We theoretically study the dynamical phase diagram of the Dicke model in both classical and quantum limits using large, experimentally relevant system sizes.Our analysis elucidates that the model features dynamical critical points that are strongly influenced by features of chaos and emergent integrability in the model.Moreover, our numerical calculations demonstrate that mean-field features of the dynamics remain valid in the exact quantum dynamics, but we also find that in regimes where quantum effects dominate signatures of the dynamical phases and chaos can persist in purely quantum metrics such as entanglement and correlations.Our predictions can be verified in current quantum simulators of the Dicke model including arrays of trapped ions.
We theoretically study the dynamical phase diagram of the Dicke model in both classical and quantum limits using large, experimentally relevant system sizes.Our analysis elucidates that the model features dynamical critical points that are strongly influenced by features of chaos and emergent integrability in the model.Moreover, our numerical calculations demonstrate that mean-field features of the dynamics remain valid in the exact quantum dynamics, but we also find that in regimes where quantum effects dominate signatures of the dynamical phases and chaos can persist in purely quantum metrics such as entanglement and correlations.Our predictions can be verified in current quantum simulators of the Dicke model including arrays of trapped ions.
Quantum many-body systems driven far from equilibrium can exhibit phase transitions, chaos and entanglement, but probing these phenomena in large, nearly closed systems remains challenging. The Dicke model, which couples an ensemble of two-level systems collectively to a single bosonic mode, provides a fundamental framework for exploring these phenomena in light-matter interactions. Here we show that a two-dimensional crystal of approximately 100 trapped ions realizes this model and accesses integrable dynamical phase transitions, signatures of chaotic dynamics and fluctuation-driven spin-phonon excitation growth. Adiabatic elimination of the vibrational mode reveals ferromagnetic and paramagnetic dynamical spin phases, whereas strong spin-phonon coupling produces irregular trajectories and local relaxation consistent with quantum thermalization. Following a quench from an unstable fixed point, correlated excitation growth precedes generalized vacuum Rabi collapses and revivals; calibrated calculations identify two-mode squeezing 2.6 dB below the standard quantum limit, supported by reconstruction from spin measurements. By connecting collective dynamical instabilities to experimentally accessible signatures of quantum correlations, these results establish large ion crystals as a scalable platform for investigating non-equilibrium light-matter dynamics and generating resources for quantum-enhanced sensing.
Under the condition of classical limit,quantized Dicke model shows the dynamical behavior of quantum chaos.The numerical calculation shows that there are some particular points in the classical phase-space at which the quantum chaos is present.The impact of initial conditions of these particular positions on entanglement of the model was analyzed respectively under RWA(rotating-wave approximation) or non-RWA.The evolutionary characteristics of the overall dynamics were studied in the phase-space for all the phase points considered to be under the initial condition.The conclusion obtained is that classical chaos will accelerate the generation of entanglement.
We investigate the quantum-chaotic properties of the Dicke Hamiltonian; a quantum-optical model that describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N --> infinity limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N, and by analyzing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase transition. Our considerations of the wave function indicate that this is connected with a delocalization of the system and the emergence of macroscopic coherence. We also derive a semiclassical Dicke model that exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.
We study dynamical phase transitions in the generalized dissipative Dicke model in an array of trapped Rydberg ions, where their density-density interactions compete with the collective spin-phonon coupling, laser driving and dissipation. This setting offers a versatile approach to study equilibrium as well as non-equilibrium many-body phenomena, as parameters, such as the Ising interaction, laser-ion and spin-phonon coupling can be tuned. Through analyzing the mean-field phase diagram, we find a variety of distinct phases and the emergence of a tricritical point that are sensitively dependent of the interaction between Rydberg ions. We then study the quantum dynamics for a finite system size and characterize parameter dependent dynamics using the spin average, entropy, and Loschmidt echo. Distinctive signatures of the dynamical phases, such as slow relaxation and metastability, arise near the phase transition. This analysis predicts rich quantum dynamics of the finite system that link to the non-equilibrium mean-field phases. Our study widens the exploration of collective and non-equilibrium phases in Dicke models, and reveals that the Rydberg ion interaction drastically affects the phase diagram and dynamics.
Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.
We study a periodically driven macrospin system with anisotropic long-range interactions and collective dissipation, described by a Lindblad master equation. In the thermodynamic limit (N→∞), a mean-field treatment yields classical equations of motion, whose dynamics are characterized via the maximal Lyapunov exponent (MLE). Focusing on the thermodynamic limit, we map out chaotic, quasiperiodic, and periodic phases via bifurcation diagrams, MLEs, and Fourier spectra of evolved observables, identifying classic period-doubling bifurcations and fractal boundaries in the regions of attractors. Finite-size quantum simulations in the Dicke basis reveal that while both quantum and classical systems exhibit diverse dynamical phases, finite-size effects suppress some behaviors present in the thermodynamic limit. The sign of λmax serves as a key indicator of convergence between quantum and classical dynamics, which agree over timescales up to the Lyapunov time. Analysis of the density matrix shows that convergence occurs only when its nonzero elements are sharply localized. However, the nonconvergence does not imply a fundamental difference between quantum and classical dynamics: in chaotic regimes, although the evolution orbits of quantum and classical systems show significant differences, quantum evolution becomes mixed and diffusively explores the Hilbert space, signaling quantum chaos, which can be confirmed by the delocalized nature of the density matrix.