Abstract Simulating cavity quantum electrodynamics in synthetic platforms offers a route to studying light--matter physics without real photons. We reassess the frequently invoked analogy between harmonically trapped, spin--orbit-coupled atoms and the quantum Rabi and Dicke models, with particular emphasis on squeezing and entanglement. A single non-interacting atom realizes the quantum Rabi Hamiltonian exactly, up to elementary spin and phase-space rotations. For $N$ non-interacting atoms, however, the center-of-mass mode is only one member of a complete orthonormal set containing $N-1$ relative modes. We prove that, after all modes are included, the spin--spin terms generated by the collective mode cancel exactly against those generated by the relative modes. Equivalently, the original Hamiltonian is a sum of independent one-particle Hamiltonians and therefore cannot create interparticle entanglement from a separable state. Contact interactions invalidate this cancellation but do not remove the relative modes or turn the exact many-body Hamiltonian into a Dicke model. A one-mode Dicke description can arise only as a controlled low-energy approximation after all relevant relative excitations have been shown to be spectrally suppressed. We discuss this distinction together with experimental scales, finite temperature, and possible mode-selection strategies. We also distinguish the single-particle interference underlying density fringes from the interaction-stabilized stripe supersolid observed in many-body condensates.
Abstract Simulating cavity quantum electrodynamics in synthetic platforms offers a route to studying light--matter physics without real photons. We reassess the frequently invoked analogy between harmonically trapped, spin--orbit-coupled atoms and the quantum Rabi and Dicke models, with particular emphasis on squeezing and entanglement. A single non-interacting atom realizes the quantum Rabi Hamiltonian exactly, up to elementary spin and phase-space rotations. For N non-interacting atoms, however, the center-of-mass mode is only one member of a complete orthonormal set containing N−1 relative modes. We prove that, after all modes are included, the spin--spin terms generated by the collective mode cancel exactly against those generated by the relative modes. Equivalently, the original Hamiltonian is a sum of independent one-particle Hamiltonians and therefore cannot create interparticle entanglement from a separable state. Contact interactions invalidate this cancellation but do not remove the relative modes or turn the exact many-body Hamiltonian into a Dicke model. A one-mode Dicke description can arise only as a controlled low-energy approximation after all relevant relative excitations have been shown to be spectrally suppressed. We discuss this distinction together with experimental scales, finite temperature, and possible mode-selection strategies. We also distinguish the single-particle interference underlying density fringes from the interaction-stabilized stripe supersolid observed in many-body condensates.
Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.
The interaction of confined atoms with a single mode radiation field is the main subject in the theory of cavity quantum electrodynamics . The constraints imposed by the cavity on matter and radiation fields give rise to collective phenomena. One possible outcome is the enhanced and coherent spontaneous emission of photons by the atoms: the superradiance. As predicted by Dicke, conservation laws are essential in superradiance and are derived from the matter-interaction Hamiltonian . Here, we consider N two-level ultracold atoms interacting with a single mode bosonic field, in the Dicke Hamiltonian, and trapped inside a non-dissipative optical cavity . Numerical and analytical results derived from finite size regime indicate the matter–radiation coupling strength, λ , is insufficient to draw the complete picture of the system. Instead, they support the relevance of U ( 1 ) symmetry, which prompts the study of (i) particle and angular momentum conservation, (ii) the constraints imposed to correlation functions and (iii) the influence of symmetries in the system dynamics . Further exploring the U ( 1 ) and rotational symmetries permits a simple interpretation of antirotating contributions as spin–orbit operators. As application, we show two species of ultracold clouds develop interactions due to antirotating operators.
The coupled dynamics of the atom and photon fields in optical ring cavities with two counterpropagating modes give rise to both spin-orbit interactions as well as long-ranged interactions between atoms of a many-body system. At zero temperature, the interplay between the two-body and cavity-mediated interactions determines the ground state of a Bose-Einstein condensate. In this work, we find that cavity quantum electrodynamics in the weak-coupling regime favors a stripe-phase state over a plane-wave phase as the strength of cavity-mediated interactions increases. Indeed, the stripe phase is energetically stabilized even for condensates with attractive intraspecies and interspecies interactions for sufficiently large cavity interactions. The elementary excitation spectra in both phases correspond to linear dispersion relation at long wavelengths, indicating that both phases exhibit superfluidity, although the plane-wave phase also displays a characteristic roton-type feature. The results suggest that even in the weak-coupling regime, cavities can yield interesting new physics in ultracold quantum gases.
Abstract Spin–orbit–coupled Bose–Einstein condensates are a central platform for exploring quantum phase transitions and synthetic quantum matter, yet how entanglement behaves across these transitions remains largely unexplored. We analyze bipartite entanglement between synthetically dressed pseudo–spin states in a cavity–QED environment using a quantum–Langevin approach, where the coupled atom–photon fluctuations are governed by a non-Hermitian drift matrix. Steady-state quantum correlations are quantified through logarithmic negativity and entanglement fidelity. When cavity loss dominates over atomic dissipation, the cavity mediates only dispersive coupling between the pseudo-spins, and the entanglement remains weak and broadly distributed across the transition from the stripe-like mixed state to the plane-wave state. When atomic dissipation becomes the dominant channel, the fluctuation spectrum undergoes a qualitative and topological change: a set of spin-localized, edge-like photonic modes emerges. These non-Hermitian topological edge modes act as spectrally selective pathways that confine cavity-generated fluctuations around the pseudo–spin manifold, enhance their phase-space overlap, and produce sharply bounded regions of strong spin–spin entanglement in the Raman parameter plane. Entanglement fidelity verifies that the enhancement originates from topological edge-mode localization rather than from dissipation itself. Thus, non-Hermitian topological edge physics reorganizes the entanglement landscape across the phase transition of synthetically dressed atomic states, revealing a pathway to edge-mode-enhanced quantum entanglement in hybrid quantum systems.
We review the recent developments and the current status in the field of quantum-gas cavity QED. Since the first experimental demonstration of atomic self-ordering in a system composed of a Bose–Einstein condensate coupled to a quantized electromagnetic mode of a high-Q optical cavity, the field has rapidly evolved over the past decade. The composite quantum-gas-cavity systems offer the opportunity to implement, simulate, and experimentally test fundamental solid-state Hamiltonians, as well as to realize non-equilibrium many-body phenomena beyond conventional condensed-matter scenarios. This hinges on the unique possibility to design and control in open quantum environments photon-induced tunable-range interaction potentials for the atoms using tailored pump lasers and dynamic cavity fields. Notable examples range from Hubbard-like models with long-range interactions exhibiting a lattice-supersolid phase, over emergent magnetic orderings and quasicrystalline symmetries, to the appearance of dynamic gauge potentials and non-equilibrium topological phases. Experiments have managed to load spin-polarized as well as spinful quantum gases into various cavity geometries and engineer versatile tunable-range atomic interactions. This led to the experimental observation of spontaneous discrete and continuous symmetry breaking with the appearance of soft-modes as well as supersolidity, density and spin self-ordering, dynamic spin-orbit coupling, and non-equilibrium dynamical self-ordered phases among others. In addition, quantum-gas-cavity setups offer new platforms for quantum-enhanced measurements. In this review, starting from an introduction to basic models, we pedagogically summarize a broad range of theoretical developments and put them in perspective with the current and near future state-of-art experiments.
Present-day experiments have started to couple traditional simulations of ultracold atom experiments with quantum light-fields in cavities. This has provided a wealth of op- portunities to enlarge the number of interaction potentials: cavity mediated long-range interactions compete with kinetic energies, longitudinal fields, short-ranged collisional or magnetic spin-spin interactions. The intracavity many-body lattice models often have to be maintained far from equilibrium through the presence of external driving lasers that help to boost and engineer the various interaction potentials. The steady influx of energy is compensated by a steady stream of energy out of the atom-cavity system for example by photon losses or atomic spontaneous emission. Several experiments have demonstrated that such environments can give rise to new competing quantum phases. \nBut this long-standing ambition to push for models with tailorable interaction potentials can bring with it also considerable challenges in their theoretical description, since sponta- neous symmetry breaking transitions in many body lattice systems coupled to dynamical light-fields with single-photon character occur in the presence of drive and dissipation for the photonic force carriers. This clearly calls for model systems where the above men- tioned interplay of interactions, drive, dissipation and cooperative many-body behaviour can be theoretically studied to provide simple, experimentally verifiable predictions. \nThe Dicke model is, through its simplicity (an exactly solved ferromagnet with infinite range atom-atom interactions mediated by a single cavity mode), an exceptionally well- suited candidate. As the generic model for atom-light interactions, it has been experimen- tally realized in a variety of modern quantum optical systems, highlighting its relevance for present-day research. The Dicke model is also highly versatile itself. It has been extended into the dissipative realm, was promoted to account for multiple optical light modes and was used to describe multiple, coupled single-mode cavity structures. It was adapted to treat spin-selective coupling to a cavity to describe superradiance phase tran- sitions in multi-level atomic systems. Moreover, it was realised in electronic circuits where the dipole coupling of real atoms to single mode fields is replaced by a capacitive cou- pling of artificial atoms to a resonator mode. This illustrates that the Dicke model and its extended variants are ’future-proof’ and continue to be of relevance for fundamental light-matter interactions and for driven-dissipative phase transitions. \nIn this thesis, we investigate magnetic phase transitions in driven-dissipative atomic en- sembles interacting with quantum light. We present three research projects on variants of cooperative radiation of an ensemble of laser driven two-level atoms in a single mode optical cavity, as described by the Dicke model. \nThroughout the chapters 2,3 and 4 that contain the main body of research of this thesis, we investigate phase transitions between non-equilibrium stationary states in engineered quantum-optical systems each of which extends the conventional Dicke model physics. As a starting point, we map the quantum equations of motion onto a set of semiclassical nonlinear stochastic equations and analyse their stationary states and instabilities with master equations for atomic spin and photon mean-field amplitudes. These are used to obtain experimentally relevant parameters such as critical atom-light couplings for phase transitions, phase diagrams and properties of stationary non-equilibrium states in addition to cavity output spectra that identify the imprint of magnetic correlations in the light-field. \nIn chapter 2, we help resolve a discrepancy between earlier experimental investigations of the critical atom-light coupling strength for the superradiance transition in the Dicke model: higher external pumping strengths than theoretically predicted were needed to observe a coherent, superradiant state of the light field in an optical cavity. By including incoherent spontaneous emission of atomic excitations, we extend the dissipative Dicke model to a two loss channel variant containing both photon leakage and atomic decay that reproduces the experimentally observed critical atom-light coupling. \nRecent experiments have started to interface quantum many body lattice models with coherent cavity fields, thereby allowing to realize new quantum phases through competing atom-cavity and atom-atom interactions. In chapter 3, we consider a simplified model for such a set-up where a single quantized mode of the light-field interacts with an ensemble of Rydberg-dressed atoms inside a high finesse optical cavity. This model provides a base case for further studies of quantum magnets in optical cavities. At the heart of this model is a competition of short- (dipolar atom-atom) and long-range (atom-light) interactions at the Hamiltonian level in the presence of both spontaneous emission and photon leak- age through the cavity mirrors. We show that different magnetic phases can coexist with coherent atomic radiation and provide clear experimental signatures to identify the mag- netic structure and intra-cavity dynamics. We suggest an experimental level-scheme for a quantum optical implementation of our model. \nIn chapter 4 we consider a generic, collective decay for many-body excitations in the paradigmatic Dicke model. This extension drastically enriches the dynamics as it induces a bicritical point and a bistable regime dominated by true non-equilibrium fluctuations that induce a dissipative first-order phase transition that can only be resolved by including finite fluctuation corrections with the help of stochastic Langevin equations. We investigate the hysteretic response to time-dependent ramps of the atom-light coupling. Discontinuous first-order phase transitions where metastable states coexist in a hysteresis domain have been investigated in recent dissipative quantum-optical experiments. We review noise- activation far from thermal equilibrium in chapter 5.