Atom-cavity System Research Articles

Atom cavity encoding for NP-complete problems

We consider an atom-cavity system having long-range atomic interactions mediated by cavity modes. It has been shown that quantum simulations of spin models with this system can naturally be used to solve number partition problems. Here, we present encoding schemes for numerous nondeterministic polynomial-time complete (NP-complete) problems, encompassing the majority of Karp’s 21 NP-complete problems. We find a number of such computation problems can be encoded by the atom-cavity system at a linear cost of atom number. There are still certain problems that cannot be encoded by the atom-cavity as efficiently, such as quadratic unconstrained binary optimization (QUBO), and the Hamiltonian cycle. For these problems, we provide encoding schemes with a quadratic or quartic cost in the atom number. We expect this work to provide important guidance to search for the practical quantum advantage of the atom-cavity system in solving NP-complete problems. Moreover, the encoding schemes we develop here may also be adopted in other optical systems for solving NP-complete problems, where a similar form of Mattis-type spin glass Hamiltonian as in the atom-cavity system can be implemented.

Symmetry breaking and non-ergodicity in a driven-dissipative ensemble of multilevel atoms in a cavity

Dissipative light-matter systems can display emergent collective behavior. Here, we report a Z2-symmetry-breaking phase transition in a system of multilevel Rb87 atoms strongly coupled to a weakly driven two-mode optical cavity. In the symmetry-broken phase, nonergodic dynamics manifests in the emergence of multiple stationary states with disjoint basins of attraction. This feature enables the amplification of a small atomic population imbalance into a characteristic macroscopic cavity transmission signal. Our experiment does not only showcase strongly dissipative atom-cavity systems as platforms for probing nontrivial collective many-body phenomena, but also highlights their potential for hosting technological applications in the context of sensing, density classification, and pattern retrieval dynamics within associative memories. Published by the American Physical Society 2024

Magnetically induced perfect absorption and slow light trapping in a double-cavity structure with strontium atoms.

Photon manipulation using quantum interference is crucial for understanding the physical meaning of optical phenomena and promoting photonic quantum technologies. Here, two fundamentally optical phenomena, including coherent perfect absorption (CPA) and slow light trapping, are proposed simultaneously in a double-cavity structure with strontium atoms. When two counterpropagating probe fields are injected into the coupled atom-cavity system, we demonstrate that double-cavity-mediated interference assisted by the atomic Zeeman effect can be utilized to control multiple mode splitting in the transmission light. According to the analytical CPA criterion, we report that these splitting modes in the output spectra can be completely absorbed, forming multiple perfect or nearly perfect absorption. More importantly, we illustrate that sizable intracavity field localization can be found at the multiple CPA points, as an amount of system energy stores in the intracavity fields and the atomic excited states. In this case, the dispersion property of the system enables the localized intracavity fields to operate in the long-lived slow-light regime, whose group delay is tuned to be in the order of microseconds.

Analytical solution for Ξ-type qutrit interacting nonlinearly with a cavity field through Kerr-like medium with intrinsic noise present

This paper presents an analytical solution for the Milburn equation describing the interaction between a 3-level atom in a [Formula: see text]-configuration, a cavity field, and a nonlinear Kerr-like medium. The Hamiltonian of the model is presented in the rotating wave approximation (RWA) under specific conditions. The obtained analytical solution accounts for the impact of intrinsic decoherence and nonlinear terms on the dynamics of various physical phenomena. Specifically, we explore the behavior of atomic population, entropy functions, entanglement, negativity, and correlation, highlighting their dependence on the physical parameters of the [Formula: see text]-level atom-cavity system.

Spontaneous breaking of time translation symmetry in a system without periodic external driving.

It is known that spontaneous time translation symmetry-breaking can occur in systems periodically driven at a certain period. We predict a spontaneous breaking of time translation symmetry in an atom-cavity system without external driving, in which a time scale is determined by the time of light bypass of the resonator. We demonstrate that there is a parameter range, in which a system state returns to its initial state only after two bypasses of the resonator. We believe that the predicted phenomenon opens a way to a new direction in the time crystal field.

Observation of a phase transition from a continuous to a discrete time crystal

Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry. DTCs are periodically driven systems that oscillate with a subharmonic of the external drive, while CTCs are continuously driven and oscillate with a frequency intrinsic to the system. Here, we explore a phase transition from a continuous time crystal to a discrete time crystal. A CTC with a characteristic oscillation frequency ωCTC is prepared in a continuously pumped atom-cavity system. Modulating the pump intensity of the CTC with a frequency ωdr close to 2ωCTC leads to robust locking of ωCTC to ωdr/2 , and hence a DTC arises. This phase transition in a quantum many-body system is related to subharmonic injection locking of non-linear mechanical and electronic oscillators or lasers.

Cavity-Induced Optical Nonreciprocity Based on Degenerate Two-Level Atoms.

We developed and experimentally realized a scheme of optical nonreciprocity (ONR) by using degenerate two-level atoms embedded in an optical ring cavity. For the degenerate transition Fg = 4 ↔ Fe = 3, we first studied the cavity-transmission property in different coupling field configurations and verified that under the strong-coupling regime, the single-dark-state peak formed by electromagnetically induced transparency (EIT) showed ONR. The stable ground-state Zeeman coherence for Λ-chains involved in the degenerate two-level system was found to be important in the formation of intracavity EIT. However, different from the three-level atom-cavity system, in the degenerate two-level system, the ONR effect based on intracavity EIT occurred only at a low probe intensity, because the cavity-atom coupling strength was weakened in the counter-propagating probe and coupling field configuration. Furthermore, ONR transmission with a high contrast and linewidth-narrowing was experimentally demonstrated.

High-efficiency all-optical switching based on broadband coherent perfect absorption in an atom-cavity system

We propose an ultrahigh-efficiency and broadband all-optical switching scheme based on coherent perfect absorption (CPA) in linear and nonlinear excitation regimes in a cavity quantum electrodynamics (CQED) system. Two separate atomic transitions are excited simultaneously by two signal fields coupled from two ends of an optical cavity under the collective strong coupling condition. Three polariton eigenstates are produced which can be tuned freely by varying system parameters. The output field intensities of multiple channels are zero when the CPA criterion is satisfied. However, destructive quantum interference can be induced by a free-space weak control laser when it is tuned to be resonant to the polariton state. As a consequence, the CQED system acts as a coherent perfect light absorber/transmitter as the control field is turned on/off the polariton resonances. In particular, the proposed scheme may be used to realize broadband multi-throw all-optical switching in the nonlinear excitation regime. The proposed scheme is useful for constructing all-optical routing, all-optical communication networks and various all-optical logic elements.

Enhanced quantum resources via two distant atom-cavity systems under the influence of atomic dissipation

Quantum resources such as entanglement and coherence are the holy grail for modern quantum technologies. Although the unwanted environmental effects tackle quantum information processing tasks, suprisingly these key quantum resources may be protected and even enhanced by the implementation of some special hybrid open quantum systems. Here, we aim to show how a dissipative atom-cavity-system can be accomplished to generate enhanced quantum resources. To do so, we consider a couple of dissipative cavities, where each one contains two effective two-level atoms interacting with a single-mode cavity field. In practical applications, a classical laser field may be applied to drive each atomic subsystem. After driving the system, a Bell-state measurement is performed on the output of the system to quantify the entanglement and coherence. The obtained results reveal that the remote entanglement and coherence between the atoms existing inside the two distant cavities are not only enhanced, but can be stabilized, even under the action of dissipation. In contrast, the local entanglement between two atoms inside each dissipative cavity attenuates due to the presence of unwanted environmental effects. Nevertheless, the local coherence may show the same behavior as the remote coherence. Besides, the system provides the steady state entanglement in various interaction regimes, particularly in the strong atom-cavity coupling and with relatively large detuning. More interestingly, our numerical analyses demonstrate that the system may show a memory effect due to the fact that the death and revival of the entanglement take place during the interaction. Our proposed model may find potential applications for the implementation of long distance quantum networks. In particular, it facilitates the distribution of quantum resources between the nodes of large-scale quantum networks for secure communication.

Coherent and incoherent pumping of a three-level laser

This article investigates the quantum and semi-classical aspects of a three-level atom-cavity system within the context of cavity quantum electrodynamics. The study examines the behavior of the system through a quantum perspective and a semi-classical approximation. The steady-state master equation is solved in the atom-cavity basis, resulting in a closed set of equations describing the atom’s level occupancies and the cavity’s photon number. The accuracy of the semi-classical approximation is assessed by comparing it with quantum simulations. The research analyzes the system’s behavior near the laser threshold, highlighting the interplay between semi-classical and quantum behaviors. Additionally, the conversion of the three-level atom to a two-level atom is explored under specific conditions, enabling an investigation into the weak driving limit. Quantum simulation results are used to validate the proposed approximations. This work contributes to the understanding of atom-cavity interactions and provides insights into the transition from semi-classical to quantum behavior in such systems.

Ancilla-assisted protection of information: application to atom–cavity systems

Ancilla-assisted protection of information: application to atom–cavity systems

Unconventional photon blockade in the two-photon Jaynes–Cummings model with two-frequency cavity drivings and atom driving

In a two-frequency cavity driving and atom driving atom-cavity system, we find the photon blockade effect. In a truncated eigenstates space, we calculate the zero-delay second-order correlation function of the cavity mode analytically and obtain an optimal condition for the photon blockade. By including three transition pathways, we find that higher excitations of the cavity mode can be further suppressed and the zero-delay second-order correlation function can be reduced additionally. Based on the master equation, we simulate the system evolution and find that the analytical solutions match well with the numerical results. Our scheme is robust with small fluctuations of parameters and may be used as a new type of single photon source.

Universal Quantum Optimization with Cold Atoms in an Optical Cavity.

Cold atoms in an optical cavity have been widely used for quantum simulations of many-body physics, where the quantum control capability has been advancing rapidly in recent years. Here, we show the atom cavity system is universal for quantum optimization with arbitrary connectivity. We consider a single-mode cavity and develop a Raman coupling scheme by which the engineered quantum Hamiltonian for atoms directly encodes number partition problems. The programmability is introduced by placing the atoms at different positions in the cavity with optical tweezers. The number partition problem solution is encoded in the ground state of atomic qubits coupled through a photonic cavity mode, which can be reached by adiabatic quantum computing. We construct an explicit mapping for the 3-SAT and vertex cover problems to be efficiently encoded by the cavity system, which costs linear overhead in the number of atomic qubits. The atom cavity encoding is further extended to quadratic unconstrained binary optimization problems. The encoding protocol is optimal in the cost of atom number scaling with the number of binary degrees of freedom of the computation problem. Our theory implies the atom cavity system is a promising quantum optimization platform searching for practical quantum advantage.

Condensate Formation in a Dark State of a Driven Atom-Cavity System.

We demonstrate the formation of a condensate in a dark state of momentum states, in a pumped and shaken cavity-BEC system. The system consists of an ultracold quantum gas in a high-finesse cavity, which is pumped transversely by a phase-modulated laser. This phase-modulated pumping couples the atomic ground state to a superposition of excited momentum states, which decouples from the cavity field. We demonstrate how to achieve condensation in this state, supported by time-of-flight and photon emission measurements. With this, we show that the dark state concept provides a general approach to efficiently prepare complex many-body states in an open quantum system.

Quantum Nondemolition Measurements with Optical Parametric Amplifiers for Ultrafast Universal Quantum Information Processing

Realization of a room-temperature ultrafast photon-number-resolving quantum nondemolition (QND) measurement would have significant implications for photonic quantum information processing, enabling, for example, deterministic quantum computation in discrete-variable architectures, but the requirement for strong coupling has hampered the development of scalable implementations. In this work, we propose and analyze a nonlinear-optical route to photon-number-resolving QND using quadratic (i.e., χ(2)) nonlinear interactions. We show that the coherent pump field driving a frequency-detuned optical parametric amplifier (OPA) experiences displacements conditioned on the number of signal Bogoliubov excitations. A measurement of the pump displacement thus provides a QND measurement of the signal Bogoliubov excitations, projecting the signal mode to a squeezed photon-number state. We then show how our nonlinear OPA dynamics can be utilized to deterministically generate Gottesman-Kitaev-Preskill states with only additional Gaussian resources, offering an all-optical route for fault-tolerant quantum information processing in continuous-variable systems. Finally, we place these QND schemes into a more traditional context by highlighting analogies between the frequency-detuned optical parametric oscillator and multilevel atom-cavity quantum electrodynamics systems by showing how continuous monitoring of the outcoupled pump quadrature induces conditional localization of the intracavity signal mode onto squeezed photon-number states. Our analysis suggests that our proposal may be viable in near-term χ(2) nonlinear nanophotonics, highlighting the rich potential of the OPA as a universal tool for ultrafast non-Gaussian quantum state engineering and quantum computation.Received 18 October 2022Accepted 8 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.010333Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum computationQuantum engineeringQuantum information processingQuantum information processing with continuous variablesQuantum opticsQuantum state engineeringSecond order nonlinear optical processesQuantum InformationAtomic, Molecular & Optical

Tunable nonlinear coherent perfect absorption in cavity QED

We propose and analyze a scheme for tunable coherent perfect absorption (CPA) and near-perfect reflection (near CPR) in a three-level $\mathrm{\ensuremath{\Lambda}}$-type atom-cavity system. With electromagnetically-induced-transparency-type interference induced by a coherent coupling laser, it provides a method of tunable near CPR at two-photon resonance. By virtue of different coupling strengths, CPA can be tuned from the linear regime to the nonlinear or bistable regime at a fixed input-field frequency. In addition, the CPA regime can be switched to the near-CPR regime with variable linear absorption or gain by an incoherent pump field. This work suggests a mechanism for manipulation on perfect absorption and reflection theoretically which can potentially be applied to logical gates and optical switches for coherent optical computing and communication.

Single-photon switching in a Floquet waveguide-QED system with time-modulated coupling constants

The dynamical control of single-photon scattering in a one-dimensional waveguide coupled to a Floquet atom-cavity system with time-modulated coupling constants is investigated. The analytical expressions for determining the scattering properties are obtained by using an effective Floquet Hamiltonian in real space. The photon transport is extremely sensitive to the time-modulated atom-cavity coupling strengths. Two cases, i.e., the effective Floquet Hamiltonian either includes or excludes a static coupling term, are discussed in detail. The results show that, with such Floquet atom-cavity configuration, an active photonic switch with nearly ideal switching contrast could be implemented. The transmission of the waveguide photons with different frequencies can dynamically be switched on or off via adjusting the modulated amplitude or relative modulated phase no matter whether the static coupling between the atom and the two cavity modes is considered or not. The application of the dynamic modulated atom-cavity coupling strengths instead of a purely static one makes our photonic switch more tunable. These results are expected to be applicable in quantum information processing and in active quantum device design involving dynamical modulation.

Self-organized limit cycles in red-detuned atom-cavity systems

Recent experimental advances in the field of cold-atom cavity QED provide a powerful tool for exploring nonequilibrium correlated quantum phenomena beyond conventional condensed-matter scenarios. We present the dynamical phase diagram of a driven Bose-Einstein condensate coupled with the light field of a cavity, with a transverse driving field red-detuned from atomic resonance. We identify regions in parameter space showing dynamical instabilities in the form of limit cycles, which evolve into chaotic behavior in the strong driving limit. Such limit cycles originate from the interplay between cavity dissipation and atom-induced resonance frequency shift, which modifies the phase of cavity mode and gives excessive negative feedback on the atomic density modulation, leading to instabilities of the superradiant scattering. We find interesting merging of the limit cycles related by a ${Z}_{2}$ symmetry, and identify a limit cycle formed by purely atomic excitations. The effects of quantum fluctuations and atomic interactions are also investigated.

Coherent resonant coupling between atoms and a mechanical oscillator mediated by cavity-vacuum fluctuations

We show that an atom can be coupled to a mechanical oscillator via quantum vacuum fluctuations of a cavity field enabling energy transfer processes between them. In a hybrid quantum system consisting of a cavity resonator with a movable mirror and an atom, these processes are dominated by two pair-creation mechanisms: the counterrotating (atom-cavity system) and dynamical Casimir interaction terms (optomechanical system). Because of these two pair-creation mechanisms, the resonant atom-mirror coupling is the result of high-order virtual processes with different transition paths well described in our theoretical framework. We perform a unitary transformation to the atom-mirror system Hamiltonian, exhibiting two kinds of multiple-order transitions of the pair creation. By tuning the frequency of the atom, we show that photon frequency conversion can be realized within a cavity of multiple modes. Furthermore, when involving two atoms coupled to the same mechanical mode, a single vibrating excitation of the mechanical oscillator can be simultaneously absorbed by the two atoms. Considering recent advances in strong and ultrastrong coupling for cavity optomechanics and other systems, we believe our proposals can be implemented using available technology.

Gaussian-wave-packet model for single-photon generation based on cavity quantum electrodynamics under adiabatic and nonadiabatic conditions

For single-photon generation based on cavity quantum electrodynamics, we investigate a practical model assuming a Gaussian wavepacket. This model makes it possible to comprehensively analyze the temporal dynamics of an atom-cavity system with both adiabatic and nonadiabatic conditions using analytical expressions. These results enable us to clarify the relationship between pulse width and maximum success probability, over the full range of coupling regimes, for arbitrary detunings. We demonstrate how to achieve a high success probability while keeping a short pulse width by optimizing the cavity transmittance parameter. Our formulations provide a practical tool for efficient single-photon generation in a wide variety of experimental platforms.