@article {3410, title = {Clifford operations and homological codes for rotors and oscillators}, year = {2023}, month = {11/13/2023}, abstract = {

We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This n-rotor Clifford group, U(1)n(n+1)/2⋊GLn(Z), is represented by continuous U(1) gates generated by polynomials quadratic in angular momenta, as well as discrete GLn(Z) momentum sign-flip and sum gates. We classify homological rotor error-correcting codes [arXiv:2303.13723] and various rotor states based on equivalence under Clifford operations.
Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes [arXiv:1903.12615].

}, url = {https://arxiv.org/abs/2311.07679}, author = {Yijia Xu and Yixu Wang and Victor V. Albert} } @article {3295, title = {Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison}, journal = {PRX Quantum}, volume = {4}, year = {2023}, month = {6/14/2023}, pages = {020342}, abstract = {

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP)\ \–\ stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog or Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing and formulate qudit versions of GKP-stabilizer codes.

}, doi = {10.1103/PRXQuantum.4.020342}, url = {https://arxiv.org/abs/2209.04573}, author = {Xu, Yijia and Wang, Yixu and Kuo, En-Jui and Victor V. Albert} } @article {3067, title = {Boson Sampling for Generalized Bosons}, year = {2022}, month = {5/2/2022}, abstract = {

We introduce the notion of \"generalized bosons\" whose exchange statistics resemble those of bosons, but the local bosonic commutator [ai,a\†i]=1 is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms.

}, url = {https://arxiv.org/abs/2204.08389}, author = {En-Jui Kuo and Yijia Xu and Dominik Hangleiter and Andrey Grankin and Mohammad Hafezi} } @article {2910, title = {Efficient Product Formulas for Commutators and Applications to Quantum Simulation}, journal = {Physical Review Research}, volume = {4}, year = {2022}, month = {03/10/2022}, chapter = {013191}, abstract = {

We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator differential method. We then derive higher-order product formulas recursively from the third-order formula. We improve over previous recursive constructions, reducing the number of gates required to achieve the same accuracy. In addition, we demonstrate that the constituent linear terms in the commutator can be included at no extra cost. As an application, we show how to use the product formulas in a digital protocol for counterdiabatic driving, which increases the fidelity for quantum state preparation. We also discuss applications to quantum simulation of one-dimensional fermion chains with nearest- and next-nearest-neighbor hopping terms, and two-dimensional fractional quantum Hall phases.

}, doi = {https://doi.org/10.1103/PhysRevResearch.4.013191}, url = {https://arxiv.org/abs/2111.12177}, author = {Yu-An Chen and Andrew M. Childs and Mohammad Hafezi and Zhang Jiang and Hwanmun Kim and Yijia Xu} } @article {3153, title = {Error-correcting codes for fermionic quantum simulation}, year = {2022}, month = {10/16/2022}, abstract = {

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

}, keywords = {FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2210.08411}, url = {https://arxiv.org/abs/2210.08411}, author = {Chen, Yu-An and Alexey V. Gorshkov and Xu, Yijia} } @article {3124, title = {Quantum Many-Body Scars from Einstein-Podolsky-Rosen States in Bilayer Systems}, year = {2022}, month = {9/12/2022}, abstract = {

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

}, keywords = {FOS: Physical sciences, Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2209.05527}, url = {https://arxiv.org/abs/2209.05527}, author = {Wildeboer, Julia and Langlett, Christopher M. and Yang, Zhi-Cheng and Alexey V. Gorshkov and Iadecola, Thomas and Xu, Shenglong} } @article {3204, title = {A scheme to create and verify scalable entanglement in optical lattice}, journal = {npj Quantum Information}, volume = {8}, year = {2022}, month = {9/4/2022}, abstract = {

To achieve scalable quantum information processing, great efforts have been devoted to the creation of large-scale entangled states in various physical systems. Ultracold atom in optical lattice is considered as one of the promising platforms due to its feasible initialization and parallel manipulation. In this work, we propose an efficient scheme to generate and characterize global entanglement in the optical lattice. With only two-layer quantum circuits, the generation utilizes two-qubit entangling gates based on the superexchange interaction in double wells. The parallelism of these operations enables the generation to be fast and scalable. To verify the entanglement of this non-stabilizer state, we mainly design three complementary detection protocols which are less resource-consuming compared to the full tomography. In particular, one just needs two homogenous local measurement settings to identify the entanglement property. Our entanglement generation and verification protocols provide the foundation for the further quantum information processing in optical lattice.

}, doi = {10.1038/s41534-022-00609-0}, url = {https://arxiv.org/abs/2209.01531}, author = {You Zhou and Bo Xiao and Meng-Da Li and Qi Zhao and Zhen-Sheng Yuan and Xiongfeng Ma and Jian-Wei Pan} } @article {3009, title = {Self-Testing of a Single Quantum System: Theory and Experiment}, year = {2022}, month = {3/17/2022}, abstract = {

Certifying individual quantum devices with minimal assumptions is crucial for the development of quantum technologies. Here, we investigate how to leverage single-system contextuality to realize self-testing. We develop a robust self-testing protocol based on the simplest contextuality witness for the simplest contextual quantum system, the Klyachko-Can-Binicio{\u g}lu-Shumovsky (KCBS) inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements (to an ideal configuration) as a function of the value of the witness under a pragmatic assumption on the measurements we call the KCBS orthogonality condition. We apply the method in an experiment with randomly chosen measurements on a single trapped 40Ca+ and near-perfect detection efficiency. The observed statistics allow us to self-test the system and provide the first experimental demonstration of quantum self-testing of a single system. Further, we quantify and report that deviations from our assumptions are minimal, an aspect previously overlooked by contextuality experiments.

}, keywords = {Atomic Physics (physics.atom-ph), FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.48550/arXiv.2203.09003}, url = {https://arxiv.org/abs/2203.09003}, author = {Hu, Xiao-Min and Xie, Yi and Arora, Atul Singh and Ai, Ming-Zhong and Bharti, Kishor and Zhang, Jie and Wu, Wei and Chen, Ping-Xing and Cui, Jin-Ming and Liu, Bi-Heng and Huang, Yun-Feng and Li, Chuan-Feng and Guo, Guang-Can and Roland, J{\'e}r{\'e}mie and Cabello, Ad{\'a}n and Kwek, Leong-Chuan} } @article {2808, title = {Rainbow Scars: From Area to Volume Law}, year = {2021}, month = {7/12/2021}, abstract = {

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

}, url = {https://arxiv.org/abs/2107.03416}, author = {Christopher M. Langlett and Zhi-Cheng Yang and Julia Wildeboer and Alexey V. Gorshkov and Thomas Iadecola and Shenglong Xu} } @article {2911, title = {Spin chains, defects, and quantum wires for the quantum-double edge}, year = {2021}, month = {11/23/2021}, abstract = {

Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in several topological quantum computation schemes. Underpinning their established understanding is the quantum Ising spin chain, which can be recast as a fermionic model or viewed as a standalone effective theory for the surface-code edge -- both of which harbor non-Abelian defects. We generalize these notions by deriving an effective Ising-like spin chain describing the edge of quantum-double topological order. Relating Majorana and parafermion modes to anyonic strings, we introduce quantum-double generalizations of non-Abelian defects. We develop a way to embed finite-group valued qunits into those valued in continuous groups. Using this embedding, we provide a continuum description of the spin chain and recast its non-interacting part as a quantum wire via addition of a Wess-Zumino-Novikov-Witten term and non-Abelian bosonization.

}, url = {https://arxiv.org/abs/2111.12096}, author = {Victor V. Albert and David Aasen and Wenqing Xu and Wenjie Ji and Jason Alicea and John Preskill} } @article {2299, title = {Accessing scrambling using matrix product operators}, journal = {Nature Physics }, volume = {16}, year = {2020}, month = {2/2020}, pages = {199-204}, abstract = {

Scrambling, a process in which quantum information spreads over a complex quantum system becoming inaccessible to simple probes, happens in generic chaotic quantum many-body systems, ranging from spin chains, to metals, even to black holes. Scrambling can be measured using out-of-time-ordered correlators (OTOCs), which are closely tied to the growth of Heisenberg operators. In this work, we present a general method to calculate OTOCs of local operators in local one-dimensional systems based on approximating Heisenberg operators as matrix-product operators (MPOs). Contrary to the common belief that such tensor network methods work only at early times, we show that the entire early growth region of the OTOC can be captured using an MPO approximation with modest bond dimension. We analytically establish the goodness of the approximation by showing that if an appropriate OTOC is close to its initial value, then the associated Heisenberg operator has low entanglement across a given cut. We use the method to study scrambling in a chaotic spin chain with 201 sites. Based on this data and OTOC results for black holes, local random circuit models, and non-interacting systems, we conjecture a universal form for the dynamics of the OTOC near the wavefront. We show that this form collapses the chaotic spin chain data over more than fifteen orders of magnitude.

}, doi = {https://doi.org/10.1038/s41567-019-0712-4}, url = {https://arxiv.org/abs/1802.00801}, author = {Shenglong Xu and Brian Swingle} } @article {2456, title = {The operator L{\'e}vy flight: light cones in chaotic long-range interacting systems}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {7/6/2020}, abstract = {

We propose a generic light cone phase diagram for chaotic long-range r\−α interacting systems, where a linear light cone appears for α\≥d+1/2 in d dimension. Utilizing the dephasing nature of quantum chaos, we argue that the universal behavior of the squared commutator is described by a stochastic model, for which the exact phase diagram is known. We provide an interpretation in terms of the L{\'e}vy flights and show that this suffices to capture the scaling of the squared commutator. We verify these phenomena in numerical computation of a long-range spin chain with up to 200 sites.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.124.180601}, url = {https://arxiv.org/abs/1909.08646}, author = {Tianci Zhou and Shenglong Xu and Xiao Chen and Andrew Guo and Brian Swingle} } @article {2672, title = {A Sparse Model of Quantum Holography}, year = {2020}, month = {8/5/2020}, abstract = {

We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, k, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed k. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when k is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.

}, url = {https://arxiv.org/abs/2008.02303}, author = {Shenglong Xu and Leonard Susskind and Yuan Su and Brian Swingle} } @article {2373, title = {Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization}, year = {2019}, month = {02/19/2019}, abstract = {

The many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this work, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a novel dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power-law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine-learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments.

}, url = {https://arxiv.org/abs/1902.07199}, author = {Shenglong Xu and Xiao Li and Yi-Ting Hsu and Brian Swingle and Sankar Das Sarma} } @article {2253, title = {Locality, Quantum Fluctuations, and Scrambling}, journal = {Phys. Rev. X }, volume = {9}, year = {2019}, month = {9/18/2019}, abstract = {

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront. In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wavefront. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a cross-over to a diffusively broadened wavefront. At small N we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively-broadened wavefront.

}, doi = {https://doi.org/10.1103/PhysRevX.9.031048}, url = {https://arxiv.org/abs/1805.05376}, author = {Shenglong Xu and Brian Swingle} } @article {2425, title = {The Speed of Quantum Information Spreading in Chaotic Systems}, year = {2019}, month = {08/19/2019}, abstract = {

We present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out and scramble into a form that is inaccessible to local measurements. To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state. As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed. We verify that the formula holds both for a quantum chaotic spin chain and in field theories with an AdS/CFT gravity dual. For the second case, we study in detail the dynamics of entanglement in two-sided Vaidya-AdS-Reissner-Nordstrom black branes. We also show that, with an appropriate decoding process, quantum information can be construed as moving at the information speed, and, in the case of AdS/CFT, we show that a locally detectable signal propagates at the information speed in a spatially local variant of the traversable wormhole setup.

}, url = {https://arxiv.org/abs/1908.06993}, author = {Josiah Couch and Stefan Eccles and Phuc Nguyen and Brian Swingle and Shenglong Xu} } @article {2203, title = {Scrambling dynamics across a thermalization-localization quantum phase transition}, year = {2018}, abstract = {

We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the operator dynamics is not very sensitive to the actual eigenstate localization transition. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.

}, url = {https://arxiv.org/abs/1807.06086}, author = {Subhayan Sahu and Shenglong Xu and Brian Swingle} } @article {1820, title = {Cooling a harmonic oscillator by optomechanical modification of its bath}, journal = {Physical Review Letters}, volume = {118}, year = {2017}, month = {2017/05/31}, pages = {223602}, abstract = {

Optomechanical systems show tremendous promise for high sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically-induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

}, doi = {doi.org/10.1103/PhysRevLett.118.223602}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.223602}, author = {Xunnong Xu and Thomas Purdy and J. M. Taylor} } @article {1913, title = {Dynamically induced robust phonon transport and chiral cooling in an optomechanical system}, journal = {Nature Communications}, volume = {8}, year = {2017}, month = {2017/06/19}, pages = {205}, abstract = {

The transport of sound and heat, in the form of phonons, has a fundamental material limit: disorder-induced scattering. In electronic and optical settings, introduction of chiral transport - in which carrier propagation exhibits broken parity symmetry - provides robustness against such disorder by preventing elastic backscattering. Here we experimentally demonstrate a path for achieving robust phonon transport even in the presence of material disorder, by dynamically inducing chirality through traveling-wave optomechanical coupling. Using this approach, we demonstrate dramatic optically-induced chiral transport for clockwise and counterclockwise phonons in a symmetric resonator. This induced chirality also enhances isolation from the thermal bath and leads to gain-free reduction of the intrinsic damping of the phonons. Surprisingly, this passive mechanism is also accompanied by a chiral reduction in heat load leading to a novel optical cooling of the mechanics. This technique has the potential to improve upon the fundamental thermal limits of resonant mechanical sensor, which cannot be otherwise attained through conventional optomechanical cooling.

}, doi = {10.1038/s41467-017-00247-7}, url = {https://arxiv.org/abs/1609.08674}, author = {Seunghwi Kim and Xunnong Xu and J. M. Taylor and Gaurav Bahl} } @article {1956, title = {Optomechanically-induced chiral transport of phonons in one dimension}, year = {2017}, month = {2017/01/10}, abstract = {

Non-reciprocal devices, with one-way transport properties, form a key component for isolating and controlling light in photonic systems. Optomechanical systems have emerged as a potential platform for optical non-reciprocity, due to ability of a pump laser to break time and parity symmetry in the system. Here we consider how the non-reciprocal behavior of light can also impact the transport of sound in optomechanical devices. We focus on the case of a quasi one dimensional optical ring resonator with many mechanical modes coupled to light via the acousto-optic effect. The addition of disorder leads to finite diffusion for phonon transport in the material, largely due to elastic backscattering between clockwise and counter-clockwise phonons. We show that a laser pump field, along with the assumption of high quality-factor, sideband-resolved optical resonances, suppresses the effects of disorder and leads to the emergence of chiral diffusion, with direction-dependent diffusion emerging in a bandwidth similar to the phase-matching bandwidth for Brillouin scattering. A simple diagrammatic theory connects the observation of reduced mechanical linewidths directly to the associated phonon diffusion properties, and helps explain recent experimental results.

}, url = {https://arxiv.org/abs/1701.02699}, author = {Xunnong Xu and J. M. Taylor} } @article {1787, title = {Quantum state tomography via reduced density matrices}, journal = {Physical Review Letters}, volume = {118}, year = {2017}, month = {2017/01/09}, pages = {020401}, abstract = {

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

}, doi = {10.1103/PhysRevLett.118.020401}, url = {http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.020401}, author = {Tao Xin and Dawei Lu and Joel Klassen and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Xian Ma and Guilu Long and Bei Zeng and Raymond Laflamme} } @article {2055, title = {Thermodynamic limits for optomechanical systems with conservative potentials}, journal = {Physical Review B}, volume = {96}, year = {2017}, month = {2017/11/13}, pages = {184106}, abstract = {

The mechanical force from light \– radiation pressure \– provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a function of external parameters. This non-analyticity, a key feature of thermodynamic phase transitions, suggests that there could be an effective thermodynamic description of optomechanical systems. Here we explicitly define the thermodynamic limit for optomechanical systems and derive a set of sufficient constraints on the system parameters as the mechanical system grows large. As an example, we show how these constraints can be satisfied in a system with Z2 symmetry and derive a free energy, allowing us to characterize this as an equilibrium phase transition.

}, doi = {10.1103/PhysRevB.96.184106}, url = {https://arxiv.org/abs/1707.05771}, author = {Stephen Ragole and Haitan Xu and John Lawall and J. M. Taylor} } @article {1957, title = {A quasi-mode theory of chiral phonons}, year = {2016}, month = {2016/12/29}, abstract = {

The coherence properties of mechanical resonators are often limited by multiple unavoidable forms of loss -- including phonon-phonon and phonon-defect scattering -- which result in the scattering of sound into other resonant modes and into the phonon bath. Dynamic suppression of this scattering loss can lift constraints on device structure and can improve tolerance to defects in the material, even after fabrication. Inspired by recent experiments, here we introduce a model of phonon losses resulting from disorder in a whispering gallery mode resonator with acousto-optical coupling between optical and mechanical modes. We show that a typical elastic scattering mechanism of high quality factor (Q) mechanical modes flips the direction of phonon propagation via high-angle scattering, leading to damping into modes with the opposite parity. When the optical mode overlaps co-propagating high-Q and bulk mechanical modes, the addition of laser cooling via sideband-resolved damping of the mechanical mode of a chosen parity also damps and modifies the response of the bulk modes of the same parity. This, in turn, simultaneously improves the quality factor and reduces the thermal load of the counter-propagating high-Q modes, leading to the dynamical creation of a cold phononic shield. We compare our theoretical results to the recent experiments of Kim et al., and find quantitative agreement with our theory.

}, url = {https://arxiv.org/abs/1612.09240}, author = {Xunnong Xu and Seunghwi Kim and Gaurav Bahl and J. M. Taylor} } @article {1907, title = {Steady-state superradiance with Rydberg polaritons}, journal = {arXiv:1611.00797}, year = {2016}, month = {2016/11/02}, abstract = {

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

}, url = {https://arxiv.org/abs/1611.00797}, author = {Zhe-Xuan Gong and Minghui Xu and Michael Foss-Feig and James K. Thompson and Ana Maria Rey and Murray Holland and Alexey V. Gorshkov} } @article {1689, title = {Tomography is necessary for universal entanglement detection with single-copy observables}, journal = {Physical Review Letters}, volume = {116}, year = {2016}, month = {2016/06/07}, pages = {230501}, abstract = {Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.}, doi = {10.1103/PhysRevLett.116.230501}, url = {http://arxiv.org/abs/1511.00581}, author = {Dawei Lu and Tao Xin and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Guilu Long and Jonathan Baugh and Xinhua Peng and Bei Zeng and Raymond Laflamme} } @article {1337, title = {From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating}, journal = {Annalen der Physik}, volume = {527}, year = {2015}, month = {2015/01/02}, pages = {81 - 88}, abstract = {We demonstrate a "membrane in the middle" optomechanical system using a silicon nitride membrane patterned as a subwavelength grating. The grating has a reflectivity of over 99.8\%, effectively creating two sub-cavities, with free spectral ranges of 6 GHz, optically coupled via photon tunneling. Measurements of the transmission and reflection spectra show an avoided crossing where the two sub-cavities simultaneously come into resonance, with a frequency splitting of 54 MHz. We derive expressions for the lineshapes of the symmetric and antisymmetric modes at the avoided crossing, and infer the grating reflection, transmission, absorption, and scattering through comparison with the experimental data. }, doi = {10.1002/andp.201400142}, url = {http://arxiv.org/abs/1407.1709v1}, author = {Corey Stambaugh and Haitan Xu and Utku Kemiktarak and J. M. Taylor and John Lawall} } @article {1604, title = {Observation of optomechanical buckling phase transitions}, year = {2015}, month = {2015/10/16}, abstract = {

Correlated phases of matter provide long-term stability for systems as diverse as solids, magnets, and potential exotic quantum materials. Mechanical systems, such as relays and buckling transition spring switches can yield similar stability by exploiting non-equilibrium phase transitions. Curiously, in the optical domain, observations of such phase transitions remain elusive. However, efforts to integrate optical and mechanical systems -- optomechanics -- suggest that a hybrid approach combining the quantum control of optical systems with the engineerability of mechanical systems may provide a new avenue for such explorations. Here we report the first observation of the buckling of an optomechanical system, in which transitions between stable mechanical states corresponding to both first- and second-order phase transitions are driven by varying laser power and detuning. Our results enable new applications in photonics and, given rapid progress in pushing optomechanical systems into the quantum regime, the potential for explorations of quantum phase transitions.

}, url = {http://arxiv.org/abs/1510.04971v1}, author = {Haitan Xu and Utku Kemiktarak and Jingyun Fan and Stephen Ragole and John Lawall 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 {1339, title = {Tunable Spin Qubit Coupling Mediated by a Multi-Electron Quantum Dot}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/06/04}, pages = {226803}, abstract = {We present an approach for entangling electron spin qubits localized on spatially separated impurity atoms or quantum dots via a multi-electron, two-level quantum dot. The effective exchange interaction mediated by the dot can be understood as the simplest manifestation of Ruderman-Kittel-Kasuya-Yosida exchange, and can be manipulated through gate voltage control of level splittings and tunneling amplitudes within the system. This provides both a high degree of tuneability and a means for realizing high-fidelity two-qubit gates between spatially separated spins, yielding an experimentally accessible method of coupling donor electron spins in silicon via a hybrid impurity-dot system. }, doi = {10.1103/PhysRevLett.114.226803}, url = {http://arxiv.org/abs/1312.1711v3}, author = {V. Srinivasa and H. Xu and J. M. Taylor} } @article {1350, title = {Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/7/26}, abstract = {Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multi-qubit gates, for all anyon models from Chern-Simons-Witten SU(2)$_k$ theory that support universal quantum computation by braiding ($k\geq 3,\ k \neq 4$). In the process, we show how the constructions of topological quantum memory and gates for $k=2,4$ connect naturally to those for $k\geq 3,\ k \neq 4$, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of Chern-Simons-Witten field theory. }, doi = {10.1103/PhysRevA.84.012332}, url = {http://arxiv.org/abs/1001.4085v2}, author = {Haitan Xu and J. M. Taylor} } @article {1850, title = {Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms}, journal = {Nature Phys.}, volume = {6}, year = {2010}, pages = {289}, url = {http://www.nature.com/nphys/journal/v6/n4/abs/nphys1535.html}, author = {Alexey V. Gorshkov and Hermele, M and Gurarie, V and Xu, C and Julienne, P S and Ye, J and Zoller, P and Demler, E and Lukin, M D and Rey, A M} } @article {1854, title = {Optimizing Slow and Stored Light for Multidisciplinary Applications}, journal = {Proc. SPIE}, volume = {6904}, year = {2008}, pages = {69040C}, url = {http://spie.org/x648.xml?product_id=772216\&Search_Origin=QuickSearch\&Search_Results_URL=http://spie.org/x1636.xml\&Alternate_URL=http://spie.org/x18509.xml\&Alternate_URL_Name=timeframe\&Alternate_URL_Value=Exhibitors\&UseJavascript=1\&Please_Wait_URL=http://s}, author = {Klein, M and Xiao, Y and Alexey V. Gorshkov and M Hohensee and C D Leung and M R Browning and Phillips, D F and Novikova, I and Walsworth, R L} } @article {1857, title = {Optimization of slow and stored light in atomic vapor}, journal = {Proc. SPIE}, volume = {6482}, year = {2007}, pages = {64820M}, url = {http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PSISDG00648200000164820M000001\&idtype=cvips\&gifs=Yes\&bproc=volrange\&scode=6400\%20-\%206499}, author = {Novikova, I and Alexey V. Gorshkov and Phillips, D F and Xiao, Y and Klein, M and Walsworth, R L} } @article {1297, title = {Sodium Bose-Einstein Condensates in an Optical Lattice}, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/10/10}, abstract = { The phase transition from a superfluid to a Mott insulator has been observed in a $^{23}$Na Bose-Einstein condensate. A dye laser detuned $\approx 5$nm red of the Na $3^2$S$ \to 3^2$P$_{1/2}$ transition was used to form the three dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the timescale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the Na$_2$ $(1) ^3\Sigma_g^+$ state. }, doi = {10.1103/PhysRevA.72.043604}, url = {http://arxiv.org/abs/cond-mat/0507288v1}, author = {K. Xu and Y. Liu and J. R. Abo-Shaeer and T. Mukaiyama and J. K. Chin and D. E. Miller and W. Ketterle and Kevin M. Jones and Eite Tiesinga} }