We use Nielsen'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.

UR - https://arxiv.org/abs/1902.10720 ER - TY - JOUR T1 - Complexity phase diagram for interacting and long-range bosonic Hamiltonians Y1 - 2019 A1 - Nishad Maskara A1 - Abhinav Deshpande A1 - Minh C. Tran A1 - Adam Ehrenberg A1 - Bill Fefferman A1 - Alexey V. Gorshkov AB -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.

UR - https://arxiv.org/abs/1906.04178 ER - TY - JOUR T1 - Confined Dynamics in Long-Range Interacting Quantum Spin Chains JF - Phys. Rev. Lett. Y1 - 2019 A1 - Fangli Liu A1 - Rex Lundgren A1 - Paraj Titum A1 - Guido Pagano A1 - Jiehang Zhang A1 - Christopher Monroe A1 - Alexey V. Gorshkov AB -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.

VL - 122 UR - https://arxiv.org/abs/1810.02365 CP - 150601 U5 - https://doi.org/10.1103/PhysRevLett.122.150601 ER - TY - JOUR T1 - Fluctuation-induced torque on a topological insulator out of thermal equilibrium JF - Phys. Rev. Lett. (in press) Y1 - 2019 A1 - M. F. Maghrebi A1 - Alexey V. Gorshkov A1 - J. D. Sau AB -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.

UR - https://arxiv.org/abs/1811.06080 ER - TY - JOUR T1 - Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks Y1 - 2019 A1 - Kevin Qian A1 - Zachary Eldredge A1 - Wenchao Ge A1 - Guido Pagano A1 - Christopher Monroe A1 - James V. Porto A1 - Alexey V. Gorshkov AB -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.

UR - https://arxiv.org/abs/1901.09042 ER - TY - JOUR T1 - Interacting Qubit-Photon Bound States with Superconducting Circuits JF - Phys. Rev. Y1 - 2019 A1 - Neereja M. Sundaresan A1 - Rex Lundgren A1 - Guanyu Zhu A1 - Alexey V. Gorshkov A1 - Andrew A. Houck AB -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' 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.

VL - X 9 UR - http://arxiv.org/abs/1801.10167 CP - 011021 U5 - https://doi.org/10.1103/PhysRevX.9.011021 ER - TY - JOUR T1 - Interaction-induced transition in the quantum chaotic dynamics of a disordered metal JF - Ann. Phys. Y1 - 2019 A1 - S. V. Syzranov A1 - Alexey V. Gorshkov A1 - V. M. Galitski AB -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.

VL - 405 UR - https://arxiv.org/abs/1709.09296 CP - 1 U5 - https://doi.org/10.1016/j.aop.2019.03.008 ER - TY - JOUR T1 - Locality and digital quantum simulation of power-law interactions JF - Phys. Rev. X 9, 031006 Y1 - 2019 A1 - Minh Cong Tran A1 - Andrew Y. Guo A1 - Yuan Su A1 - James R. Garrison A1 - Zachary Eldredge A1 - Michael Foss-Feig A1 - Andrew M. Childs A1 - Alexey V. Gorshkov AB -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).

VL - 9 UR - https://arxiv.org/abs/1808.05225 CP - 031006 U5 - https://doi.org/10.1103/PhysRevX.9.031006 ER - TY - JOUR T1 - Non-equilibrium fixed points of coupled Ising models Y1 - 2019 A1 - Jeremy T. Young A1 - Alexey V. Gorshkov A1 - Michael Foss-Feig A1 - Mohammad F. Maghrebi AB -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.

UR - https://arxiv.org/abs/1903.02569 ER - TY - JOUR T1 - Opportunities for Nuclear Physics & Quantum Information Science Y1 - 2019 A1 - I. C. Cloët A1 - Matthew R. Dietrich A1 - John Arrington A1 - Alexei Bazavov A1 - Michael Bishof A1 - Adam Freese A1 - Alexey V. Gorshkov A1 - Anna Grassellino A1 - Kawtar Hafidi A1 - Zubin Jacob A1 - Michael McGuigan A1 - Yannick Meurice A1 - Zein-Eddine Meziani A1 - Peter Mueller A1 - Christine Muschik A1 - James Osborn A1 - Matthew Otten A1 - Peter Petreczky A1 - Tomas Polakovic A1 - Alan Poon A1 - Raphael Pooser A1 - Alessandro Roggero A1 - Mark Saffman A1 - Brent VanDevender A1 - Jiehang Zhang A1 - Erez Zohar AB -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.

UR - https://arxiv.org/abs/1903.05453 ER - TY - JOUR T1 - Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator JF - Phys. Rev. Lett Y1 - 2019 A1 - Su-Kuan Chu A1 - Guanyu Zhu A1 - James R. Garrison A1 - Zachary Eldredge A1 - Ana Valdés Curiel A1 - Przemyslaw Bienias A1 - I. B. Spielman A1 - Alexey V. Gorshkov AB -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.

VL - 122 UR - https://arxiv.org/abs/1807.11486 CP - 120502 U5 - https://doi.org/10.1103/PhysRevLett.122.120502 ER - TY - JOUR T1 - Signaling and Scrambling with Strongly Long-Range Interactions Y1 - 2019 A1 - Andrew Y. Guo A1 - Minh C. Tran A1 - Andrew M. Childs A1 - Alexey V. Gorshkov A1 - Zhe-Xuan Gong AB -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.

UR - https://arxiv.org/abs/1906.02662 ER - TY - JOUR T1 - Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics JF - Phys. Rev. Lett Y1 - 2018 A1 - Fangli Liu A1 - James R. Garrison A1 - Dong-Ling Deng A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov AB -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.

VL - 121 UR - https://arxiv.org/abs/1809.02614 CP - 250404 U5 - https://doi.org/10.1103/PhysRevLett.121.250404 ER - TY - JOUR T1 - Coherent optical nano-tweezers for ultra-cold atoms Y1 - 2018 A1 - P. Bienias A1 - S. Subhankar A1 - Y. Wang A1 - T-C Tsui A1 - F. Jendrzejewski A1 - T. Tiecke A1 - G. Juzeliūnas A1 - L. Jiang A1 - S. L. Rolston A1 - J. V. Porto A1 - Alexey V. Gorshkov AB -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.

UR - https://arxiv.org/abs/1808.02487 ER - TY - JOUR T1 - Dark state optical lattice with sub-wavelength spatial structure JF - Phys. Rev. Lett. Y1 - 2018 A1 - Yang Wang A1 - Sarthak Subhankar A1 - Przemyslaw Bienias A1 - Mateusz Lacki A1 - Tsz-Chun Tsui A1 - Mikhail A. Baranov A1 - Alexey V. Gorshkov A1 - Peter Zoller A1 - James V. Porto A1 - Steven L. Rolston AB -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.

VL - 120 U4 - 083601 UR - https://link.aps.org/doi/10.1103/PhysRevLett.120.083601 U5 - 10.1103/PhysRevLett.120.083601 ER - TY - JOUR T1 - Dissipation induced dipole blockade and anti-blockade in driven Rydberg systems JF - Phys. Rev. A Y1 - 2018 A1 - Jeremy T. Young A1 - Thomas Boulier A1 - Eric Magnan A1 - Elizabeth A. Goldschmidt A1 - Ryan M. Wilson A1 - Steven L. Rolston A1 - James V. Porto A1 - Alexey V. Gorshkov AB -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'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'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.

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.

UR - https://arxiv.org/abs/1707.06655 U5 - https://doi.org/10.1103/PhysRevLett.121.043604 ER - TY - JOUR T1 - Distributed Quantum Metrology and the Entangling Power of Linear Networks Y1 - 2018 A1 - Wenchao Ge A1 - Kurt Jacobs A1 - Zachary Eldredge A1 - Alexey V. Gorshkov A1 - Michael Foss-Feig AB -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.

UR - https://arxiv.org/abs/1707.06655 U5 - https://doi.org/10.1103/PhysRevLett.121.043604 ER - TY - JOUR T1 - Dynamical phase transitions in sampling complexity JF - Phys. Rev. Lett. Y1 - 2018 A1 - Abhinav Deshpande A1 - Bill Fefferman A1 - Minh C. Tran A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -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

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

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.

UR - https://arxiv.org/abs/1809.04493 ER - TY - JOUR T1 - Observation of three-photon bound states in a quantum nonlinear medium JF - Science Y1 - 2018 A1 - Qi-Yu Liang A1 - Aditya V. Venkatramani A1 - Sergio H. Cantu A1 - Travis L. Nicholson A1 - Michael J. Gullans A1 - Alexey V. Gorshkov A1 - Jeff D. Thompson A1 - Cheng Chin A1 - Mikhail D. Lukin A1 - Vladan Vuletic AB -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.

VL - 359 U4 - 783-786 UR - http://science.sciencemag.org/content/359/6377/783 CP - 6377 U5 - 10.1126/science.aao7293 ER - TY - JOUR T1 - Optimal and Secure Measurement Protocols for Quantum Sensor Networks Y1 - 2018 A1 - Zachary Eldredge A1 - Michael Foss-Feig A1 - Steven L. Rolston A1 - Alexey V. Gorshkov AB -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.

UR - http://arxiv.org/abs/1607.04646 U5 - https://doi.org/10.1103/PhysRevA.97.042337 ER - TY - JOUR T1 - Optimization of photon storage fidelity in ordered atomic arrays JF - New Journal of Physics Y1 - 2018 A1 - M. T. Manzoni A1 - M. Moreno-Cardoner A1 - A. Asenjo-Garcia A1 - J. V. Porto A1 - Alexey V. Gorshkov A1 - D. E. Chang AB -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.

VL - 20 UR - https://arxiv.org/abs/1710.06312 CP - 083048 U5 - https://doi.org/10.1088/1367-2630/aadb74 ER - TY - JOUR T1 - Photon propagation through dissipative Rydberg media at large input rates Y1 - 2018 A1 - Przemyslaw Bienias A1 - James Douglas A1 - Asaf Paris-Mandoki A1 - Paraj Titum A1 - Ivan Mirgorodskiy A1 - Christoph Tresp A1 - Emil Zeuthen A1 - Michael J. Gullans A1 - Marco Manzoni A1 - Sebastian Hofferberth A1 - Darrick Chang A1 - Alexey V. Gorshkov AB -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.

UR - https://arxiv.org/abs/1807.07586 ER - TY - JOUR T1 - Photon Subtraction by Many-Body Decoherence Y1 - 2018 A1 - Callum R. Murray A1 - Ivan Mirgorodskiy A1 - Christoph Tresp A1 - Christoph Braun A1 - Asaf Paris-Mandoki A1 - Alexey V. Gorshkov A1 - Sebastian Hofferberth A1 - Thomas Pohl AB -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.

UR - https://arxiv.org/abs/1710.10047 U5 - https://doi.org/10.1103/PhysRevLett.120.113601 ER - TY - JOUR T1 - Probing ground-state phase transitions through quench dynamics Y1 - 2018 A1 - Paraj Titum A1 - Joseph T. Iosue A1 - James R. Garrison A1 - Alexey V. Gorshkov A1 - Zhe-Xuan Gong AB -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.

UR - https://arxiv.org/abs/1809.06377 ER - TY - JOUR T1 - Single-photon bound states in atomic ensembles Y1 - 2018 A1 - Yidan Wang A1 - Michael J. Gullans A1 - Antoine Browaeys A1 - J. V. Porto A1 - Darrick E. Chang A1 - Alexey V. Gorshkov AB -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'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.

UR - https://arxiv.org/abs/1809.01147 ER - TY - JOUR T1 - Spectrum estimation of density operators with alkaline-earth atoms Y1 - 2018 A1 - Michael E. Beverland A1 - Jeongwan Haah A1 - Gorjan Alagic A1 - Gretchen K. Campbell A1 - Ana Maria Rey A1 - Alexey V. Gorshkov AB -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.

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.

UR - https://arxiv.org/abs/1808.07876 ER - TY - JOUR T1 - Complexity of sampling as an order parameter Y1 - 2017 A1 - Abhinav Deshpande A1 - Bill Fefferman A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time

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.

VL - 119 U4 - 043602 UR - https://arxiv.org/abs/1608.06068 CP - 4 U5 - 10.1103/PhysRevLett.119.043602 ER - TY - JOUR T1 - Entanglement area laws for long-range interacting systems JF - Physical Review Letters Y1 - 2017 A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Fernando G. S. L. Brandão A1 - Alexey V. Gorshkov AB -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.

VL - 119 U4 - 050501 UR - https://arxiv.org/abs/1702.05368 CP - 5 U5 - 10.1103/PhysRevLett.119.050501 ER - TY - JOUR T1 - Efimov States of Strongly Interacting Photons JF - Physical Review Letters Y1 - 2017 A1 - M. J. Gullans A1 - S. Diehl A1 - S. T. Rittenhouse A1 - B. P. Ruzic A1 - J. P. D'Incao A1 - P. Julienne A1 - Alexey V. Gorshkov A1 - J. M. Taylor AB -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.

VL - 119 U4 - 233601 UR - https://arxiv.org/abs/1709.01955 CP - 23 U5 - 10.1103/PhysRevLett.119.233601 ER - TY - JOUR T1 - Emergent equilibrium in many-body optical bistability JF - Physical Review A Y1 - 2017 A1 - Michael Foss-Feig A1 - Pradeep Niroula A1 - Jeremy T. Young A1 - Mohammad Hafezi A1 - Alexey V. Gorshkov A1 - Ryan M. Wilson A1 - Mohammad F. Maghrebi AB -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.

VL - 95 U4 - 043826 UR - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826 U5 - doi.org/10.1103/PhysRevA.95.043826 ER - TY - JOUR T1 - Exact sampling hardness of Ising spin models JF - Physical Review A Y1 - 2017 A1 - Bill Fefferman A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -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 für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

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.

VL - 95 UR - http://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.045309 U5 - 10.1103/PhysRevB.95.045309 ER - TY - JOUR T1 - Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions JF - Physical Review Letters Y1 - 2017 A1 - Zachary Eldredge A1 - Zhe-Xuan Gong A1 - Ali Hamed Moosavian A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -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

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.

UR - https://arxiv.org/abs/1705.04355 U5 - https://doi.org/10.1103/PhysRevA.96.052334 ER - TY - JOUR T1 - Lieb-Robinson bounds on n-partite connected correlations JF - Physical Review A Y1 - 2017 A1 - Minh Cong Tran A1 - James R. Garrison A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov AB -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

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.

VL - 95 U4 - 042133 UR - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.042133 U5 - doi.org/10.1103/PhysRevA.95.042133 ER - TY - JOUR T1 - Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator JF - Nature Y1 - 2017 A1 - J. Zhang A1 - G. Pagano A1 - P. W. Hess A1 - A. Kyprianidis A1 - P. Becker A1 - H. Kaplan A1 - Alexey V. Gorshkov A1 - Z. -X. Gong A1 - C. Monroe AB -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.

VL - 551 U4 - 601-604 UR - https://www.nature.com/articles/nature24654 U5 - 10.1038/nature24654 ER - TY - JOUR T1 - Out-of-time-order correlators in finite open systems Y1 - 2017 A1 - S. V. Syzranov A1 - Alexey V. Gorshkov A1 - V. Galitski AB -We study out-of-time order correlators (OTOCs) of the form hAˆ(t)Bˆ(0)Cˆ(t)Dˆ(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.

UR - https://arxiv.org/abs/1704.08442 U5 - https://doi.org/10.1103/PhysRevB.97.161114 ER - TY - JOUR T1 - A solvable family of driven-dissipative many-body systems JF - Physical Review Letters Y1 - 2017 A1 - Michael Foss-Feig A1 - Jeremy T. Young A1 - Victor V. Albert A1 - Alexey V. Gorshkov A1 - Mohammad F. Maghrebi AB -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.

VL - 119 UR - https://arxiv.org/abs/1703.04626 CP - 19 U5 - 10.1103/PhysRevLett.119.190402 ER - TY - JOUR T1 - Anomalous broadening in driven dissipative Rydberg systems JF - Physical Review Letters Y1 - 2016 A1 - E. A. Goldschmidt A1 - T. Boulier A1 - R. C. Brown A1 - S. B. Koller A1 - J. T. Young A1 - Alexey V. Gorshkov A1 - S. L. Rolston A1 - J. V. Porto AB - 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. VL - 116 U4 - 113001 UR - http://arxiv.org/abs/1510.08710 CP - 11 U5 - 10.1103/PhysRevLett.116.113001 ER - TY - JOUR T1 - Causality and quantum criticality in long-range lattice models JF - Physical Review B Y1 - 2016 A1 - Mohammad F. Maghrebi A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov VL - 93 U4 - 125128 UR - http://link.aps.org/doi/10.1103/PhysRevB.93.125128 U5 - 10.1103/PhysRevB.93.125128 ER - TY - JOUR T1 - Causality and quantum criticality with long-range interactions JF - Physical Review B Y1 - 2016 A1 - Mohammad F. Maghrebi A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB - 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. VL - 92 U4 - 125128 UR - http://arxiv.org/abs/1508.00906 CP - 12 U5 - 10.1103/PhysRevB.93.125128 ER - TY - JOUR T1 - Collective phases of strongly interacting cavity photons JF - Physical Review A Y1 - 2016 A1 - Ryan M. Wilson A1 - Khan W. Mahmud A1 - Anzi Hu A1 - Alexey V. Gorshkov A1 - Mohammad Hafezi A1 - Michael Foss-Feig AB -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.

VL - 94 U4 - 033801 UR - http://arxiv.org/abs/1601.06857 CP - 3 U5 - http://dx.doi.org/10.1103/PhysRevA.94.033801 ER - TY - JOUR T1 - Effective Field Theory for Rydberg Polaritons JF - Physical Review Letters Y1 - 2016 A1 - Michael Gullans A1 - J. D. Thompson A1 - Y. Wang A1 - Q. -Y. Liang A1 - V. Vuletic A1 - M. D. Lukin A1 - Alexey V. Gorshkov AB -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.

VL - 117 U4 - 113601 UR - http://arxiv.org/abs/1605.05651 CP - 11 U5 - http://dx.doi.org/10.1103/PhysRevLett.117.113601 ER - TY - JOUR T1 - Entanglement and spin-squeezing without infinite-range interactions Y1 - 2016 A1 - Michael Foss-Feig A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov A1 - Charles W. Clark AB -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.

UR - https://arxiv.org/abs/1612.07805 ER - TY - JOUR T1 - Kaleidoscope of quantum phases in a long-range interacting spin-1 chain JF - Physical Review B Y1 - 2016 A1 - Zhe-Xuan Gong A1 - Mohammad F. Maghrebi A1 - Anzi Hu A1 - Michael Foss-Feig A1 - Philip Richerme A1 - Christopher Monroe A1 - Alexey V. Gorshkov AB - 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. VL - 93 U4 - 205115 UR - http://arxiv.org/abs/1510.02108 CP - 20 U5 - http://dx.doi.org/10.1103/PhysRevB.93.205115 ER - TY - JOUR T1 - Many-body decoherence dynamics and optimised operation of a single-photon switch JF - New Journal of Physics Y1 - 2016 A1 - Callum R. Murray A1 - Alexey V. Gorshkov A1 - Thomas Pohl AB -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.

VL - 18 U4 - 092001 UR - http://iopscience.iop.org/article/10.1088/1367-2630/18/9/092001 U5 - 10.1088/1367-2630/18/9/092001 ER - TY - JOUR T1 - Nonequilibrium many-body steady states via Keldysh formalism JF - Physical Review B Y1 - 2016 A1 - Mohammad F. Maghrebi A1 - Alexey V. Gorshkov AB - 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. VL - 93 U4 - 014307 UR - http://arxiv.org/abs/1507.01939 CP - 1 U5 - 10.1103/PhysRevB.93.014307 ER - TY - JOUR T1 - Observation of Prethermalization in Long-Range Interacting Spin Chains Y1 - 2016 A1 - B. Neyenhuis A1 - J. Smith A1 - A. C. Lee A1 - J. Zhang A1 - P. Richerme A1 - P. W. Hess A1 - Z. -X. Gong A1 - Alexey V. Gorshkov A1 - C. Monroe AB -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.

UR - https://arxiv.org/abs/1608.00681 ER - TY - JOUR T1 - Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms JF - Physical Review A Y1 - 2016 A1 - Michael E. Beverland A1 - Gorjan Alagic A1 - Michael J. Martin A1 - Andrew P. Koller A1 - Ana M. Rey A1 - Alexey V. Gorshkov AB -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.

VL - 93 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.051601 CP - 5 U5 - 10.1103/PhysRevA.93.051601 ER - TY - JOUR T1 - Self-organization of atoms coupled to a chiral reservoir JF - Physical Review A Y1 - 2016 A1 - Zachary Eldredge A1 - Pablo Solano A1 - Darrick Chang A1 - Alexey V. Gorshkov AB -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.

VL - 94 U4 - 053855 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.053855 CP - 5 U5 - 10.1103/PhysRevA.94.053855 ER - TY - JOUR T1 - Steady-state superradiance with Rydberg polaritons JF - arXiv:1611.00797 Y1 - 2016 A1 - Zhe-Xuan Gong A1 - Minghui Xu A1 - Michael Foss-Feig A1 - James K. Thompson A1 - Ana Maria Rey A1 - Murray Holland A1 - Alexey V. Gorshkov AB -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

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.

VL - 94 U4 - 063422 UR - http://link.aps.org/doi/10.1103/PhysRevA.94.063422 CP - 6 U5 - 10.1103/PhysRevA.94.063422 ER - TY - JOUR T1 - Topological phases with long-range interactions JF - Physical Review B Y1 - 2016 A1 - Zhe-Xuan Gong A1 - Mohammad F. Maghrebi A1 - Anzi Hu A1 - Michael L. Wall A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB - 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. VL - 93 U4 - 041102 UR - http://arxiv.org/abs/1505.03146 CP - 4 U5 - 10.1103/PhysRevB.93.041102 ER - TY - JOUR T1 - Atom induced cavities and tunable long-range interactions between atoms trapped near photonic crystals JF - Nature Photon. 9, 326 (2015) Y1 - 2015 A1 - J S Douglas A1 - H Habibian A1 - Alexey V. Gorshkov A1 - H J Kimble A1 - D E Chang AB -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.

UR - http://www.nature.com/nphoton/journal/v9/n5/full/nphoton.2015.57.html U5 - doi:10.1038/nphoton.2015.57 ER - TY - JOUR T1 - Bilayer fractional quantum Hall states with ultracold dysprosium JF - Physical Review A Y1 - 2015 A1 - Norman Y. Yao A1 - Steven D. Bennett A1 - Chris R. Laumann A1 - Benjamin L. Lev A1 - Alexey V. Gorshkov AB - 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. VL - 92 U4 - 033609 UR - http://arxiv.org/abs/1505.03099v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.92.033609 ER - TY - JOUR T1 - Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov AB - 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. UR - http://arxiv.org/abs/1510.01325 ER - TY - JOUR T1 - Coulomb bound states of strongly interacting photons JF - Physical Review Letters Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Michael Gullans A1 - P. Bienias A1 - S. Choi A1 - I. Martin A1 - O. Firstenberg A1 - M. D. Lukin A1 - H. P. Büchler A1 - Alexey V. Gorshkov AB - 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. VL - 115 U4 - 123601 UR - http://arxiv.org/abs/1505.03859v1 CP - 12 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.115.123601 ER - TY - JOUR T1 - Fractional Quantum Hall States of Rydberg Polaritons JF - Physical Review A Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Norman Y. Yao A1 - Mohammad Hafezi A1 - Thomas Pohl A1 - Ofer Firstenberg A1 - Alexey V. Gorshkov AB - 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. VL - 91 U4 - 033838 UR - http://arxiv.org/abs/1411.6624v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.91.033838 ER - TY - JOUR T1 - Nearly-linear light cones in long-range interacting quantum systems JF - Physical Review Letters Y1 - 2015 A1 - Michael Foss-Feig A1 - Zhe-Xuan Gong A1 - Charles W. Clark A1 - Alexey V. Gorshkov AB - 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. VL - 114 U4 - 157201 UR - http://arxiv.org/abs/1410.3466v1 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.114.157201 ER - TY - JOUR T1 - Parafermionic zero modes in ultracold bosonic systems JF - Physical Review Letters Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Sriram Ganeshan A1 - David J. Clarke A1 - Alexey V. Gorshkov A1 - Jay D. Sau AB - 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. VL - 115 U4 - 065301 UR - http://arxiv.org/abs/1504.04012v2 CP - 6 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.115.065301 ER - TY - JOUR T1 - Quantum many-body models with cold atoms coupled to photonic crystals JF - Nature Photonics Y1 - 2015 A1 - Douglas, J. S. A1 - Habibian, H. A1 - Hung, C.-L. A1 - Alexey V. Gorshkov A1 - Kimble, H. J. A1 - Chang, D. E. VL - 9 U4 - 326 - 331 UR - http://www.nature.com/doifinder/10.1038/nphoton.2015.57 CP - 5 J1 - Nature Photon U5 - 10.1038/nphoton.2015.57 ER - TY - JOUR T1 - Beyond the spin model approximation for Ramsey spectroscopy JF - Phys. Rev. Lett. Y1 - 2014 A1 - A P Koller A1 - M Beverland A1 - Alexey V. Gorshkov A1 - A M Rey VL - 112 U4 - 123001 UR - http://link.aps.org/doi/10.1103/PhysRevLett.112.123001 ER - TY - JOUR T1 - Kitaev chains with long-range pairing JF - Physical Review Letters Y1 - 2014 A1 - Davide Vodola A1 - Luca Lepori A1 - Elisa Ercolessi A1 - Alexey V. Gorshkov A1 - Guido Pupillo AB - 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. VL - 113 UR - http://arxiv.org/abs/1405.5440v2 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.113.156402 ER - TY - JOUR T1 - Non-local propagation of correlations in long-range interacting quantum systems JF - Nature Y1 - 2014 A1 - Philip Richerme A1 - Zhe-Xuan Gong A1 - Aaron Lee A1 - Crystal Senko A1 - Jacob Smith A1 - Michael Foss-Feig A1 - Spyridon Michalakis A1 - Alexey V. Gorshkov A1 - Christopher Monroe AB - 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. VL - 511 U4 - 198 - 201 UR - http://arxiv.org/abs/1401.5088v1 CP - 7508 J1 - Nature U5 - 10.1038/nature13450 ER - TY - JOUR T1 - Persistence of locality in systems with power-law interactions JF - Physical Review Letters Y1 - 2014 A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Spyridon Michalakis A1 - Alexey V. Gorshkov AB - 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. VL - 113 UR - http://arxiv.org/abs/1401.6174v2 CP - 3 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.113.030602 ER - TY - JOUR T1 - Probing many-body interactions in an optical lattice clock JF - Ann. Phys. Y1 - 2014 A1 - Rey, A M A1 - Alexey V. Gorshkov A1 - Kraus, C V A1 - Martin, M J A1 - Bishof, M A1 - Swallows, M D A1 - Zhang, X A1 - Benko, C A1 - Ye, J A1 - Lemke, N D A1 - Ludlow, A D VL - 340 U4 - 311 UR - http://www.sciencedirect.com/science/article/pii/S0003491613002546 ER - TY - JOUR T1 - Scattering resonances and bound states for strongly interacting Rydberg polaritons JF - Physical Review A Y1 - 2014 A1 - P. Bienias A1 - S. Choi A1 - O. Firstenberg A1 - Mohammad F. Maghrebi A1 - Michael Gullans A1 - M. D. Lukin A1 - Alexey V. Gorshkov A1 - H. P. Büchler AB - 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. VL - 90 UR - http://arxiv.org/abs/1402.7333v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.90.053804 ER - TY - JOUR T1 - Attractive Photons in a Quantum Nonlinear Medium JF - Nature (London) Y1 - 2013 A1 - Ofer Firstenberg A1 - Thibault Peyronel A1 - Qi-Yu Liang A1 - Alexey V. Gorshkov A1 - Mikhail D. Lukin A1 - Vladan Vuletic VL - 502 U4 - 71 UR - http://dx.doi.org/10.1038/nature12512 ER - TY - JOUR T1 - Controllable quantum spin glasses with magnetic impurities embedded in quantum solids JF - Physical Review B Y1 - 2013 A1 - Mikhail Lemeshko A1 - Norman Y. Yao A1 - Alexey V. Gorshkov A1 - Hendrik Weimer A1 - Steven D. Bennett A1 - Takamasa Momose A1 - Sarang Gopalakrishnan AB - 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. VL - 88 UR - http://arxiv.org/abs/1307.1130v1 CP - 1 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.88.014426 ER - TY - JOUR T1 - Dissipative Many-body Quantum Optics in Rydberg Media JF - Physical Review Letters Y1 - 2013 A1 - Alexey V. Gorshkov A1 - Rejish Nath A1 - Thomas Pohl AB - 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. VL - 110 UR - http://arxiv.org/abs/1211.7060v1 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.110.153601 ER - TY - JOUR T1 - Kitaev honeycomb and other exotic spin models with polar molecules JF - Molecular Physics Y1 - 2013 A1 - Alexey V. Gorshkov A1 - Kaden R. A. Hazzard A1 - Ana Maria Rey AB - 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. VL - 111 U4 - 1908 - 1916 UR - http://arxiv.org/abs/1301.5636v1 CP - 12-13 J1 - Molecular Physics U5 - 10.1080/00268976.2013.800604 ER - TY - JOUR T1 - Quantum Logic between Remote Quantum Registers JF - Physical Review A Y1 - 2013 A1 - Norman Y. Yao A1 - Zhe-Xuan Gong A1 - Chris R. Laumann A1 - Steven D. Bennett A1 - L. -M. Duan A1 - Mikhail D. Lukin A1 - Liang Jiang A1 - Alexey V. Gorshkov AB - 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. VL - 87 UR - http://arxiv.org/abs/1206.0014v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.87.022306 ER - TY - JOUR T1 - A quantum many-body spin system in an optical lattice clock JF - Science Y1 - 2013 A1 - M J Martin A1 - Bishof, M A1 - Swallows, M D A1 - X Zhang A1 - C Benko A1 - J von-Stecher A1 - Alexey V. Gorshkov A1 - Rey, A M A1 - Jun Ye VL - 341 U4 - 632 UR - http://www.sciencemag.org/content/341/6146/632.abstract ER - TY - JOUR T1 - Quantum Nonlinear Optics: Strongly Interacting Photons JF - Opt. Photonics News Y1 - 2013 A1 - Firstenberg, O A1 - Lukin, M D A1 - Peyronel, T A1 - Liang, Q -Y A1 - Vuletic, V A1 - Alexey V. Gorshkov A1 - Hofferberth, S A1 - Pohl, T VL - 24 U4 - 48 UR - http://www.osa-opn.org/abstract.cfm?URI=opn-24-12-48 ER - TY - JOUR T1 - Realizing Fractional Chern Insulators with Dipolar Spins JF - Physical Review Letters Y1 - 2013 A1 - Norman Y. Yao A1 - Alexey V. Gorshkov A1 - Chris R. Laumann A1 - Andreas M. Läuchli A1 - Jun Ye A1 - Mikhail D. Lukin AB - 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. VL - 110 UR - http://arxiv.org/abs/1212.4839v1 CP - 18 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.110.185302 ER - TY - JOUR T1 - Topological phases in ultracold polar-molecule quantum magnets JF - Physical Review B Y1 - 2013 A1 - Salvatore R. Manmana A1 - E. M. Stoudenmire A1 - Kaden R. A. Hazzard A1 - Ana Maria Rey A1 - Alexey V. Gorshkov AB - 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. VL - 87 UR - http://arxiv.org/abs/1210.5518v2 CP - 8 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.87.081106 ER - TY - JOUR T1 - Topologically Protected Quantum State Transfer in a Chiral Spin Liquid JF - Nature Communications Y1 - 2013 A1 - Norman Y. Yao A1 - Chris R. Laumann A1 - Alexey V. Gorshkov A1 - Hendrik Weimer A1 - Liang Jiang A1 - J. Ignacio Cirac A1 - Peter Zoller A1 - Mikhail D. Lukin AB - 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. VL - 4 U4 - 1585 UR - http://arxiv.org/abs/1110.3788v1 J1 - Nat Comms U5 - 10.1038/ncomms2531 ER - TY - JOUR T1 - Cavity QED with atomic mirrors JF - New J. Phys. Y1 - 2012 A1 - D E Chang A1 - Jiang, L A1 - Alexey V. Gorshkov A1 - H J Kimble VL - 14 U4 - 063003 UR - http://iopscience.iop.org/1367-2630/14/6/063003/ ER - TY - JOUR T1 - Quantum nonlinear optics with single photons enabled by strongly interacting atoms JF - Nature (London) Y1 - 2012 A1 - Peyronel, Thibault A1 - Firstenberg, Ofer A1 - Liang, Qi-Yu A1 - Hofferberth, Sebastian A1 - Alexey V. Gorshkov A1 - Pohl, Thomas A1 - Lukin, Mikhail D. A1 - Vuletic, Vladan VL - 488 U4 - 57 UR - http://www.nature.com/nature/journal/v488/n7409/full/nature11361.html ER - TY - JOUR T1 - Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor JF - Nature Communications Y1 - 2012 A1 - Norman Y. Yao A1 - Liang Jiang A1 - Alexey V. Gorshkov A1 - Peter C. Maurer A1 - Geza Giedke A1 - J. Ignacio Cirac A1 - Mikhail D. Lukin AB - 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. VL - 3 U4 - 800 UR - http://arxiv.org/abs/1012.2864v1 J1 - Nat Comms U5 - 10.1038/ncomms1788 ER - TY - JOUR T1 - Topological Flat Bands from Dipolar Spin Systems JF - Physical Review Letters Y1 - 2012 A1 - Norman Y. Yao A1 - Chris R. Laumann A1 - Alexey V. Gorshkov A1 - Steven D. Bennett A1 - Eugene Demler A1 - Peter Zoller A1 - Mikhail D. Lukin AB - 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. VL - 109 UR - http://arxiv.org/abs/1207.4479v3 CP - 26 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.109.266804 ER - TY - JOUR T1 - d-Wave Superfluidity in Optical Lattices of Ultracold Polar Molecules JF - Physical Review A Y1 - 2011 A1 - Kevin A. Kuns A1 - Ana Maria Rey A1 - Alexey V. Gorshkov AB - 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. VL - 84 UR - http://arxiv.org/abs/1110.5330v2 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.84.063639 ER - TY - JOUR T1 - Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing JF - Physical Review A Y1 - 2011 A1 - Nathaniel B. Phillips A1 - Alexey V. Gorshkov A1 - Irina Novikova AB - 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. VL - 83 UR - http://arxiv.org/abs/1103.2131v1 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.83.063823 ER - TY - JOUR T1 - Photon-Photon Interactions via Rydberg Blockade JF - Physical Review Letters Y1 - 2011 A1 - Alexey V. Gorshkov A1 - Johannes Otterbach A1 - Michael Fleischhauer A1 - Thomas Pohl A1 - Mikhail D. Lukin AB - 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. VL - 107 UR - http://arxiv.org/abs/1103.3700v1 CP - 13 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.107.133602 ER - TY - JOUR T1 - Quantum Magnetism with Polar Alkali Dimers JF - Physical Review A Y1 - 2011 A1 - Alexey V. Gorshkov A1 - Salvatore R. Manmana A1 - Gang Chen A1 - Eugene Demler A1 - Mikhail D. Lukin A1 - Ana Maria Rey AB - 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. VL - 84 UR - http://arxiv.org/abs/1106.1655v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.84.033619 ER - TY - JOUR T1 - Quantum magnetism with polar alkali-metal dimers JF - Phys. Rev. A Y1 - 2011 A1 - Alexey V. Gorshkov A1 - Manmana, S R A1 - Chen, G A1 - Demler, E A1 - Lukin, M D A1 - Rey, A M VL - 84 U4 - 033619 UR - http://link.aps.org/abstract/PRA/v84/e033619/ ER - TY - JOUR T1 - Resolved atomic interaction sidebands in an optical clock transition JF - Physical Review Letters Y1 - 2011 A1 - Michael Bishof A1 - Yige Lin A1 - Matthew D. Swallows A1 - Alexey V. Gorshkov A1 - Jun Ye A1 - Ana Maria Rey AB - 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. VL - 106 UR - http://arxiv.org/abs/1102.1016v2 CP - 25 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.106.250801 ER - TY - JOUR T1 - Robust Quantum State Transfer in Random Unpolarized Spin Chains JF - Physical Review Letters Y1 - 2011 A1 - Norman Y. Yao A1 - Liang Jiang A1 - Alexey V. Gorshkov A1 - Zhe-Xuan Gong A1 - Alex Zhai A1 - L. -M. Duan A1 - Mikhail D. Lukin AB - 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. VL - 106 UR - http://arxiv.org/abs/1011.2762v2 CP - 4 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.106.040505 ER - TY - JOUR T1 - Spectroscopy of dipolar fermions in 2D pancakes and 3D lattices JF - Physical Review A Y1 - 2011 A1 - Kaden R. A. Hazzard A1 - Alexey V. Gorshkov A1 - Ana Maria Rey AB - 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. VL - 84 UR - http://arxiv.org/abs/1106.1718v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.84.033608 ER - TY - JOUR T1 - Spectroscopy of dipolar fermions in layered two-dimensional and three-dimensional lattices JF - Phys. Rev. A Y1 - 2011 A1 - Hazzard, K R A A1 - Alexey V. Gorshkov A1 - Rey, A M VL - 84 U4 - 033608 UR - http://link.aps.org/abstract/PRA/v84/e033608/ ER - TY - JOUR T1 - Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules JF - Physical Review Letters Y1 - 2011 A1 - Alexey V. Gorshkov A1 - Salvatore R. Manmana A1 - Gang Chen A1 - Jun Ye A1 - Eugene Demler A1 - Mikhail D. Lukin A1 - Ana Maria Rey AB - 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. VL - 107 UR - http://arxiv.org/abs/1106.1644v1 CP - 11 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.107.115301 ER - TY - JOUR T1 - Far-field optical imaging and manipulation of individual spins with nanoscale resolution JF - Nature Phys. Y1 - 2010 A1 - Maurer, P C A1 - Maze, J R A1 - Stanwix, P L A1 - Jiang, L A1 - Alexey V. Gorshkov A1 - Zibrov, A A A1 - Harke, B A1 - Hodges, J S A1 - Zibrov, A S A1 - Yacoby, A A1 - Twitchen, D A1 - Hell, S W A1 - Walsworth, R L A1 - Lukin, M D VL - 6 U4 - 912 UR - http://www.nature.com/nphys/journal/v6/n11/abs/nphys1774.html ER - TY - JOUR T1 - Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection JF - Physical Review A Y1 - 2010 A1 - Jonatan B. Brask A1 - Liang Jiang A1 - Alexey V. Gorshkov A1 - Vladan Vuletic A1 - Anders S. Sorensen A1 - Mikhail D. Lukin AB - 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. VL - 81 UR - http://arxiv.org/abs/0907.3839v2 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.81.020303 ER - TY - JOUR T1 - Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain JF - Physical Review Letters Y1 - 2010 A1 - Alexey V. Gorshkov A1 - Johannes Otterbach A1 - Eugene Demler A1 - Michael Fleischhauer A1 - Mikhail D. Lukin AB - 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. VL - 105 UR - http://arxiv.org/abs/1001.0968v3 CP - 6 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.105.060502 ER - TY - JOUR T1 - Thesis: Novel Systems and Methods for Quantum Communication, Quantum Computation, and Quantum Simulation JF - Harvard University Physics Department Y1 - 2010 A1 - Alexey V. Gorshkov VL - Ph.D. Thesis ER - TY - JOUR T1 - Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms JF - Nature Phys. Y1 - 2010 A1 - Alexey V. Gorshkov A1 - Hermele, M A1 - Gurarie, V A1 - Xu, C A1 - Julienne, P S A1 - Ye, J A1 - Zoller, P A1 - Demler, E A1 - Lukin, M D A1 - Rey, A M VL - 6 U4 - 289 UR - http://www.nature.com/nphys/journal/v6/n4/abs/nphys1535.html ER - TY - JOUR T1 - Alkaline-Earth-Metal Atoms as Few-Qubit Quantum Registers JF - Physical Review Letters Y1 - 2009 A1 - Alexey V. Gorshkov A1 - Ana Maria Rey A1 - Andrew J. Daley A1 - Martin M. Boyd A1 - Jun Ye A1 - Peter Zoller A1 - Mikhail D. Lukin AB - 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. VL - 102 UR - http://arxiv.org/abs/0812.3660v2 CP - 11 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.102.110503 ER - TY - JOUR T1 - Many-Body Treatment of the Collisional Frequency Shift in Fermionic Atoms JF - Phys. Rev. Lett. Y1 - 2009 A1 - Rey, A M A1 - Alexey V. Gorshkov A1 - Rubbo, C VL - 103 U4 - 260402 UR - http://link.aps.org/abstract/PRL/v103/e260402/ ER - TY - JOUR T1 - Realization of Coherent Optically Dense Media via Buffer-Gas Cooling JF - Physical Review A Y1 - 2009 A1 - Tao Hong A1 - Alexey V. Gorshkov A1 - David Patterson A1 - Alexander S. Zibrov A1 - John M. Doyle A1 - Mikhail D. Lukin A1 - Mara G. Prentiss AB - 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. VL - 79 UR - http://arxiv.org/abs/0805.1416v2 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.79.013806 ER - TY - JOUR T1 - Slow light propagation and amplification via electromagnetically induced transparency and four-wave mixing in an optically dense atomic vapor JF - J. Mod. Opt. Y1 - 2009 A1 - Phillips, N B A1 - Alexey V. Gorshkov A1 - Novikova, I VL - 56 U4 - 1916 UR - http://www.informaworld.com/smpp/content db=all content=a913545405 ER - TY - JOUR T1 - Anyonic interferometry and protected memories in atomic spin lattices JF - Nature Physics Y1 - 2008 A1 - Liang Jiang A1 - Gavin K. Brennen A1 - Alexey V. Gorshkov A1 - Klemens Hammerer A1 - Mohammad Hafezi A1 - Eugene Demler A1 - Mikhail D. Lukin A1 - Peter Zoller AB - 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. VL - 4 U4 - 482 - 488 UR - http://arxiv.org/abs/0711.1365v1 CP - 6 J1 - Nat Phys U5 - 10.1038/nphys943 ER - TY - JOUR T1 - Coherent Quantum Optical Control with Subwavelength Resolution JF - Physical Review Letters Y1 - 2008 A1 - Alexey V. Gorshkov A1 - Liang Jiang A1 - Markus Greiner A1 - Peter Zoller A1 - Mikhail D. Lukin AB - 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. VL - 100 UR - http://arxiv.org/abs/0706.3879v2 CP - 9 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.100.093005 ER - TY - JOUR T1 - Optimal light storage in atomic vapor JF - Physical Review A Y1 - 2008 A1 - Nathaniel B. Phillips A1 - Alexey V. Gorshkov A1 - Irina Novikova AB - 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. VL - 78 UR - http://arxiv.org/abs/0805.3348v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.78.023801 ER - TY - JOUR T1 - Optimal light storage with full pulse shape control JF - Physical Review A Y1 - 2008 A1 - Irina Novikova A1 - Nathaniel B. Phillips A1 - Alexey V. Gorshkov AB - 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. VL - 78 UR - http://arxiv.org/abs/0805.1927v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.78.021802 ER - TY - JOUR T1 - Optimal light storage with full pulse-shape control JF - Phys. Rev. A Y1 - 2008 A1 - Novikova, I A1 - Phillips, N B A1 - Alexey V. Gorshkov VL - 78 U4 - 021802(R) UR - http://link.aps.org/abstract/PRA/v78/e021802/ ER - TY - JOUR T1 - Optimizing Slow and Stored Light for Multidisciplinary Applications JF - Proc. SPIE Y1 - 2008 A1 - Klein, M A1 - Xiao, Y A1 - Alexey V. Gorshkov A1 - M Hohensee A1 - C D Leung A1 - M R Browning A1 - Phillips, D F A1 - Novikova, I A1 - Walsworth, R L VL - 6904 U4 - 69040C UR - 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 ER - TY - JOUR T1 - Photon storage in Lambda-type optically dense atomic media. IV. Optimal control using gradient ascent JF - Physical Review A Y1 - 2008 A1 - Alexey V. Gorshkov A1 - Tommaso Calarco A1 - Mikhail D. Lukin A1 - Anders S. Sorensen AB - 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. VL - 77 UR - http://arxiv.org/abs/0710.2698v2 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.77.043806 ER - TY - JOUR T1 - Suppression of Inelastic Collisions Between Polar Molecules With a Repulsive Shield JF - Phys. Rev. Lett. Y1 - 2008 A1 - Alexey V. Gorshkov A1 - Rabl, P A1 - Pupillo, G A1 - Micheli, A A1 - Zoller, P A1 - Lukin, M D A1 - Büchler, H P VL - 101 U4 - 073201 UR - http://link.aps.org/abstract/PRL/v101/e073201/ ER - TY - JOUR T1 - Multi-photon Entanglement: From Quantum Curiosity to Quantum Computing and Quantum Repeaters JF - Proc. SPIE Y1 - 2007 A1 - Walther, P A1 - Eisaman, M D A1 - Nemiroski, A A1 - Alexey V. Gorshkov A1 - Zibrov, A S A1 - Zeilinger, A A1 - Lukin, M D VL - 6664 U4 - 66640G UR - http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG00666400000166640G000001&idtype=cvips&gifs=Yes&bproc=volrange&scode=6600%20-%206699 ER - TY - JOUR T1 - Optimal control of light pulse storage and retrieval JF - Physical Review Letters Y1 - 2007 A1 - Irina Novikova A1 - Alexey V. Gorshkov A1 - David F. Phillips A1 - Anders S. Sorensen A1 - Mikhail D. Lukin A1 - Ronald L. Walsworth AB - 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. VL - 98 UR - http://arxiv.org/abs/quant-ph/0702266v1 CP - 24 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.98.243602 ER - TY - JOUR T1 - Optimization of slow and stored light in atomic vapor JF - Proc. SPIE Y1 - 2007 A1 - Novikova, I A1 - Alexey V. Gorshkov A1 - Phillips, D F A1 - Xiao, Y A1 - Klein, M A1 - Walsworth, R L VL - 6482 U4 - 64820M UR - http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG00648200000164820M000001&idtype=cvips&gifs=Yes&bproc=volrange&scode=6400%20-%206499 ER - TY - JOUR T1 - Photon storage in Lambda-type optically dense atomic media. I. Cavity model JF - Physical Review A Y1 - 2007 A1 - Alexey V. Gorshkov A1 - Axel Andre A1 - Mikhail D. Lukin A1 - Anders S. Sorensen AB - 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. VL - 76 UR - http://arxiv.org/abs/quant-ph/0612082v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.76.033804 ER - TY - JOUR T1 - Photon storage in Lambda-type optically dense atomic media. II. Free-space model JF - Physical Review A Y1 - 2007 A1 - Alexey V. Gorshkov A1 - Axel Andre A1 - Mikhail D. Lukin A1 - Anders S. Sorensen AB - 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)]. VL - 76 UR - http://arxiv.org/abs/quant-ph/0612083v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.76.033805 ER - TY - JOUR T1 - Photon storage in Lambda-type optically dense atomic media. III. Effects of inhomogeneous broadening JF - Physical Review A Y1 - 2007 A1 - Alexey V. Gorshkov A1 - Axel Andre A1 - Mikhail D. Lukin A1 - Anders S. Sorensen AB - 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. VL - 76 UR - http://arxiv.org/abs/quant-ph/0612084v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.76.033806 ER - TY - JOUR T1 - Signatures of incoherence in a quantum information processor Y1 - 2007 A1 - Michael K. Henry A1 - Alexey V. Gorshkov A1 - Yaakov S. Weinstein A1 - Paola Cappellaro A1 - Joseph Emerson A1 - Nicolas Boulant A1 - Jonathan S. Hodges A1 - Chandrasekhar Ramanathan A1 - Timothy F. Havel A1 - Rudy Martinez A1 - David G. Cory AB - 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. UR - http://arxiv.org/abs/0705.3666v2 ER - TY - JOUR T1 - Universal Approach to Optimal Photon Storage in Atomic Media JF - Physical Review Letters Y1 - 2007 A1 - Alexey V. Gorshkov A1 - Axel Andre A1 - Michael Fleischhauer A1 - Anders S. Sorensen A1 - Mikhail D. Lukin AB - 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. VL - 98 UR - http://arxiv.org/abs/quant-ph/0604037v3 CP - 12 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.98.123601 ER -