@article {3506, title = {Clifford-Deformed Surface Codes}, journal = {PRX Quantum}, volume = {5}, year = {2024}, month = {3/19/2024}, abstract = {

Various realizations of Kitaev\&$\#$39;s surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by applying single-qubit Clifford operators. We first analyze CDSCs on the 3\×3 square lattice and find that, depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance d\′, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSC families with 50\% threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations outperform the thresholds and subthreshold logical error rates, at finite bias, of the best-known translationally invariant codes. We demonstrate the practical relevance of these random CDSC families by constructing a translation-invariant CDSC belonging to a high-performance random CDSC family. We also show that our translation-invariant CDSC outperforms well-known translation-invariant CDSCs such as the XZZX and XY codes.

}, issn = {2691-3399}, doi = {http://dx.doi.org/10.1103/PRXQuantum.5.010347}, url = {https://arxiv.org/abs/2201.07802}, author = {Dua, Arpit and Kubica, Aleksander and Jiang, Liang and Flammia, Steven T. and Michael Gullans} } @article {3504, title = {Phase transition in magic with random quantum circuits}, year = {2024}, month = {4/11/2024}, abstract = {

Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytic, numeric and experimental probes. Below a critical error rate, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate syndrome measurements concentrate magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup and pave pathways for more efficient magic state generation.

}, url = {https://arxiv.org/abs/2304.10481}, author = {Pradeep Niroula and Christopher David White and Qingfeng Wang and Sonika Johri and Daiwei Zhu and Christopher Monroe and Crystal Noel and Michael Gullans} } @article {3483, title = {Zero-temperature entanglement membranes in quantum circuits}, year = {2024}, month = {4/3/2024}, abstract = {

In chaotic quantum systems, the entanglement of a region A can be described in terms of the surface tension of a spacetime membrane pinned to the boundary of A. Here, we interpret the tension of this entanglement membrane in terms of the rate at which information \"flows\" across it. For any orientation of the membrane, one can define (generically nonunitary) dynamics across the membrane; we explore this dynamics in various space-time translation-invariant (STTI) stabilizer circuits in one and two spatial dimensions. We find that the flux of information across the membrane in these STTI circuits reaches a steady state. In the cases where this dynamics is nonunitary and the steady state flux is nonzero, this occurs because the dynamics across the membrane is unitary in a subspace of extensive entropy. This generalized unitarity is present in a broad class of STTI stabilizer circuits, and is also present in some special non-stabilizer models. The existence of multiple unitary (or generalized unitary) directions forces the entanglement membrane tension to be a piecewise linear function of the orientation of the membrane; in this respect, the entanglement membrane behaves like an interface in a zero-temperature classical lattice model. We argue that entanglement membranes in random stabilizer circuits that produce volume-law entanglement are also effectively at zero temperature.

}, url = {https://arxiv.org/abs/2404.02975}, author = {Grace M. Sommers and Sarang Gopalakrishnan and Michael Gullans and David A. Huse} } @article {3310, title = {Bell sampling from quantum circuits}, year = {2023}, month = {6/19/2023}, abstract = {

A central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. In this work, we find a model of quantum computation, Bell sampling, that can be used for both of those tasks and thus provides an ideal stepping stone towards fault-tolerance. In Bell sampling, we measure two copies of a state prepared by a quantum circuit in the transversal Bell basis. We show that the Bell samples are classically intractable to produce and at the same time constitute what we call a circuit shadow: from the Bell samples we can efficiently extract information about the quantum circuit preparing the state, as well as diagnose circuit errors. In addition to known properties that can be efficiently extracted from Bell samples, we give two new and efficient protocols, a test for the depth of the circuit and an algorithm to estimate a lower bound to the number of T gates in the circuit. With some additional measurements, our algorithm learns a full description of states prepared by circuits with low T-count.

}, url = {https://arxiv.org/abs/2306.00083}, author = {Dominik Hangleiter and Michael Gullans} } @article {3365, title = {Bell sampling from quantum circuits}, year = {2023}, month = {10/6/2023}, abstract = {

A central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. In this work, we find a universal model of quantum computation, Bell sampling, that can be used for both of those tasks and thus provides an ideal stepping stone towards fault-tolerance. In Bell sampling, we measure two copies of a state prepared by a quantum circuit in the transversal Bell basis. We show that the Bell samples are classically intractable to produce and at the same time constitute what we call a circuit shadow: from the Bell samples we can efficiently extract information about the quantum circuit preparing the state, as well as diagnose circuit errors. In addition to known properties that can be efficiently extracted from Bell samples, we give two new and efficient protocols, a test for the depth of the circuit and an algorithm to estimate a lower bound to the number of T gates in the circuit. With some additional measurements, our algorithm learns a full description of states prepared by circuits with low T-count.

}, url = {https://arxiv.org/abs/2306.00083}, author = {Dominik Hangleiter and Michael Gullans} } @article {3415, title = {Compressed gate characterization for quantum devices with time-correlated noise}, year = {2023}, month = {12/22/2023}, abstract = {

As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one and two-qubit gates can be compressed by 10x and 100x, respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two qubit interleaved randomized benchmarking fidelities of 99.8\% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large-arrays of quantum devices with non-Markovian noise.

}, url = {https://arxiv.org/abs/2307.14432}, author = {Michael Gullans and M. Caranti and A. R. Mills and J. R. Petta} } @article {3396, title = {Data Needs and Challenges of Quantum Dot Devices Automation: Workshop Report}, year = {2023}, month = {12/21/2023}, abstract = {

Gate-defined quantum dots are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. However, present-day quantum dot devices suffer from imperfections that must be accounted for, which hinders the characterization, tuning, and operation process. Moreover, with an increasing number of quantum dot qubits, the relevant parameter space grows sufficiently to make heuristic control infeasible. Thus, it is imperative that reliable and scalable autonomous tuning approaches are developed. In this report, we outline current challenges in automating quantum dot device tuning and operation with a particular focus on datasets, benchmarking, and standardization. We also present ideas put forward by the quantum dot community on how to overcome them.

}, doi = {https://doi.org/10.48550/arXiv.2312.14322}, url = {https://arxiv.org/abs/2312.14322}, author = {Justyna P. Zwolak and Jacob M. Taylor and Reed Andrews and Jared Benson and Garnett Bryant and Donovan Buterakos and Anasua Chatterjee and Sankar Das Sarma and Mark A. Eriksson and Eli{\v s}ka Greplov{\'a} and Michael Gullans and Fabian Hader and Tyler J. Kovach and Pranav S. Mundada and Mick Ramsey and Torbjoern Rasmussen and Brandon Severin and Anthony Sigillito and Brennan Undseth and Brian Weber} } @article {3307, title = {Effect of non-unital noise on random circuit sampling}, year = {2023}, month = {6/28/2023}, abstract = {

In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the presence of unital sources like the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates \— meaning it is never too \"flat\" \— regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As consequences, our results have interesting algorithmic implications on both the hardness and easiness of noisy random circuit sampling, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.

}, url = {https://arxiv.org/abs/2306.16659}, author = {Bill Fefferman and Soumik Ghosh and Michael Gullans and Kohdai Kuroiwa and Kunal Sharma} } @article {3256, title = {Error Mitigation Thresholds in Noisy Quantum Circuits}, year = {2023}, month = {2/8/2023}, abstract = {

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the performance of such strategies when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of an error mitigation threshold for random spatially local circuits in spatial dimensions D\≥2: characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an O(1) time for any imperfection in the characterization of disorder. We discuss implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.

}, url = {https://arxiv.org/abs/2302.04278}, author = {Pradeep Niroula and Sarang Gopalakrishnan and Michael Gullans} } @article {3359, title = {Fault-tolerant hyperbolic Floquet quantum error correcting codes}, year = {2023}, month = {9/18/2023}, abstract = {

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

}, url = {https://arxiv.org/abs/2309.10033}, author = {Ali Fahimniya and Hossein Dehghani and Kishor Bharti and Sheryl Mathew and Alicia J. Koll{\'a}r and Alexey V. Gorshkov and Michael Gullans} } @article {3404, title = {Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes}, year = {2023}, month = {11/29/2023}, abstract = {

Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless. In this work, we design a fault-tolerant distillation protocol for preparing encoded states of one-dimensional random circuit codes even when all gates and measurements are subject to noise. This is sufficient for fault-tolerant quantum memory since these encoded states can then be used as ancillas for Steane error correction. We show through numerical simulations that our protocol can correct erasure errors up to an error rate of 2\%. In addition, we also extend results in the code capacity setting by developing a maximum likelihood decoder for depolarizing noise similar to work by Darmawan et al. As in their work, we formulate the decoding problem as a tensor network contraction and show how to contract the network efficiently by exploiting the low-depth structure. Replacing the tensor network with a so-called \&$\#$39;\&$\#$39;tropical\&$\#$39;\&$\#$39; tensor network, we also show how to perform minimum weight decoding. With these decoders, we are able to numerically estimate the depolarizing error threshold of finite-rate random circuit codes and show that this threshold closely matches the hashing bound even when the decoding is sub-optimal.

}, url = {https://arxiv.org/abs/2311.17985}, author = {Jon Nelson and Gregory Bentsen and Steven T. Flammia and Michael Gullans} } @article {3401, title = {Logical quantum processor based on reconfigurable atom arrays}, journal = {Nature}, year = {2023}, month = {12/7/2023}, issn = {1476-4687}, doi = {10.1038/s41586-023-06927-3}, url = {https://arxiv.org/abs/2312.03982}, author = {Bluvstein, Dolev and Evered, Simon J. and Geim, Alexandra A. and Li, Sophie H. and Zhou, Hengyun and Manovitz, Tom and Ebadi, Sepehr and Cain, Madelyn and Kalinowski, Marcin and Hangleiter, Dominik and Ataides, J. Pablo Bonilla and Maskara, Nishad and Cong, Iris and Gao, Xun and Rodriguez, Pedro Sales and Karolyshyn, Thomas and Semeghini, Giulia and Michael Gullans and Greiner, Markus and Vuletic, Vladan and Lukin, Mikhail D.} } @article {3247, title = {The maximum refractive index of an atomic crystal - from quantum optics to quantum chemistry}, year = {2023}, month = {3/20/2023}, abstract = {

All known optical materials have an index of refraction of order unity. Despite the tremendous implications that an ultrahigh index could have for optical technologies, little research has been done on why the refractive index of materials is universally small, and whether this observation is fundamental. Here, we investigate the index of an ordered arrangement of atoms, as a function of atomic density. At dilute densities, this problem falls into the realm of quantum optics, where atoms do not interact with one another except via the scattering of light. On the other hand, when the lattice constant becomes comparable to the Bohr radius, the electronic orbitals begin to overlap, giving rise to quantum chemistry. We present a minimal model that allows for a unifying theory of index spanning these two regimes. A key aspect is the treatment of multiple light scattering, which can be highly non-perturbative over a large density range, and which is the reason that conventional theories of the index break down. In the quantum optics regime, we show that ideal light-matter interactions can have a single-mode nature, allowing for a purely real refractive index that grows with density as (N/V)1/3. At the onset of quantum chemistry, we show how two physical mechanisms (excited electron tunneling dynamics and the buildup of electronic density-density correlations) can open up inelastic or spatial multi-mode light scattering processes, which ultimately reduce the index back to order unity while introducing absorption. Around the onset of chemistry, our theory predicts that ultrahigh index (n\∼30), low-loss materials could in principle be allowed by the laws of nature.\ 

}, url = {https://arxiv.org/abs/2303.10998}, author = {Francesco Andreoli and Bennet Windt and Stefano Grava and Gian Marcello Andolina and Michael Gullans and Alexander A. High and Darrick E. Chang} } @article {3420, title = {Precision Bounds on Continuous-Variable State Tomography using Classical Shadows}, year = {2023}, month = {12/15/2023}, abstract = {

Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with a high probability, we show that homodyne detection requires an order O(N4+1/3) measurements in the worst case, whereas PNR and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in N. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.

}, url = {https://arxiv.org/abs/2211.05149}, author = {Srilekha Gandhari and Victor V. Albert and Thomas Gerrits and Jacob M. Taylor and Michael Gullans} } @article {3362, title = {Quantum Lego Expansion Pack: Enumerators from Tensor Networks}, year = {2023}, month = {8/9/2023}, abstract = {

We provide the first tensor network method for computing quantum weight enumerator polynomials in the most general form. As a corollary, if a quantum code has a known tensor network construction of its encoding map, our method produces an algorithm that computes its distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can provide up to an exponential speed up compared to the current methods. We also introduce a few novel applications of different weight enumerators. In particular, for any code built from the quantum lego method, we use enumerators to construct its (optimal) decoders under any i.i.d. single qubit or qudit error channels and discuss their applications for computing logical error rates. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the 2d Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force.

}, url = {https://arxiv.org/abs/2308.05152}, author = {ChunJun Cao and Michael Gullans and Brad Lackey and Zitao Wang} } @article {3355, title = {Quantum Sensing with Erasure Qubits}, year = {2023}, month = {10/2/2023}, abstract = {

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

}, url = {https://arxiv.org/abs/2310.01512}, author = {Pradeep Niroula and Jack Dolde and Xin Zheng and Jacob Bringewatt and Adam Ehrenberg and Kevin C. Cox and Jeff Thompson and Michael Gullans and Shimon Kolkowitz and Alexey V. Gorshkov} } @article {3264, title = {Self-dual quasiperiodic percolation}, journal = {Phys. Rev. E}, volume = {107}, year = {2023}, month = {2/27/2023}, pages = {024137}, abstract = {

How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has emergent discrete scale invariance, but none of the additional emergent conformal symmetry of critical random percolation. From the discrete sequences of critical clusters, we find fractal dimensions of Df=1.911943(1) and Df=1.707234(40) for the two models, significantly different from Df=91/48=1.89583... of random percolation. The critical exponents ν, determined through a numerical study of cluster sizes and wrapping probabilities on a torus, are also well below the ν=4/3 of random percolation. While these new models do not appear to belong to a universality class, they demonstrate how the removal of randomness can fundamentally change the critical behavior.

}, doi = {10.1103/PhysRevE.107.024137}, url = {https://arxiv.org/abs/2206.11290}, author = {Sommers, Grace M. and Michael Gullans and Huse, David A.} } @article {3312, title = {A sharp phase transition in linear cross-entropy benchmarking}, year = {2023}, month = {5/8/2023}, abstract = {

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

}, url = {https://arxiv.org/abs/2305.04954}, author = {Brayden Ware and Abhinav Deshpande and Dominik Hangleiter and Pradeep Niroula and Bill Fefferman and Alexey V. Gorshkov and Michael Gullans} } @article {3418, title = {Thresholds in the Robustness of Error Mitigation in Noisy Quantum Dynamics}, year = {2023}, month = {10/30/2023}, abstract = {

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of such strategies when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of a threshold in the robustness of error mitigation for random spatially local circuits in spatial dimensions D\≥2: noise characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an O(1) time for any imperfection in the characterization of disorder. As a result, error mitigation is only a practical method for sufficiently well-characterized noise. We discuss further implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.

}, url = {https://arxiv.org/abs/2302.04278}, author = {Pradeep Niroula and Sarang Gopalakrishnan and Michael Gullans} } @article {3183, title = {Continuous-variable quantum state designs: theory and applications}, year = {2022}, month = {11/9/2022}, abstract = {

We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state t-designs from Comm. Math. Phys. 326, 755 (2014), no state designs exist for t\≥2. Similarly, we prove that no CV unitary t-designs exist for t\≥2. We propose an alternative definition for CV state designs, which we call rigged t-designs, and provide explicit constructions for t=2. As an application of rigged designs, we develop a design-based shadow-tomography protocol for CV states. Using energy-constrained versions of rigged designs, we define an average fidelity for CV quantum channels and relate this fidelity to the CV entanglement fidelity. As an additional result of independent interest, we establish a connection between torus 2-designs and complete sets of mutually unbiased bases.

}, keywords = {FOS: Physical sciences, Mathematical Physics (math-ph), Optics (physics.optics), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.05127}, url = {https://arxiv.org/abs/2211.05127}, author = {Iosue, Joseph T. and Sharma, Kunal and Michael Gullans and Victor V. Albert} } @article {3182, title = {Continuous-Variable Shadow Tomography}, year = {2022}, month = {11/9/2022}, abstract = {

Shadow tomography is a framework for constructing succinct descriptions of quantum states, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable tomography in the classical-shadow framework, obtaining rigorous bounds on the sample complexity for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with a high probability, we show that homodyne detection requires an order O(N5) measurements in the worst case, whereas PNR and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in N. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.05149}, url = {https://arxiv.org/abs/2211.05149}, author = {Gandhari, Srilekha and Victor V. Albert and Gerrits, Thomas and Taylor, Jacob M. and Michael Gullans} } @article {3070, title = {Infinite-randomness criticality in monitored quantum dynamics with static disorder}, year = {2022}, month = {5/27/2022}, abstract = {

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size l scales as S\∼l\√; moreover, the dynamical critical exponent z=\∞. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion.\ 

}, url = {https://arxiv.org/abs/2205.14002}, author = {Aidan Zabalo and Justin H. Wilson and Michael Gullans and Romain Vasseur and Sarang Gopalakrishnan and David A. Huse and J. H. Pixley} } @article {3006, title = {Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions}, journal = {Physical Review Letters}, volume = {128}, year = {2022}, month = {2/11/2022}, abstract = {

Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large onsite Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

}, doi = {10.1103/physrevlett.128.050602}, url = {https://arxiv.org/abs/2107.03393}, author = {Aidan Zabalo and Michael Gullans and Justin H. Wilson and Romain Vasseur and Andreas W. W. Ludwig and Sarang Gopalakrishnan and David A. Huse and J. H. Pixley} } @article {3030, title = {Universal scattering with general dispersion relations}, journal = {Phys. Rev. Research}, volume = {4}, year = {2022}, month = {4/6/2022}, chapter = {023014}, abstract = {

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

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

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

}, doi = {https://doi.org/10.48550/arXiv.2103.09830}, url = {https://arxiv.org/abs/2103.09830}, author = {Yidan Wang and Michael Gullans and Xuesen Na and Alexey V. Gorshkov} } @article {2857, title = {Chiral transport of hot carriers in graphene in the quantum Hall regime}, year = {2021}, month = {10/3/2021}, abstract = {

Photocurrent (PC) measurements can reveal the relaxation dynamics of photo-excited hot carriers beyond the linear response of conventional transport experiments, a regime important for carrier multiplication. In graphene subject to a magnetic field, PC measurements are able to probe the existence of Landau levels with different edge chiralities which is exclusive to relativistic electron systems. Here, we report the accurate measurement of PC in graphene in the quantum Hall regime. Prominent PC oscillations as a function of gate voltage on samples\&$\#$39; edges are observed. These oscillation amplitudes form an envelope which depends on the strength of the magnetic field, as does the PCs\&$\#$39; power dependence and their saturation behavior. We explain these experimental observations through a model using optical Bloch equations, incorporating relaxations through acoustic-, optical- phonons and Coulomb interactions. The simulated PC agrees with our experimental results, leading to a unified understanding of the chiral PC in graphene at various magnetic field strengths, and providing hints for the occurrence of a sizable carrier multiplication.\ 

}, url = {https://arxiv.org/abs/2110.01079}, author = {Bin Cao and Tobias Grass and Olivier Gazzano and Kishan Ashokbhai Patel and Jiuning Hu and Markus M{\"u}ller and Tobias Huber and Luca Anzi and Kenji Watanabe and Takashi Taniguchi and David Newell and Michael Gullans and Roman Sordan and Mohammad Hafezi and Glenn Solomon} } @article {2939, title = {Constructing quantum many-body scar Hamiltonians from Floquet automata}, year = {2021}, month = {12/22/2021}, abstract = {

We provide a systematic approach for constructing approximate quantum many-body scars(QMBS) starting from two-layer Floquet automaton circuits that exhibit trivial many-body revivals. We do so by applying successively more restrictions that force local gates of the automaton circuit to commute concomitantly more accurately when acting on select scar states. With these rules in place, an effective local, Floquet Hamiltonian is seen to capture dynamics of the automata over a long prethermal window, and neglected terms can be used to estimate the relaxation of revivals. We provide numerical evidence for such a picture and use our construction to derive several QMBS models, including the celebrated PXP model.

}, url = {https://arxiv.org/abs/2112.12153}, author = {Pierre-Gabriel Rozon and Michael Gullans and Kartiek Agarwal} } @article {2724, title = {Entanglement and purification transitions in non-Hermitian quantum mechanics}, journal = {Phys. Rev. Lett., in press}, year = {2021}, month = {12/2/2020}, abstract = {

A quantum system subject to continuous measurement and post-selection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the rate of post-selection, this non-Hermitian Hamiltonian undergoes a spectral phase transition. On one side of this phase transition (for weak post-selection) an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which PT symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analytically tractable mean-field theory; these methods yield consistent conclusions.

}, url = {https://arxiv.org/abs/2012.01435}, author = {Sarang Gopalakrishnan and Michael Gullans} } @article {2776, title = {Entanglement Phase Transitions in Measurement-Only Dynamics}, journal = {Physical Review X}, volume = {11}, year = {2021}, month = {1/2/2021}, abstract = {

Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This motivates us to introduce \emph{measurement-only models}, in which the \"scrambling\" and \"un-scrambling\" effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. This represents a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is \emph{frustration}, or mutual incompatibility, of the measurements. Suprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local (≳3-body) operators. We identify a class of exceptions to this behavior (\"bipartite ensembles\") which cannot sustain an entangling phase, but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light-cone, despite the non-locality inherent to quantum measurements.

}, doi = {10.1103/PhysRevX.11.011030}, url = {https://arxiv.org/abs/2004.09560}, author = {Ippoliti, Matteo and Michael Gullans and Gopalakrishnan, Sarang and Huse, David A. and Khemani, Vedika} } @article {2777, title = {Maximum Refractive Index of an Atomic Medium}, journal = {Physical Review X}, volume = {11}, year = {2021}, month = {2/18/2021}, abstract = {

It is interesting to observe that all optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, though, a deep understanding of the mechanisms that lead to this universal behavior seems to be lacking. Moreover, this observation is difficult to reconcile with the fact that a single, isolated atom is known to have a giant optical response, as characterized by a resonant scattering cross section that far exceeds its physical size. Here, we theoretically and numerically investigate the evolution of the optical properties of an ensemble of ideal atoms as a function of density, starting from the dilute gas limit, including the effects of multiple scattering and near-field interactions. Interestingly, despite the giant response of an isolated atom, we find that the maximum index does not indefinitely grow with increasing density, but rather reaches a limiting value n\≈1.7. We propose an explanation based upon strong-disorder renormalization group theory, in which the near-field interaction combined with random atomic positions results in an inhomogeneous broadening of atomic resonance frequencies. This mechanism ensures that regardless of the physical atomic density, light at any given frequency only interacts with at most a few near-resonant atoms per cubic wavelength, thus limiting the maximum index attainable. Our work is a promising first step to understand the limits of refractive index from a bottom-up, atomic physics perspective, and also introduces renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.

}, doi = {10.1103/PhysRevX.11.011026}, url = {https://arxiv.org/abs/2006.01680}, author = {Andreoli, Francesco and Michael Gullans and High, Alexander A. and Browaeys, Antoine and Chang, Darrick E.} } @article {2805, title = {Observation of measurement-induced quantum phases in a trapped-ion quantum computer}, year = {2021}, month = {6/10/2021}, abstract = {

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

}, url = {https://arxiv.org/abs/2106.05881}, author = {Crystal Noel and Pradeep Niroula and Daiwei Zhu and Andrew Risinger and Laird Egan and Debopriyo Biswas and Marko Cetina and Alexey V. Gorshkov and Michael Gullans and David A. Huse and Christopher Monroe} } @article {2761, title = {Singularities in nearly-uniform 1D condensates due to quantum diffusion}, year = {2021}, month = {3/10/2021}, abstract = {

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

}, url = {https://arxiv.org/abs/2103.06293}, author = {Christopher L. Baldwin and P. Bienias and Alexey V. Gorshkov and Michael Gullans and M. Maghrebi} } @article {2909, title = {Tight bounds on the convergence of noisy random circuits to uniform}, year = {2021}, month = {12/1/2021}, abstract = {

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

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

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

}, url = {https://arxiv.org/abs/2009.13599}, author = {Dalia P. Ornelas Huerta and Przemyslaw Bienias and Alexander N. Craddock and Michael Gullans and Andrew J. Hachtel and Marcin Kalinowski and Mary E. Lyon and Alexey V. Gorshkov and Steven L. Rolston and J. V. Porto} } @article {2779, title = {Coherent transport of spin by adiabatic passage in quantum dot arrays}, journal = {Physical Review B}, volume = {102}, year = {2020}, month = {9/17/2020}, abstract = {

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (\>95\%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

}, issn = {2469-9950}, doi = {10.1103/PhysRevB.102.155404}, url = {https://arxiv.org/abs/2007.10582}, author = {Michael Gullans and Petta, J. R.} } @article {2683, title = {Coherent transport of spin by adiabatic passage in quantum dot arrays}, journal = {Phys. Rev. B}, volume = {102}, year = {2020}, month = {9/17/2020}, abstract = {

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (\>95\%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

}, doi = {https://doi.org/10.1103/PhysRevB.102.155404}, url = {https://arxiv.org/abs/2007.10582}, author = {Michael Gullans and J. R. Petta} } @article {2778, title = {Dynamical Purification Phase Transition Induced by Quantum Measurements}, journal = {Physical Review X}, volume = {10}, year = {2020}, month = {7/30/2020}, abstract = {

Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate, and (ii) a \"mixed\" phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace where quantum information is reliably encoded against the future non-unitary evolution of the system. We show that these codes are of potential relevance to fault-tolerant quantum computation as they are often highly degenerate and satisfy optimal tradeoffs between encoded information densities and error thresholds. In spatially local models in 1+1 dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. The mutual information of an initially completely-mixed state in 1+1 dimensions grows sublinearly in time due to the formation of the error protected subspace. The purification transition studied here also generalizes to systems with long-range interactions, where conventional notions of entanglement transitions have to be reformulated. Purification dynamics is likely a more robust probe of the transition in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of non-equilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.

}, doi = {10.1103/PhysRevX.10.041020}, url = {https://arxiv.org/abs/1905.05195}, author = {Michael Gullans and Huse, David A.} } @article {2567, title = {Exotic photonic molecules via Lennard-Jones-like potentials}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {9/19/2020}, abstract = {

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

}, doi = {https://doi.org/10.1103/PhysRevLett.125.093601}, url = {https://arxiv.org/abs/2003.07864}, author = {Przemyslaw Bienias and Michael Gullans and Marcin Kalinowski and Alexander N. Craddock and Dalia P. Ornelas-Huerta and Steven L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {2680, title = {Quantum coding with low-depth random circuits}, year = {2020}, month = {10/19/2020}, abstract = {

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity in D\≥1 spatial dimensions to generate quantum error-correcting codes. For random stabilizer codes and the erasure channel, we find strong evidence that a depth O(logN) random circuit is necessary and sufficient to converge (with high probability) to zero failure probability for any finite amount below the channel capacity for any D. Previous results on random circuits have only shown that O(N1/D) depth suffices or that O(log3N) depth suffices for all-to-all connectivity (D\→\∞). We then study the critical behavior of the erasure threshold in the so-called moderate deviation limit, where both the failure probability and the distance to the channel capacity converge to zero with N. We find that the requisite depth scales like O(logN) only for dimensions D\≥2, and that random circuits require O(N\−\−\√) depth for D=1. Finally, we introduce an \"expurgation\" algorithm that uses quantum measurements to remove logical operators that cause the code to fail by turning them into either additional stabilizers or into gauge operators in a subsystem code. With such targeted measurements, we can achieve sub-logarithmic depth in D\≥2 spatial dimensions below capacity without increasing the maximum weight of the check operators. We find that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in D=2 dimensions. These results indicate that finite-rate quantum codes are practically relevant for near-term devices and may significantly reduce the resource requirements to achieve fault tolerance for near-term applications.\ 

}, url = {https://arxiv.org/abs/2010.09775}, author = {Michael Gullans and Stefan Krastanov and David A. Huse and Liang Jiang and Steven T. Flammia} } @article {2681, title = {Resonant enhancement of three-body loss between strongly interacting photons}, year = {2020}, month = {10/19/2020}, abstract = {

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

}, url = {https://arxiv.org/abs/2010.09772}, author = {Marcin Kalinowski and Yidan Wang and Przemyslaw Bienias and Michael Gullans and Dalia P. Ornelas-Huerta and Alexander N. Craddock and Steven L. Rolston and J. V. Porto and Hans Peter B{\"u}chler and Alexey V. Gorshkov} } @article {2269, title = {Bose Condensation of Photons Thermalized via Laser Cooling of Atoms}, year = {2018}, abstract = {

A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number-conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. Here we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline earth atoms) inside a Fabry-Perot cavity.

}, url = {https://arxiv.org/abs/1809.07777}, author = {Chiao-Hsuan Wang and Michael Gullans and J. V. Porto and William D. Phillips and J. M. Taylor} } @article {2256, title = {Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal}, year = {2018}, abstract = {

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

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

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

}, doi = {10.1126/science.aao7293}, url = {http://science.sciencemag.org/content/359/6377/783}, author = {Qi-Yu Liang and Aditya V. Venkatramani and Sergio H. Cantu and Travis L. Nicholson and Michael Gullans and Alexey V. Gorshkov and Jeff D. Thompson and Cheng Chin and Mikhail D. Lukin and Vladan Vuletic} } @article {2218, title = {Photon propagation through dissipative Rydberg media at large input rates}, year = {2018}, abstract = {

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

}, url = {https://arxiv.org/abs/1807.07586}, author = {Przemyslaw Bienias and James Douglas and Asaf Paris-Mandoki and Paraj Titum and Ivan Mirgorodskiy and Christoph Tresp and Emil Zeuthen and Michael Gullans and Marco Manzoni and Sebastian Hofferberth and Darrick Chang and Alexey V. Gorshkov} } @article {2135, title = {Photon thermalization via laser cooling of atoms}, journal = {Phys. Rev. A 98, 013834}, year = {2018}, month = {2018}, abstract = {

Laser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that non-interacting photons can thermalize with the atoms to a grand canonical ensemble with a non-zero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential set by the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare earth atoms. With the addition of photon-photon interactions, this system could provide a new platform for exploring many-body physics.

}, doi = {https://doi.org/10.1103/PhysRevA.98.013834}, url = {https://arxiv.org/abs/1712.08643}, author = {Chiao-Hsuan Wang and Michael Gullans and J. V. Porto and William D. Phillips and J. M. Taylor} } @article {2146, title = {Probing electron-phonon interactions in the charge-photon dynamics of cavity-coupled double quantum dots}, journal = {Physical Review B}, volume = {97}, year = {2018}, month = {2018/01/16}, pages = {035305}, abstract = {

Electron-phonon coupling is known to play an important role in the charge dynamics of semiconductor quantum dots. Here we explore its role in the combined charge-photon dynamics of cavity-coupled double quantum dots. Previous work on these systems has shown that strong electron-phonon coupling leads to a large contribution to photoemission and gain from phonon-assisted emission and absorption processes. We compare the effects of this phonon sideband in three commonly investigated gate-defined quantum dot material systems: InAs nanowires and GaAs and Si two-dimensional electron gases (2DEGs). We compare our theory with existing experimental data from cavity-coupled InAs nanowire and GaAs 2DEG double quantum dots and find quantitative agreement only when the phonon sideband and photoemission processes during lead tunneling are taken into account. Finally, we show that the phonon sideband also leads to a sizable renormalization of the cavity frequency, which allows for direct spectroscopic probes of the electron-phonon coupling in these systems.

}, doi = {10.1103/PhysRevB.97.035305}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.035305}, author = {Michael Gullans and J. M. Taylor and J. R. Petta} } @article {2213, title = {Single-photon bound states in atomic ensembles}, year = {2018}, abstract = {

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

}, url = {https://arxiv.org/abs/1809.01147}, author = {Yidan Wang and Michael Gullans and Antoine Browaeys and J. V. Porto and Darrick E. Chang and Alexey V. Gorshkov} } @article {1814, title = {Correlated Photon Dynamics in Dissipative Rydberg Media}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/07/26}, pages = {043602}, abstract = {

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

}, doi = {10.1103/PhysRevLett.119.043602}, url = {https://arxiv.org/abs/1608.06068}, author = {Emil Zeuthen and Michael Gullans and Mohammad F. Maghrebi and Alexey V. Gorshkov} } @article {2059, title = {Efimov States of Strongly Interacting Photons}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/12/04}, pages = {233601}, abstract = {

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

}, doi = {10.1103/PhysRevLett.119.233601}, url = {https://arxiv.org/abs/1709.01955}, author = {Michael Gullans and S. Diehl and S. T. Rittenhouse and B. P. Ruzic and J. P. D{\textquoteright}Incao and P. Julienne and Alexey V. Gorshkov and J. M. Taylor} } @article {1955, title = {High-Order Multipole Radiation from Quantum Hall States in Dirac Materials}, journal = {Physical Review B}, volume = {95}, year = {2017}, month = {2017/06/30}, pages = {235439}, abstract = {

Topological states can exhibit electronic coherence on macroscopic length scales. When the coherence length exceeds the wavelength of light, one can expect new phenomena to occur in the optical response of these states. We theoretically characterize this limit for integer quantum Hall states in two-dimensional Dirac materials. We find that the radiation from the bulk is dominated by dipole emission, whose spectral properties vary with the local disorder potential. On the other hand, the radiation from the edge is characterized by large multipole moments in the far-field associated with the efficient transfer of angular momentum from the electrons into the scattered light. These results demonstrate that high-order multipole transitions are a necessary component for the optical spectroscopy and control of quantum Hall and related topological states in electronic systems.

}, doi = {10.1103/PhysRevB.95.235439}, url = {https://arxiv.org/abs/1701.03464}, author = {Michael Gullans and J. M. Taylor and Atac Imamoglu and Pouyan Ghaemi and Mohammad Hafezi} } @article {2061, title = {Light-induced fractional quantum Hall phases in graphene}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/12/15}, pages = {247403}, abstract = {

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

}, doi = {10.1103/PhysRevLett.119.247403}, url = {https://arxiv.org/abs/1612.08748}, author = {Areg Ghazaryan and Tobias Gra{\ss} and Michael Gullans and Pouyan Ghaemi and Mohammad Hafezi} } @article {2152, title = {Threshold Dynamics of a Semiconductor Single Atom Maser}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/08/31}, pages = {097702}, abstract = {

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

}, doi = {10.1103/PhysRevLett.119.097702}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.097702}, author = {Liu, Y.-Y. and Stehlik, J. and Eichler, C. and Mi, X. and Hartke, T. R. and Michael Gullans and J. M. Taylor and Petta, J. R.} } @article {1816, title = {Valley Blockade in a Silicon Double Quantum Dot}, journal = {Physical Review B}, volume = {96}, year = {2017}, month = {2017/11/13}, pages = {205302}, abstract = {

Electrical transport in double quantum dots (DQDs) illuminates many interesting features of the dots\&$\#$39; carrier states. Recent advances in silicon quantum information technologies have renewed interest in the valley states of electrons confined in silicon. Here we show measurements of DC transport through a mesa-etched silicon double quantum dot. Comparing bias triangles (i.e., regions of allowed current in DQDs) at positive and negative bias voltages we find a systematic asymmetry in the size of the bias triangles at the two bias polarities. Asymmetries of this nature are associated with blocking of tunneling events due to the occupation of a metastable state. Several features of our data lead us to conclude that the states involved are not simple spin states. Rather, we develop a model based on selective filling of valley states in the DQD that is consistent with all of the qualitative features of our data.

}, doi = {10.1103/PhysRevB.96.205302}, url = {https://arxiv.org/abs/1607.06107}, author = {Justin K. Perron and Michael Gullans and J. M. Taylor and M. D. Stewart, Jr. and Neil M. Zimmerman} } @article {1815, title = {Double Quantum Dot Floquet Gain Medium}, journal = {Physical Review X}, volume = {6}, year = {2016}, month = {2016/11/07}, pages = {041027}, abstract = {

Strongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here we show that a single electron in a periodically driven DQD functions as a \"Floquet gain medium,\" where population imbalances in the DQD Floquet quasi-energy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intra-cavity photon number n_c in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current -- one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of non-classical light and thermalization of driven quantum systems.

}, doi = {10.1103/PhysRevX.6.041027}, url = {http://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041027}, author = {J. Stehlik and Y.-Y. Liu and C. Eichler and T. R. Hartke and X. Mi and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1784, title = {Effective Field Theory for Rydberg Polaritons}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/09/09}, pages = {113601}, abstract = {

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

}, doi = {http://dx.doi.org/10.1103/PhysRevLett.117.113601}, url = {http://arxiv.org/abs/1605.05651}, author = {Michael Gullans and J. D. Thompson and Y. Wang and Q. -Y. Liang and V. Vuletic and M. D. Lukin and Alexey V. Gorshkov} } @article {1692, title = {Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/07/25}, pages = {056801}, abstract = {

A strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.

}, doi = {http://dx.doi.org/10.1103/PhysRevLett.117.056801}, url = {http://arxiv.org/abs/1512.01248}, author = {Michael Gullans and J. Stehlik and Y. -Y. Liu and J. R. Petta and J. M. Taylor} } @article {1507, title = {Coulomb bound states of strongly interacting photons}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/09/16}, pages = {123601}, abstract = { We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. }, doi = {10.1103/PhysRevLett.115.123601}, url = {http://arxiv.org/abs/1505.03859v1}, author = {Mohammad F. Maghrebi and Michael Gullans and P. Bienias and S. Choi and I. Martin and O. Firstenberg and M. D. Lukin and H. P. B{\"u}chler and Alexey V. Gorshkov} } @article {1500, title = {Injection Locking of a Semiconductor Double Quantum Dot Micromaser}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/11/02}, pages = {053802}, abstract = { Emission linewidth is an important figure of merit for masers and lasers. We recently demonstrated a semiconductor double quantum dot (DQD) micromaser where photons are generated through single electron tunneling events. Charge noise directly couples to the DQD energy levels, resulting in a maser linewidth that is more than 100 times larger than the Schawlow-Townes prediction. Here we demonstrate a linewidth narrowing of more than a factor 10 by locking the DQD emission to a coherent tone that is injected to the input port of the cavity. We measure the injection locking range as a function of cavity input power and show that it is in agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models. }, doi = {10.1103/PhysRevA.92.053802}, url = {http://arxiv.org/abs/1508.04147}, author = {Y. -Y. Liu and J. Stehlik and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1329, title = {Optical Control of Donor Spin Qubits in Silicon}, journal = {Physical Review B}, volume = {92}, year = {2015}, month = {2015/11/11}, pages = {195411}, abstract = {We show how to achieve optical, spin-selective transitions from the ground state to excited orbital states of group-V donors (P, As, Sb, Bi) in silicon. We consider two approaches based on either resonant, far-infrared (IR) transitions of the neutral donor or resonant, near-IR excitonic transitions. For far-IR light, we calculate the dipole matrix elements between the valley-orbit and spin-orbit split states for all the goup-V donors using effective mass theory. We then calculate the maximum rate and amount of electron-nuclear spin-polarization achievable through optical pumping with circularly polarized light. We find this approach is most promising for Bi donors due to their large spin-orbit and valley-orbit interactions. Using near-IR light, spin-selective excitation is possible for all the donors by driving a two-photon $\Lambda$-transition from the ground state to higher orbitals with even parity. We show that externally applied electric fields or strain allow similar, spin-selective $\Lambda$-transition to odd-parity excited states. We anticipate these results will be useful for future spectroscopic investigations of donors, quantum control and state preparation of donor spin qubits, and for developing a coherent interface between donor spin qubits and single photons. }, doi = {10.1103/PhysRevB.92.195411}, url = {http://arxiv.org/abs/1507.07929}, author = {Michael Gullans and J. M. Taylor} } @article {1332, title = {Phonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/05/13}, pages = {196802}, abstract = {We develop a microscopic model for the recently demonstrated double quantum dot (DQD) maser. In characterizing the gain of this device we find that, in addition to the direct stimulated emission of photons, there is a large contribution from the simultaneous emission of a photon and a phonon, i.e., the phonon sideband. We show that this phonon-assisted gain typically dominates the overall gain which leads to masing. Recent experimental data are well fit with our model. }, doi = {10.1103/PhysRevLett.114.196802}, url = {http://arxiv.org/abs/1501.03499v3}, author = {Michael Gullans and Y. -Y. Liu and J. Stehlik and J. R. Petta and J. M. Taylor} } @article {1494, title = {Quantum Nonlinear Optics Near Optomechanical Instabilities}, journal = {Physical Review A}, volume = {91}, year = {2015}, month = {2015/01/09}, pages = {013818}, abstract = { Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak-coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new figure of merit for realizing strong nonlinearity which scales with the single-photon optomechanical coupling and the sideband resolution of the mechanical mode with respect to the cavity linewidth. We find that current devices based on optomechanical crystals, thought to be in the weak-coupling regime, can still achieve strong quantum nonlinearity; enabling deterministic interactions between single photons. }, doi = {10.1103/PhysRevA.91.013818}, url = {http://arxiv.org/abs/1404.3726v2}, author = {Xunnong Xu and Michael Gullans and J. M. Taylor} } @article {1499, title = {Semiconductor double quantum dot micromaser}, journal = {Science}, volume = {347}, year = {2015}, month = {2015/01/15}, pages = {285 - 287}, abstract = { The coherent generation of light, from masers to lasers, relies upon the specific structure of the individual emitters that lead to gain. Devices operating as lasers in the few-emitter limit provide opportunities for understanding quantum coherent phenomena, from THz sources to quantum communication. Here we demonstrate a maser that is driven by single electron tunneling events. Semiconductor double quantum dots (DQDs) serve as a gain medium and are placed inside of a high quality factor microwave cavity. We verify maser action by comparing the statistics of the emitted microwave field above and below the maser threshold. }, doi = {10.1126/science.aaa2501}, url = {http://arxiv.org/abs/1507.06359v1}, author = {Y. -Y. Liu and J. Stehlik and C. Eichler and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1495, title = {A Quantum Network of Silicon Qubits using Mid-Infrared Graphene Plasmons}, year = {2014}, month = {2014/07/25}, abstract = { We consider a quantum network of mid-infrared, graphene plasmons coupled to the hydrogen-like excited states of group-V donors in silicon. First, we show how to use plasmon-enhanced light-matter interactions to achieve single-shot spin readout of the donor qubits via optical excitation and electrical detection of the emitted plasmons. We then show how plasmons in high mobility graphene nanoribbons can be used to achieve high-fidelity, two-qubit gates and entanglement of distant Si donor qubits. The proposed device is readily compatible with existing technology and fabrication methods. }, url = {http://arxiv.org/abs/1407.7035v1}, author = {Michael Gullans and J. M. Taylor} } @article {1506, title = {Scattering resonances and bound states for strongly interacting Rydberg polaritons }, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/11/3}, abstract = { We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. }, doi = {10.1103/PhysRevA.90.053804}, url = {http://arxiv.org/abs/1402.7333v1}, author = {P. Bienias and S. Choi and O. Firstenberg and Mohammad F. Maghrebi and Michael Gullans and M. D. Lukin and Alexey V. Gorshkov and H. P. B{\"u}chler} } @article {1505, title = {All-Optical Switch and Transistor Gated by One Stored Photon}, journal = {Science}, volume = {341}, year = {2013}, month = {2013/07/04}, pages = {768 - 770}, abstract = { The realization of an all-optical transistor where one {\textquoteright}gate{\textquoteright} photon controls a {\textquoteright}source{\textquoteright} light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realize a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation, and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates, and deterministic multiphoton entanglement. }, doi = {10.1126/science.1238169}, url = {http://arxiv.org/abs/1401.3194v1}, author = {Wenlan Chen and Kristin M. Beck and Robert B{\"u}cker and Michael Gullans and Mikhail D. Lukin and Haruka Tanji-Suzuki and Vladan Vuletic} } @article {1497, title = {Preparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots }, journal = {Physical Review B}, volume = {88}, year = {2013}, month = {2013/7/15}, abstract = { We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots. }, doi = {10.1103/PhysRevB.88.035309}, url = {http://arxiv.org/abs/1212.6953v3}, author = {Michael Gullans and J. J. Krich and J. M. Taylor and B. I. Halperin and M. D. Lukin} } @article {1504, title = {Single-photon nonlinear optics with graphene plasmons}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/12/11}, abstract = { We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch. }, doi = {10.1103/PhysRevLett.111.247401}, url = {http://arxiv.org/abs/1309.2651v3}, author = {Michael Gullans and D. E. Chang and F. H. L. Koppens and F. J. Garc{\'\i}a de Abajo and M. D. Lukin} } @article {1503, title = {Nanoplasmonic Lattices for Ultracold atoms}, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/12/6}, abstract = { We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed. }, doi = {10.1103/PhysRevLett.109.235309}, url = {http://arxiv.org/abs/1208.6293v3}, author = {Michael Gullans and T. Tiecke and D. E. Chang and J. Feist and J. D. Thompson and J. I. Cirac and P. Zoller and M. D. Lukin} } @article {1501, title = {Adiabatic preparation of many-body states in optical lattices}, journal = {Physical Review A}, volume = {81}, year = {2010}, month = {2010/6/22}, abstract = { We analyze a technique for the preparation of low entropy many body states of atoms in optical lattices based on adiabatic passage. In particular, we show that this method allows preparation of strongly correlated states as stable highest energy states of Hamiltonians that have trivial ground states. As an example, we analyze the generation of antiferromagnetically ordered states by adiabatic change of a staggered field acting on the spins of bosonic atoms with ferromagnetic interactions. }, doi = {10.1103/PhysRevA.81.061603}, url = {http://arxiv.org/abs/0906.2567v3}, author = {Anders S. Sorensen and Ehud Altman and Michael Gullans and J. V. Porto and Mikhail D. Lukin and Eugene Demler} } @article {1353, title = {Dynamic Nuclear Polarization in Double Quantum Dots}, journal = {Physical Review Letters}, volume = {104}, year = {2010}, month = {2010/6/4}, abstract = {We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. We show that in the case of unequal dots, build up of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, build up of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process. }, doi = {10.1103/PhysRevLett.104.226807}, url = {http://arxiv.org/abs/1003.4508v2}, author = {Michael Gullans and J. J. Krich and J. M. Taylor and H. Bluhm and B. I. Halperin and C. M. Marcus and M. Stopa and A. Yacoby and M. D. Lukin} }