar molecules in a checkerboard lattice consisting of weakly coupled square plaquettes. In the simplest experimentally realizable case where there is only tunneling and an XX-type spin-spin interaction, we identify the parameter regime where d-wave superfluidity occurs. We also find that the inclusion of a density-density interaction destroys the superfluid phase and that the inclusion of a spin-density or an Ising-type spin-spin interaction can enhance the superfluid phase. We also propose schemes for experimentally realizing the perturbative calculations exhibiting enhanced d-wave superfluidity. }, doi = {10.1103/PhysRevA.84.063639}, url = {http://arxiv.org/abs/1110.5330v2}, author = {Kevin A. Kuns and Ana Maria Rey and Alexey V. Gorshkov} } @article {1165, title = {Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing }, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/6/20}, abstract = { We study the modification of a traditional electromagnetically induced transparency (EIT) stored light technique that includes both EIT and four-wave mixing (FWM) in an ensemble of hot Rb atoms. The standard treatment of light storage involves the coherent and reversible mapping of one photonic mode onto a collective spin coherence. It has been shown that unwanted, competing processes such as four-wave mixing are enhanced by EIT and can significantly modify the signal optical pulse propagation. We present theoretical and experimental evidence to indicate that while a Stokes field is indeed detected upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics of the fields and the impact of FWM on the spin wave. }, doi = {10.1103/PhysRevA.83.063823}, url = {http://arxiv.org/abs/1103.2131v1}, author = {Nathaniel B. Phillips and Alexey V. Gorshkov and Irina Novikova} } @article {1174, title = {Photon-Photon Interactions via Rydberg Blockade}, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/9/22}, abstract = { We develop the theory of light propagation under the conditions of electromagnetically induced transparency (EIT) in systems involving strongly interacting Rydberg states. Taking into account the quantum nature and the spatial propagation of light, we analyze interactions involving few-photon pulses. We demonstrate that this system can be used for the generation of nonclassical states of light including trains of single photons with an avoided volume between them, for implementing photon-photon quantum gates, as well as for studying many-body phenomena with strongly correlated photons. }, doi = {10.1103/PhysRevLett.107.133602}, url = {http://arxiv.org/abs/1103.3700v1}, author = {Alexey V. Gorshkov and Johannes Otterbach and Michael Fleischhauer and Thomas Pohl and Mikhail D. Lukin} } @article {1181, title = {Quantum Magnetism with Polar Alkali Dimers}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/9/15}, abstract = { We show that dipolar interactions between ultracold polar alkali dimers in optical lattices can be used to realize a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. The model features long-range spin-spin interactions J_z and J_perp of XXZ type, long-range density-density interaction V, and long-range density-spin interaction W, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling t. The "spin" is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed matter systems. Realistic experimental imperfections are discussed. }, doi = {10.1103/PhysRevA.84.033619}, url = {http://arxiv.org/abs/1106.1655v1}, author = {Alexey V. Gorshkov and Salvatore R. Manmana and Gang Chen and Eugene Demler and Mikhail D. Lukin and Ana Maria Rey} } @article {1846, title = {Quantum magnetism with polar alkali-metal dimers}, journal = {Phys. Rev. A}, volume = {84}, year = {2011}, pages = {033619}, url = {http://link.aps.org/abstract/PRA/v84/e033619/}, author = {Alexey V. Gorshkov and Manmana, S R and Chen, G and Demler, E and Lukin, M D and Rey, A M} } @article {1183, title = {Resolved atomic interaction sidebands in an optical clock transition}, journal = {Physical Review Letters}, volume = {106}, year = {2011}, month = {2011/6/22}, abstract = { We report the observation of resolved atomic interaction sidebands (ISB) in the ${}^{87}$Sr optical clock transition when atoms at microkelvin temperatures are confined in a two-dimensional (2D) optical lattice. The ISB are a manifestation of the strong interactions that occur between atoms confined in a quasi-one-dimensional geometry and disappear when the confinement is relaxed along one dimension. The emergence of ISB is linked to the recently observed suppression of collisional frequency shifts in [1]. At the current temperatures, the ISB can be resolved but are broad. At lower temperatures, ISB are predicted to be substantially narrower and usable as powerful spectroscopic tools in strongly interacting alkaline-earth gases. }, doi = {10.1103/PhysRevLett.106.250801}, url = {http://arxiv.org/abs/1102.1016v2}, author = {Michael Bishof and Yige Lin and Matthew D. Swallows and Alexey V. Gorshkov and Jun Ye and Ana Maria Rey} } @article {1196, title = {Robust Quantum State Transfer in Random Unpolarized Spin Chains}, journal = {Physical Review Letters}, volume = {106}, year = {2011}, month = {2011/1/27}, abstract = { We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed. }, doi = {10.1103/PhysRevLett.106.040505}, url = {http://arxiv.org/abs/1011.2762v2}, author = {Norman Y. Yao and Liang Jiang and Alexey V. Gorshkov and Zhe-Xuan Gong and Alex Zhai and L. -M. Duan and Mikhail D. Lukin} } @article {1172, title = {Spectroscopy of dipolar fermions in 2D pancakes and 3D lattices}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/9/6}, abstract = { Motivated by ongoing measurements at JILA, we calculate the recoil-free spectra of dipolar interacting fermions, for example ultracold heteronuclear molecules, in a one-dimensional lattice of two-dimensional pancakes, spectroscopically probing transitions between different internal (e.g., rotational) states. We additionally incorporate p-wave interactions and losses, which are important for reactive molecules such as KRb. Moreover, we consider other sources of spectral broadening: interaction-induced quasiparticle lifetimes and the different polarizabilities of the different rotational states used for the spectroscopy. Although our main focus is molecules, some of the calculations are also useful for optical lattice atomic clocks. For example, understanding the p-wave shifts between identical fermions and small dipolar interactions coming from the excited clock state are necessary to reach future precision goals. Finally, we consider the spectra in a deep 3D lattice and show how they give a great deal of information about static correlation functions, including \textit{all} the moments of the density correlations between nearby sites. The range of correlations measurable depends on spectroscopic resolution and the dipole moment. }, doi = {10.1103/PhysRevA.84.033608}, url = {http://arxiv.org/abs/1106.1718v1}, author = {Kaden R. A. Hazzard and Alexey V. Gorshkov and Ana Maria Rey} } @article {1847, title = {Spectroscopy of dipolar fermions in layered two-dimensional and three-dimensional lattices}, journal = {Phys. Rev. A}, volume = {84}, year = {2011}, pages = {033608}, url = {http://link.aps.org/abstract/PRA/v84/e033608/}, author = {Hazzard, K R A and Alexey V. Gorshkov and Rey, A M} } @article {1198, title = {Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules }, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/9/8}, abstract = { By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. In addition to XXZ spin exchange, the model features density-density interactions and novel density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method (DMRG) to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally. }, doi = {10.1103/PhysRevLett.107.115301}, url = {http://arxiv.org/abs/1106.1644v1}, author = {Alexey V. Gorshkov and Salvatore R. Manmana and Gang Chen and Jun Ye and Eugene Demler and Mikhail D. Lukin and Ana Maria Rey} } @article {1848, title = {Far-field optical imaging and manipulation of individual spins with nanoscale resolution}, journal = {Nature Phys.}, volume = {6}, year = {2010}, pages = {912}, url = {http://www.nature.com/nphys/journal/v6/n11/abs/nphys1774.html}, author = {Maurer, P C and Maze, J R and Stanwix, P L and Jiang, L and Alexey V. Gorshkov and Zibrov, A A and Harke, B and Hodges, J S and Zibrov, A S and Yacoby, A and Twitchen, D and Hell, S W and Walsworth, R L and Lukin, M D} } @article {1182, title = {Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection }, journal = {Physical Review A}, volume = {81}, year = {2010}, month = {2010/2/12}, abstract = { Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, the entanglement rates and scalability of current approaches are limited by relatively low retrieval and single-photon detector efficiencies. We propose a scheme, which makes use of fluorescent detection of stored excitations to significantly increase the efficiency of connection and hence the rate. Practical performance and possible experimental realizations of the new protocol are discussed. }, doi = {10.1103/PhysRevA.81.020303}, url = {http://arxiv.org/abs/0907.3839v2}, author = {Jonatan B. Brask and Liang Jiang and Alexey V. Gorshkov and Vladan Vuletic and Anders S. Sorensen and Mikhail D. Lukin} } @article {1170, title = {Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain }, journal = {Physical Review Letters}, volume = {105}, year = {2010}, month = {2010/8/5}, abstract = { We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the pi phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed. }, doi = {10.1103/PhysRevLett.105.060502}, url = {http://arxiv.org/abs/1001.0968v3}, author = {Alexey V. Gorshkov and Johannes Otterbach and Eugene Demler and Michael Fleischhauer and Mikhail D. Lukin} } @article {1849, title = {Thesis: Novel Systems and Methods for Quantum Communication, Quantum Computation, and Quantum Simulation}, journal = {Harvard University Physics Department}, volume = {Ph.D. Thesis}, year = {2010}, author = {Alexey V. Gorshkov} } @article {1850, title = {Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms}, journal = {Nature Phys.}, volume = {6}, year = {2010}, pages = {289}, url = {http://www.nature.com/nphys/journal/v6/n4/abs/nphys1535.html}, author = {Alexey V. Gorshkov and Hermele, M and Gurarie, V and Xu, C and Julienne, P S and Ye, J and Zoller, P and Demler, E and Lukin, M D and Rey, A M} } @article {1193, title = {Alkaline-Earth-Metal Atoms as Few-Qubit Quantum Registers}, journal = {Physical Review Letters}, volume = {102}, year = {2009}, month = {2009/3/18}, abstract = { We propose and analyze a novel approach to quantum information processing, in which multiple qubits can be encoded and manipulated using electronic and nuclear degrees of freedom associated with individual alkaline-earth atoms trapped in an optical lattice. Specifically, we describe how the qubits within each register can be individually manipulated and measured with sub-wavelength optical resolution. We also show how such few-qubit registers can be coupled to each other in optical superlattices via conditional tunneling to form a scalable quantum network. Finally, potential applications to quantum computation and precision measurements are discussed. }, doi = {10.1103/PhysRevLett.102.110503}, url = {http://arxiv.org/abs/0812.3660v2}, author = {Alexey V. Gorshkov and Ana Maria Rey and Andrew J. Daley and Martin M. Boyd and Jun Ye and Peter Zoller and Mikhail D. Lukin} } @article {1851, title = {Many-Body Treatment of the Collisional Frequency Shift in Fermionic Atoms}, journal = {Phys. Rev. Lett.}, volume = {103}, year = {2009}, pages = {260402}, url = {http://link.aps.org/abstract/PRL/v103/e260402/}, author = {Rey, A M and Alexey V. Gorshkov and Rubbo, C} } @article {1195, title = {Realization of Coherent Optically Dense Media via Buffer-Gas Cooling}, journal = {Physical Review A}, volume = {79}, year = {2009}, month = {2009/1/6}, abstract = { We demonstrate that buffer-gas cooling combined with laser ablation can be used to create coherent optical media with high optical depth and low Doppler broadening that offers metastable states with low collisional and motional decoherence. Demonstration of this generic technique opens pathways to coherent optics with a large variety of atoms and molecules. We use helium buffer gas to cool 87Rb atoms to below 7 K and slow atom diffusion to the walls. Electromagnetically induced transparency (EIT) in this medium allows for 50\% transmission in a medium with initial OD >70 and for slow pulse propagation with large delay-bandwidth products. In the high-OD regime, we observe high-contrast spectrum oscillations due to efficient four-wave mixing. }, doi = {10.1103/PhysRevA.79.013806}, url = {http://arxiv.org/abs/0805.1416v2}, author = {Tao Hong and Alexey V. Gorshkov and David Patterson and Alexander S. Zibrov and John M. Doyle and Mikhail D. Lukin and Mara G. Prentiss} } @article {1852, title = {Slow light propagation and amplification via electromagnetically induced transparency and four-wave mixing in an optically dense atomic vapor}, journal = {J. Mod. Opt.}, volume = {56}, year = {2009}, pages = {1916}, url = {http://www.informaworld.com/smpp/content~db=all~content=a913545405}, author = {Phillips, N B and Alexey V. Gorshkov and Novikova, I} } @article {1192, title = {Anyonic interferometry and protected memories in atomic spin lattices}, journal = {Nature Physics}, volume = {4}, year = {2008}, month = {2008/4/20}, pages = {482 - 488}, abstract = { Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations. }, doi = {10.1038/nphys943}, url = {http://arxiv.org/abs/0711.1365v1}, author = {Liang Jiang and Gavin K. Brennen and Alexey V. Gorshkov and Klemens Hammerer and Mohammad Hafezi and Eugene Demler and Mikhail D. Lukin and Peter Zoller} } @article {1173, title = {Coherent Quantum Optical Control with Subwavelength Resolution}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/3/7}, abstract = { We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed. }, doi = {10.1103/PhysRevLett.100.093005}, url = {http://arxiv.org/abs/0706.3879v2}, author = {Alexey V. Gorshkov and Liang Jiang and Markus Greiner and Peter Zoller and Mikhail D. Lukin} } @article {1164, title = {Optimal light storage in atomic vapor}, journal = {Physical Review A}, volume = {78}, year = {2008}, month = {2008/8/1}, abstract = { We study procedures for the optimization of efficiency of light storage and retrieval based on the dynamic form of electromagnetically induced transparency (EIT) in warm Rb vapor. We present a detailed analysis of two recently demonstrated optimization protocols: a time-reversal-based iteration procedure, which finds the optimal input signal pulse shape for any given control field, and a procedure based on the calculation of an optimal control field for any given signal pulse shape. We verify that the two procedures are consistent with each other, and that they both independently achieve the maximum memory efficiency for any given optical depth. We observe good agreement with theoretical predictions for moderate optical depths (<25), while at higher optical depths the experimental efficiency falls below the theoretically predicted values. We identify possible effects responsible for this reduction in memory efficiency. }, doi = {10.1103/PhysRevA.78.023801}, url = {http://arxiv.org/abs/0805.3348v1}, author = {Nathaniel B. Phillips and Alexey V. Gorshkov and Irina Novikova} } @article {1163, title = {Optimal light storage with full pulse shape control}, journal = {Physical Review A}, volume = {78}, year = {2008}, month = {2008/8/20}, abstract = { We experimentally demonstrate optimal storage and retrieval of light pulses of arbitrary shape in atomic ensembles. By shaping auxiliary control pulses, we attain efficiencies approaching the fundamental limit and achieve precise retrieval into any predetermined temporal profile. Our techniques, demonstrated in warm Rb vapor, are applicable to a wide range of systems and protocols. As an example, we present their potential application to the creation of optical time-bin qubits and to controlled partial retrieval. }, doi = {10.1103/PhysRevA.78.021802}, url = {http://arxiv.org/abs/0805.1927v1}, author = {Irina Novikova and Nathaniel B. Phillips and Alexey V. Gorshkov} } @article {1853, title = {Optimal light storage with full pulse-shape control}, journal = {Phys. Rev. A}, volume = {78}, year = {2008}, pages = {021802(R)}, url = {http://link.aps.org/abstract/PRA/v78/e021802/}, author = {Novikova, I and Phillips, N B and Alexey V. Gorshkov} } @article {1854, title = {Optimizing Slow and Stored Light for Multidisciplinary Applications}, journal = {Proc. SPIE}, volume = {6904}, year = {2008}, pages = {69040C}, url = {http://spie.org/x648.xml?product_id=772216\&Search_Origin=QuickSearch\&Search_Results_URL=http://spie.org/x1636.xml\&Alternate_URL=http://spie.org/x18509.xml\&Alternate_URL_Name=timeframe\&Alternate_URL_Value=Exhibitors\&UseJavascript=1\&Please_Wait_URL=http://s}, author = {Klein, M and Xiao, Y and Alexey V. Gorshkov and M Hohensee and C D Leung and M R Browning and Phillips, D F and Novikova, I and Walsworth, R L} } @article {1169, title = {Photon storage in Lambda-type optically dense atomic media. IV. Optimal control using gradient ascent }, journal = {Physical Review A}, volume = {77}, year = {2008}, month = {2008/4/4}, abstract = { We use the numerical gradient ascent method from optimal control theory to extend efficient photon storage in Lambda-type media to previously inaccessible regimes and to provide simple intuitive explanations for our optimization techniques. In particular, by using gradient ascent to shape classical control pulses used to mediate photon storage, we open up the possibility of high efficiency photon storage in the non-adiabatic limit, in which analytical solutions to the equations of motion do not exist. This control shaping technique enables an order-of-magnitude increase in the bandwidth of the memory. We also demonstrate that the often discussed connection between time reversal and optimality in photon storage follows naturally from gradient ascent. Finally, we discuss the optimization of controlled reversible inhomogeneous broadening. }, doi = {10.1103/PhysRevA.77.043806}, url = {http://arxiv.org/abs/0710.2698v2}, author = {Alexey V. Gorshkov and Tommaso Calarco and Mikhail D. Lukin and Anders S. Sorensen} } @article {1855, title = {Suppression of Inelastic Collisions Between Polar Molecules With a Repulsive Shield}, journal = {Phys. Rev. Lett.}, volume = {101}, year = {2008}, pages = {073201}, url = {http://link.aps.org/abstract/PRL/v101/e073201/}, author = {Alexey V. Gorshkov and Rabl, P and Pupillo, G and Micheli, A and Zoller, P and Lukin, M D and B{\"u}chler, H P} } @article {1856, title = {Multi-photon Entanglement: From Quantum Curiosity to Quantum Computing and Quantum Repeaters}, journal = {Proc. SPIE}, volume = {6664}, year = {2007}, pages = {66640G}, url = {http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PSISDG00666400000166640G000001\&idtype=cvips\&gifs=Yes\&bproc=volrange\&scode=6600\%20-\%206699}, author = {Walther, P and Eisaman, M D and Nemiroski, A and Alexey V. Gorshkov and Zibrov, A S and Zeilinger, A and Lukin, M D} } @article {1203, title = {Optimal control of light pulse storage and retrieval}, journal = {Physical Review Letters}, volume = {98}, year = {2007}, month = {2007/6/15}, abstract = { We demonstrate experimentally a procedure to obtain the maximum efficiency for the storage and retrieval of light pulses in atomic media. The procedure uses time reversal to obtain optimal input signal pulse-shapes. Experimental results in warm Rb vapor are in good agreement with theoretical predictions and demonstrate a substantial improvement of efficiency. This optimization procedure is applicable to a wide range of systems. }, doi = {10.1103/PhysRevLett.98.243602}, url = {http://arxiv.org/abs/quant-ph/0702266v1}, author = {Irina Novikova and Alexey V. Gorshkov and David F. Phillips and Anders S. Sorensen and Mikhail D. Lukin and Ronald L. Walsworth} } @article {1857, title = {Optimization of slow and stored light in atomic vapor}, journal = {Proc. SPIE}, volume = {6482}, year = {2007}, pages = {64820M}, url = {http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PSISDG00648200000164820M000001\&idtype=cvips\&gifs=Yes\&bproc=volrange\&scode=6400\%20-\%206499}, author = {Novikova, I and Alexey V. Gorshkov and Phillips, D F and Xiao, Y and Klein, M and Walsworth, R L} } @article {1166, title = {Photon storage in Lambda-type optically dense atomic media. I. Cavity model }, journal = {Physical Review A}, volume = {76}, year = {2007}, month = {2007/9/7}, abstract = { In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we perform the same analysis for the cavity model. In particular, we show that the retrieval efficiency is equal to C/(1+C) independent of the retrieval technique, where C is the cooperativity parameter. We also derive the optimal strategy for storage and, in particular, demonstrate that at any detuning one can store, with the optimal efficiency of C/(1+C), any smooth input mode satisfying T C gamma >> 1 and a certain class of resonant input modes satisfying T C gamma ~ 1, where T is the duration of the input mode and 2 gamma is the transition linewidth. In the two subsequent papers of the series, we present the full analysis of the free-space model and discuss the effects of inhomogeneous broadening on photon storage. }, doi = {10.1103/PhysRevA.76.033804}, url = {http://arxiv.org/abs/quant-ph/0612082v2}, author = {Alexey V. Gorshkov and Axel Andre and Mikhail D. Lukin and Anders S. Sorensen} } @article {1167, title = {Photon storage in Lambda-type optically dense atomic media. II. Free-space model }, journal = {Physical Review A}, volume = {76}, year = {2007}, month = {2007/9/7}, abstract = { In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we presented a universal physical picture for describing a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo based techniques. This universal picture produced an optimal control strategy for photon storage and retrieval applicable to all approaches and yielded identical maximum efficiencies for all of them. In the present paper, we present the full details of this analysis as well some of its extensions, including the discussion of the effects of non-degeneracy of the two lower levels of the Lambda system. The analysis in the present paper is based on the intuition obtained from the study of photon storage in the cavity model in the preceding paper [Gorshkov et al., Phys. Rev. A 76, 033804 (2007)]. }, doi = {10.1103/PhysRevA.76.033805}, url = {http://arxiv.org/abs/quant-ph/0612083v2}, author = {Alexey V. Gorshkov and Axel Andre and Mikhail D. Lukin and Anders S. Sorensen} } @article {1168, title = {Photon storage in Lambda-type optically dense atomic media. III. Effects of inhomogeneous broadening }, journal = {Physical Review A}, volume = {76}, year = {2007}, month = {2007/9/7}, abstract = { In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and in the two preceding papers [Gorshkov et al., Phys. Rev. A 76, 033804 (2007); 76, 033805 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in homogeneously broadened Lambda-type atomic media, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we generalize this treatment to include inhomogeneous broadening. In particular, we consider the case of Doppler-broadened atoms and assume that there is a negligible difference between the Doppler shifts of the two optical transitions. In this situation, we show that, at high enough optical depth, all atoms contribute coherently to the storage process as if the medium were homogeneously broadened. We also discuss the effects of inhomogeneous broadening in solid state samples. In this context, we discuss the advantages and limitations of reversing the inhomogeneous broadening during the storage time, as well as suggest a way for achieving high efficiencies with a nonreversible inhomogeneous profile. }, doi = {10.1103/PhysRevA.76.033806}, url = {http://arxiv.org/abs/quant-ph/0612084v2}, author = {Alexey V. Gorshkov and Axel Andre and Mikhail D. Lukin and Anders S. Sorensen} } @article {1194, title = {Signatures of incoherence in a quantum information processor}, year = {2007}, month = {2007/05/24}, abstract = { Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences. The distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. The observation and control of incoherence in small Hilbert spaces is well known. Here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. As expected, it is more difficult to separate incoherence and decoherence over such processes. However, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. This result is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation. }, url = {http://arxiv.org/abs/0705.3666v2}, author = {Michael K. Henry and Alexey V. Gorshkov and Yaakov S. Weinstein and Paola Cappellaro and Joseph Emerson and Nicolas Boulant and Jonathan S. Hodges and Chandrasekhar Ramanathan and Timothy F. Havel and Rudy Martinez and David G. Cory} } @article {1180, title = {Universal Approach to Optimal Photon Storage in Atomic Media}, journal = {Physical Review Letters}, volume = {98}, year = {2007}, month = {2007/3/19}, abstract = { We present a universal physical picture for describing storage and retrieval of photon wave packets in a Lambda-type atomic medium. This physical picture encompasses a variety of different approaches to pulse storage ranging from adiabatic reduction of the photon group velocity and pulse-propagation control via off-resonant Raman fields to photon-echo based techniques. Furthermore, we derive an optimal control strategy for storage and retrieval of a photon wave packet of any given shape. All these approaches, when optimized, yield identical maximum efficiencies, which only depend on the optical depth of the medium. }, doi = {10.1103/PhysRevLett.98.123601}, url = {http://arxiv.org/abs/quant-ph/0604037v3}, author = {Alexey V. Gorshkov and Axel Andre and Michael Fleischhauer and Anders S. Sorensen and Mikhail D. Lukin} }