We study the ergodic -- non-ergodic transition in a generalized Dicke model with independent co- and counter rotating light-matter coupling terms. By studying level statistics, the average ratio of consecutive level spacings, and the quantum butterfly effect (out-of-time correlation) as a dynamical probe, we show that the ergodic -- non-ergodic transition in the Dicke model is a consequence of the proximity to the integrable limit of the model when one of the couplings is set to zero. This can be interpreted as a hint for the existence of a quantum analogue of the classical Kolmogorov-Arnold-Moser theorem. Besides, we show that there is no intrinsic relation between the ergodic -- non-ergodic transition and the precursors of the normal -- superradiant quantum phase transition.
We study the semiclassical limit of the anisotropic two-photon Dicke model with a dissipative bosonic field and describe its rich nonlinear dynamics. Besides normal and 'superradiant'-like phases, the presence of localized fixed points reflects the spectral collapse of the closed-system Hamiltonian. Through Hopf bifurcations of superradiant and normal fixed points, limit cycles are formed in certain regions of parameters. We also identify a pole-flip transition induced by anisotropy and a region of chaotic dynamics, which appears from a cascade of period-doubling bifurcations. In the chaotic r…
The classical Kolmogorov-Arnold-Moser (KAM) theorem provides the underlying mechanism for the stability of the solar system under some small chaotic perturbations. Despite many previous efforts, any quantum version of the KAM theorem remains elusive In this work, we provide a quantum KAM theorem in the context of the anisotropic Dicke model which is the most important quantum optics model. It describes a single mode of photons coupled to $ N $ qubits with both a rotating wave (RW) term and a counter-RW (CRW) term. As the ratio of the CRW over the RW term increases from zero to one, the systems…
In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite of that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Ou…
Correlations between the parts of a many-body system, and its time dynamics, lie at the heart of sciences, and they can be classical as well as quantum. Quantum correlations are traditionally viewed as constituted out of classical correlations and magnetizations. While that of course remains so, we show that quantum correlations can have statistical mechanical properties like ergodicity, which is not inherited from the corresponding classical correlations and magnetizations, for the transverse anisotropic quantum XY model in one-, two-, and quasi two-dimension, for suitably chosen transverse f…
We investigate a possibility to generate non-classical states in light-matter coupled noisy quantum systems, namely the anisotropic Rabi and Dicke models. In these hybrid quantum systems a competing influence of coherent internal dynamics and environment induced dissipation drives the system into non-equilibrium steady states (NESSs). Explicitly, for the anisotropic Rabi model the steady state is given by an incoherent mixture of two states of opposite parities, but as each parity state displays light-matter entanglement we also find that the full state is entangled. Furthermore, as a natural …
We propose the analog quantum simulation of generalized Dicke models in trapped ions. By combining bicromatic laser interactions on multiple ions we can generate all regimes of light-matter coupling in these models, where here the light mode is mimicked by a motional mode. We present numerical simulations of the three-qubit Dicke model both in the weak field (WF) regime, where the Jaynes-Cummings behaviour arises, and the ultrastrong coupling (USC) regime, where rotating-wave approximation (RWA) cannot be considered. We also simulate the two-qubit biased Dicke model in the WF and USC regimes a…
Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are key concepts reconciling seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes, and have revolutionized our understanding of non-equilibrium phenomena. Here, we demonstrate that a family of fidelity out-of-time-order correlators (FOTOCs), rece…
We compare the entire classical and quantum evolutions of the Dicke model in its regular and chaotic domains. This is a paradigmatic interacting spin-boson model of great experimental interest. By studying the classical and quantum survival probabilities of initial coherent states, we identify features of the long-time dynamics that are purely quantum and discuss their impact on the equilibration times. We show that the ratio between the quantum and classical asymptotic values of the survival probability serves as a metric to determine the proximity to a separatrix in the regular regime and to…
In a view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) non-stationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model, we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and number…
Ergodicity-breaking and slow relaxation are intriguing aspects of nonequilibrium dynamics both in classical and in quantum settings. These phenomena are typically associated with phase transitions, e.g. the emergence of metastable regimes near a first-order transition or scaling dynamics in the vicinity of critical points. Despite being of fundamental interest the associated divergent time scales are a hindrance when trying to explore steady-state properties. Here we show that the relaxation dynamics of Markovian open quantum systems can be accelerated exponentially by devising an optimal unit…
