@article {3258, title = {Candidate for a passively protected quantum memory in two dimensions}, year = {2023}, month = {3/2/2023}, abstract = {

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

}, url = {https://arxiv.org/abs/2205.09767}, author = {Simon Lieu and Yu-Jie Liu and Alexey V. Gorshkov} } @article {3073, title = {Candidate for a self-correcting quantum memory in two dimensions}, year = {2022}, month = {5/19/2022}, abstract = {

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

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

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

}, keywords = {FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.01275}, url = {https://arxiv.org/abs/2211.01275}, author = {Feng, Lei and Katz, Or and Haack, Casey and Maghrebi, Mohammad and Alexey V. Gorshkov and Gong, Zhexuan and Cetina, Marko and Monroe, Christopher} } @article {2813, title = {Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models}, year = {2021}, month = {5/13/2021}, abstract = {

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

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

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

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

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

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

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

}, url = {https://arxiv.org/abs/2105.01087}, author = {Igor Boettcher and Alexey V. Gorshkov and Alicia J. Koll{\'a}r and Joseph Maciejko and Steven Rayan and Ronny Thomale} } @article {2364, title = {Circuit Complexity across a Topological Phase Transition}, journal = {Physical Review Research }, volume = {2}, year = {2020}, month = {03/16/2020}, pages = {013323}, abstract = {

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

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

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

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

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

}, url = {https://arxiv.org/abs/2006.05593}, author = {Jonathan B. Curtis and Igor Boettcher and Jeremy T. Young and Mohammad F. Maghrebi and Howard Carmichael and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2406, title = {Complexity phase diagram for interacting and long-range bosonic Hamiltonians}, year = {2019}, month = {06/10/2019}, abstract = {

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

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

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

}, doi = {https://doi.org/10.1103/PhysRevLett.122.150601}, url = {https://arxiv.org/abs/1810.02365}, author = {Fangli Liu and Rex Lundgren and Paraj Titum and Guido Pagano and Jiehang Zhang and Christopher Monroe and Alexey V. Gorshkov} } @article {2216, title = {Coherent optical nano-tweezers for ultra-cold atoms}, year = {2018}, abstract = {

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

}, url = {https://arxiv.org/abs/1808.02487}, author = {P. Bienias and S. Subhankar and Y. Wang and T-C Tsui and F. Jendrzejewski and T. Tiecke and G. Juzeliunas and L. Jiang and S. L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {1952, title = {Complexity of sampling as an order parameter}, year = {2017}, month = {2017/03/15}, abstract = {

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

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

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

}, doi = {10.1103/PhysRevLett.119.043602}, url = {https://arxiv.org/abs/1608.06068}, author = {Emil Zeuthen and Michael Gullans and Mohammad F. Maghrebi and Alexey V. Gorshkov} } @article {1960, title = {Causality and quantum criticality in long-range lattice models}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/03/17}, pages = {125128}, doi = {10.1103/PhysRevB.93.125128}, url = {http://link.aps.org/doi/10.1103/PhysRevB.93.125128}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1179, title = {Causality and quantum criticality with long-range interactions}, journal = {Physical Review B}, volume = {92}, year = {2016}, month = {2016/03/17}, pages = {125128}, abstract = { Quantum lattice systems with long-range interactions often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model and a fermionic model with long-range interactions, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of long-range interactions, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent. }, doi = {10.1103/PhysRevB.93.125128}, url = {http://arxiv.org/abs/1508.00906}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1737, title = {Collective phases of strongly interacting cavity photons}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/09/01}, pages = {033801}, abstract = {

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

}, doi = {http://dx.doi.org/10.1103/PhysRevA.94.033801}, url = {http://arxiv.org/abs/1601.06857}, author = {Ryan M. Wilson and Khan W. Mahmud and Anzi Hu and Alexey V. Gorshkov and Mohammad Hafezi and Michael Foss-Feig} } @article {1696, title = {Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems}, year = {2015}, month = {2015/10/05}, abstract = {Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)\~{}1/rα, directly relevant to ion-trap experiments. Using bosonization and renormalization group theory, we find CSB for α smaller than a critical exponent αc(<=3) depending on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal symmetry due to long-range interactions, and is described by a new universality class akin to the Berezinskii-Kosterlitz-Thouless transition. Our analytical findings are in good agreement with a numerical calculation. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.}, url = {http://arxiv.org/abs/1510.01325}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1507, title = {Coulomb bound states of strongly interacting photons}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/09/16}, pages = {123601}, abstract = { We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. }, doi = {10.1103/PhysRevLett.115.123601}, url = {http://arxiv.org/abs/1505.03859v1}, author = {Mohammad F. Maghrebi and Michael Gullans and P. Bienias and S. Choi and I. Martin and O. Firstenberg and M. D. Lukin and H. P. B{\"u}chler and Alexey V. Gorshkov} } @article {1186, title = {Controllable quantum spin glasses with magnetic impurities embedded in quantum solids }, journal = {Physical Review B}, volume = {88}, year = {2013}, month = {2013/7/24}, abstract = { Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo$_x$Y$_{1-x}$F$_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases. }, doi = {10.1103/PhysRevB.88.014426}, url = {http://arxiv.org/abs/1307.1130v1}, author = {Mikhail Lemeshko and Norman Y. Yao and Alexey V. Gorshkov and Hendrik Weimer and Steven D. Bennett and Takamasa Momose and Sarang Gopalakrishnan} } @article {1844, title = {Cavity QED with atomic mirrors}, journal = {New J. Phys.}, volume = {14}, year = {2012}, pages = {063003}, url = {http://iopscience.iop.org/1367-2630/14/6/063003/}, author = {D E Chang and Jiang, L and Alexey V. Gorshkov and H J Kimble} } @article {1173, title = {Coherent Quantum Optical Control with Subwavelength Resolution}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/3/7}, abstract = { We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed. }, doi = {10.1103/PhysRevLett.100.093005}, url = {http://arxiv.org/abs/0706.3879v2}, author = {Alexey V. Gorshkov and Liang Jiang and Markus Greiner and Peter Zoller and Mikhail D. Lukin} }