We propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via internal states of the atoms and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model, as a function of system parameters and the prepared initial state. Our proposal paves the way for the study of non-equilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.
Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University（成均馆大学 SKKU 纳米技术高级研究所 (SAINT)）；Institute of Fundamental Physics IFF-CSIC（西班牙国家研究委员会基础物理研究所 (IFF-CSIC)）；National University of Science and Technology “MISIS”（国立科技大学 MISIS）；Lebedev Physical Institute, Russian Academy of Sciences（俄罗斯科学院列别捷夫物理研究所）；Department of Chemistry, Yonsei University（延世大学化学系）；Department of Quantum Information, Yonsei University（延世大学量子信息系）
We propose a scalable analog quantum simulator for quantum electrodynamics (QED) in two spatial dimensions. The setup for the U(1) lattice gauge field theory employs inter-species spin-changing collisions in an ultra-cold atomic mixture trapped in an optical lattice. Building on the previous one-dimensional implementation scheme of Ref. [1] we engineer spatial plaquette terms for magnetic fields, thus solving a major obstacle towards experimental realizations of realistic gauge theories in higher dimensions. We apply our approach to pure gauge theory and discuss how the phenomenon of confineme…
Quantum spin models find applications in many different areas, such as spintronics, high-Tc superconductivity, and even complex optimization problems. However, studying their many-body behaviour, especially in the presence of frustration, represents an outstanding computational challenge. To overcome it, quantum simulators based on cold, trapped atoms and ions have been built, shedding light already on many non-trivial phenomena. Unfortunately, the models covered by these simulators are limited by the type of interactions that appear naturally in these systems. Waveguide QED setups have recent…
We study information scrambling, as diagnosed by the out-of-time order correlations (OTOCs), in a system of large spins collectively interacting via spatially inhomogeneous and incommensurate exchange couplings. The model is realisable in a cavity QED system in the dispersive regime. Fast scrambling, signalled by an exponential growth of the OTOCs, is observed when the couplings do not factorise into the product of a pair of local interaction terms, and at the same time the state of the spins points initially coplanar to the equator of the Bloch sphere. When one of these conditions is not real…
Spontaneous creation of electron-positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy-momentum relation for the Dirac fermions. This fundamental prediction of Quantum Electrodynamics (QED) has not yet been confirmed experimentally as the generation of a sufficiently strong electric field extending over a large enough space-time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low energy…
We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry $\mathbb{Z}_n$, approximating the $U(1)$ theory for large $n$. We analyze the role of the finiteness of the gauge fields and the properties of physical states, that satisfy a generalized Gauss's law. We finally discuss a possible implementation strategy, that involves an effective dynamics in physical space.
We investigate the simulation of Jahn-Teller models with two non-degenerate vibrational modes using a circuit QED architecture. Typical Jahn-Teller systems are anisotropic and require at least a two-frequency description. The proposed simulator consists of two superconducting lumped-element resonators interacting with a common flux qubit in the ultrastrong coupling regime. We translate the circuit QED model of the system to a two-frequency Jahn-Teller Hamiltonian and calculate its energy eigenvalues and the emission spectrum of the cavities. It is shown that the system can be systematically tu…
High-order topological insulator (HOTI) occupies an important position in topological band theory due to its exotic bulk-edge correspondence. Recently, it has been predicted that external magnetic field can introduce rich physics into two-dimensional (2D) HOTIs. However, up to now the theoretical description is still incomplete and the experimental realization is still lacking. Here we investigate the influence of continuously varying magnetic field on 2D Su-Schriffer-Heeger lattice, which is one of the most celebrated HOTI models, and proposed a corresponding circuit quantum electrodynamics (…
We propose a class of quantum simulators for antiferromagnetic spin systems, based on coupled photonic cavities in presence of two-photon driving and dissipation. By modeling the coupling between the different cavities through a hopping term with negative amplitude, we solve numerically the quantum master equation governing the dynamics of the open system and determine its non-equilibrium steady state. Under suitable conditions, the steady state can be described in terms of the degenerate ground states of an antiferromagnetic Ising model. When the geometry of the cavity array is incommensurate…
We show how to implement a Rydberg-atom quantum simulator to study the non-equilibrium dynamics of an Abelian (1+1)-D lattice gauge theory. The implementation locally codifies the degrees of freedom of a $\mathbf{Z}_3$ gauge field, once the matter field is integrated out by means of the Gauss' local symmetries. The quantum simulator scheme is based on current available technology and scalable to considerable lattice sizes. It allows, within experimentally reachable regimes, to explore different string dynamics and to infer information about the Schwinger $U(1)$ model.
In order to examine whether or not the quantum phase transition of Dicke type exists in realistic systems, we revisit the model setup of the superconducting circuit QED from a microscopic many-body perspective based on the BCS theory with pseudo-spin presentation. By deriving the Dicke model with the correct charging terms from the minimum coupling principle, it is shown that the circuit QED system can exhibit superradiant quantum phase transition in the limit N\rightarrow\infty. The critical point could be reached at easiness by adjusting the extra parameters, the ratio of Josephson capacitan…
Recent theoretical schemes for utilizing cavity QED models as quantum simulators are reviewed. By considering a quadrature representation for the fields, it is shown how Jahn-Teller models, effective Abelian or non-Abelian gauge potentials, transverse Hall currents, and relativistic effects naturally arise in these systems. Some of the analytical predictions are verified numerically using realistic experimental parameters taking into account for system losses. Thereby demonstrating their feasibility with current experimental setups.
We show how a quantum Ising spin chain in a time-dependent transverse magnetic field can be simulated and experimentally probed in the framework of circuit QED with current technology. The proposed setup provides a new platform for observing the nonequilibrium dynamics of interacting many-body systems. We calculate its spectrum to offer a guideline for its initial experimental characterization. We demonstrate that quench dynamics and the propagation of localized excitations can be observed with the proposed setup and discuss further possible applications and modifications of this circuit QED q…
Experimental observation of Higgs oscillations and their power-law decay across pairing regimes in a cavity QED quantum simulator
JILA, NIST and University of Colorado（JILA，美国国家标准与技术研究院和科罗拉多大学）；Department of Physics, University of Colorado（科罗拉多大学物理系）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Center for Theory of Quantum Matter, University of Colorado（科罗拉多大学量子物质理论中心）；Thomas J. Watson, Sr., Laboratory of Applied Physics, Kavli Nanoscience Institute, and Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院托马斯·J·沃森Sr.应用物理实验室、卡弗里纳米科学研究所和量子信息与物质研究所）
We study several dynamical properties of a recently proposed implementation of the quantum transverse-field Ising chain in the framework of circuit QED. Particular emphasis is placed on the effects of disorder on the nonequilibrium behavior of the system. We show that small amounts of fabrication-induced disorder in the system parameters do not jeopardize the observation of previously-predicted phenomena. Based on a numerical extraction of the mean free path of the system, we also provide a simple quantitative estimate for certain disorder effects on the nonequilibrium dynamics of the circuit …
We propose an analog quantum simulator for the Holstein molecular-crystal model based on a superconducting circuit QED system in the dispersive regime. By varying the driving field on the superconducting resonators, one can readily access both the adiabatic and anti-adiabatic regimes of this model. Strong e-ph coupling required for small-polaron formation can also be reached. We show that small-polaron state of arbitrary quasimomentum can be generated by applying a microwave pulse to the resonators. We also show that significant squeezing in the resonator modes can be achieved in the polaron-c…
A way of constructing continuous matrix product states (cMPS) for coupled fields is presented here. The cMPS is a variational \emph{ansatz} for the ground state of quantum field theories in one dimension. Our proposed scheme is based in the physical interpretation in which the cMPS class can be produced by means of a dissipative dynamic of a system interacting with a bath. We study the case of coupled bosonic fields. We test the method with previous DMRG results in coupled Lieb Liniger models. Besides, we discuss a novel application for characterizing the Luttinger liquid theory emerging in th…
Analog quantum simulators can be used to study quantum correlation in novel many-body systems by emulating the Hamiltonian of these systems. One essential question in quantum simulation is to probe the properties of an emulated many-body system. Here we present a circuit QED scheme for probing such properties by measuring the spectrum of a superconducting resonator coupled to a quantum simulator. We first study a general framework of this approach, and show that the spectrum of the resonator is directly related to the correlation function of the coupling operator between the resonator and the …
Quantum transmission lines are a central to superconducting and hybrid quantum computing. Parallel to these developments are those of left-handed meta-materials. They have a wide variety of applications in photonics from the microwave to the visible range such as invisibility cloaks and perfect flat lenses. For classical guided microwaves, left-handed transmission lines have been proposed and studied on the macroscopic scale. We combine these ideas in presenting a left-handed/right-handed hybrid transmission line for applications in quantum optics on a chip. The resulting system allows circuit…
An exciting frontier in quantum information science is the realization and control of complex quantum many-body systems. Hybrid nanophotonic system with cold atoms has emerged as the paradigmatic platform for engineering long-range spin models from the bottom up, exploiting their modal geometry and group dispersion for tailored interactions. An important challenge is the physical limitation imposed by the photonic bath, constraining the types of local Hamiltonians that decompose the available physical models and restricting the spatial dimensions to that of the dielectric media. However, at th…
Recently the Rydberg blockade effect has been utilized to realize quantum spin liquid on the kagome lattice. Evidence of quantum spin liquid has been obtained experimentally by directly measuring non-local string order. In this letter, we report a BCS-type variational wave function study of the spin liquid state in this model. This wave function is motivated by mapping the Rydberg blockade model to a lattice gauge theory, where the local gauge conservations replace the role of constraints from the Rydberg blockade. We determine the variational parameter from the experimental measurement of the…
We consider a system of ultracold atoms in an optical lattice as a quantum simulator for electron-positron pair production in quantum electrodynamics (QED). For a setup in one spatial dimension, we investigate the nonequilibrium phenomenon of pair production including the backreaction leading to plasma oscillations. Unlike previous investigations on quantum link models, we focus on the infinite-dimensional Hilbert space of QED and show that it may be well approximated by experiments employing Bose-Einstein condensates interacting with fermionic atoms. The calculations based on functional integ…
We study the ground-state properties of a class of $\mathbb{Z}_n$ lattice gauge theories in 1 + 1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the $\mathrm{U}(1)$ group, preserve the unitary character of the minimal coupling, and have therefore the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-$n$ limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main …
Quantum Simulation of Strongly Correlated Fermion-Phonon Models in Circuit QED
Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum Jülich（朱利希研究中心量子计算分析研究所）；Theoretical Physics, Saarland University（萨尔兰州立大学理论物理系）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）
The Unruh effect is a quantum relativistic effect where the accelerated observer perceives the vacuum as a thermal state. Here we propose the experimental realization of the Unruh effect for interacting ultracold fermions in optical lattices by a sudden quench resulting in vacuum acceleration with varying interactions strengths in the real temperature background. We observe the inversion of statistics for the low lying excitations in the Wightman function as a result of competition between the spacetime and BCS Bogoliubov transformations. This paper opens up new perspectives for simulators of …
Quantum vacuum fluctuations are a direct manifestation of Heisenberg's uncertainty principle. The dynamical Casimir effect allows for the observation of these vacuum fluctuations by turning them into real, observable photons. However, the observation of this effect in a cavity QED experiment would require the rapid variation of the length of a cavity with relativistic velocities, a daunting challenge. Here, we propose a quantum simulation of the dynamical Casimir effect using an ion chain confined in a segmented ion trap. We derive a discrete model that enables us to map the dynamics of the mu…
Simulation of topological superconductors and their competing orders using photon-mediated interactions
JILA, NIST and Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系、NIST和JILA）；Center for Theory of Quantum Matter, University of Colorado, Boulder（科罗拉多大学博尔德分校量子物质理论中心）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）
Laser cooled and quantum degenerate atoms are widely being pursued as quantum simulators that may explain the behavior of strongly correlated material systems, and as the basis of today's most precise sensors. A key challenge towards these goals is to understand and control coherent interactions between the atoms. Here, we observe long-range exchange interactions mediated by an optical cavity, which manifest as tunable spin-spin interactions on the pseudo spin-1/2 system composed of the millihertz linewidth clock transition in strontium. We observe the so-called one axis twisting dynamics, the…
Quantum simulators based on atoms or molecules often have long-range interactions due to dipolar or Coulomb interactions. We present a method based on Floquet engineering to turn a long-range interaction into a short-range one. By modulating a magnetic-field gradient with one or a few frequencies, one reshapes the interaction profile, such that the system behaves as if it only had nearest-neighbor interactions. Our approach works in both one and two dimensions and for both spin-1/2 and spin-1 systems. It does not require individual addressing, and is applicable to all experimental systems with…
Lattice models of fermions, bosons, and spins have long served to elucidate the essential physics of quantum phase transitions in a variety of systems. Generalizing such models to incorporate driving and dissipation has opened new vistas to investigate nonequilibrium phenomena and dissipative phase transitions in interacting many-body systems. We present a framework for the treatment of such open quantum lattices based on a resummation scheme for the Lindblad perturbation series. Employing a convenient diagrammatic representation, we utilize this method to obtain relevant observables for the o…
Quantum simulations of High Energy Physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge and Lorentz invariance. In this paper we discuss these special requirements, and present a new method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interac…
Quantised sound waves -- phonons -- govern the elastic response of crystalline materials, and also play an integral part in determining their thermodynamic properties and electrical response (e.g., by binding electrons into superconducting Cooper pairs). The physics of lattice phonons and elasticity is absent in simulators of quantum solids constructed of neutral atoms in periodic light potentials: unlike real solids, traditional optical lattices are silent because they are infinitely stiff. Optical-lattice realisations of crystals therefore lack some of the central dynamical degrees of freedo…
Analog quantum simulation - the technique of using one experimentally well-controlled physical system to mimic the behavior of another - has quickly emerged as one of the most promising near term strategies for studying strongly correlated quantum many-body systems. In particular, systems of interacting photons, realizable in solid-state cavity and circuit QED frameworks, for example, hold tremendous promise for the study of nonequilibrium many-body phenomena due to the capability to locally create and destroy photons. These systems are typically modeled using a Jaynes-Cummings-Hubbard (JCH) H…
Tunable-Size Unruh-DeWitt Detector in a Multimode Cavity
Institut für Theoretische Physik, Universität Innsbruck（因斯布鲁克大学理论物理研究所）；Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Institute of Physics, Maria Curie-Skłodowska University（玛丽亚·居里-斯克沃多夫斯卡大学物理研究所）
Recently quantum simulators have been constructed to investigate experimentally the most prominent theoretical four-point many-body system described by the Hubbard model. By varying the coupling strength of the four-point interaction in relation to the kinetic term, one can analyze the phase structure of the model. This intriguing fact leads us to investigate whether similar Hamiltonians with four-point interactions can also be studied as a function of their four-point coupling strength. In this paper, we reexamine the Nambu-Jona-Lasinio model, regarding it generally beyond the context of quan…
