Chaos and Thermalization in the Spin-Boson Dicke Model

Reinforcement Learning Optimization of the Charging of a Dicke Quantum Battery

Quantum batteries are energy-storing devices, governed by quantum mechanics, that promise high charging performance thanks to collective effects. Because of its experimental feasibility, the Dicke battery-which comprises N two-level systems coupled to a common photon mode-is one of the most promising designs for quantum batteries. However, the chaotic nature of the model severely hinders the extractable energy (ergotropy). Here, we use reinforcement learning to optimize the charging process of a Dicke battery either by modulating the coupling strength, or the system-cavity detuning. We find that the ergotropy and quantum mechanical energy fluctuations (charging precision) can be greatly improved with respect to standard charging strategies by countering the detrimental effect of quantum chaos. Notably, the collective speedup of the charging time can be preserved even when nearly fully charging the battery.

Onset of quantum thermalization in the Jahn-Teller model

We investigate the onset of quantum thermalization in a system governed by the Jahn-Teller Hamiltonian, which describes the interaction between a single spin and two bosonic modes. We find that the Jahn-Teller model exhibits a finite-size quantum phase transition between the normal phase and two types of super-radiant phase when the ratios of spin-level splitting to each of the two bosonic frequencies grow to infinity. We test the prediction of the eigenstate thermalization hypothesis in the Jahn-Teller model. We show that the expectation value of the spin observable quickly approaches its long-time average value. We find that the distance between the diagonal ensemble average and the microcanonical ensemble average of the spin observable decreases with the effective thermodynamic parameter. Furthermore, we show that the mean time fluctuations of the spin observable are small and are inversely proportional to the effective system dimension.

Phase and Amplitude Modes in the Anisotropic Dicke Model with Matter Interactions

Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein-Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms.

Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit

How the mixed eigenstates vary when approaching the semiclassical limit in mixed-type many-body quantum systems is an interesting but still less known question. Here, we address this question in the Dicke model, a celebrated many-body model that has a well defined semiclassical limit and undergoes a transition to chaos in both quantum and classical cases. Using the Husimi function, we show that the eigenstates of the Dicke model with mixed-type classical phase space can be classified into different types. To quantitatively characterize the types of eigenstates, we study the phase space overlap index, which is defined in terms of the Husimi function. We look at the probability distribution of the phase space overlap index and investigate how it changes with increasing system size, that is, when approaching the semiclassical limit. We show that increasing the system size gives rise to a power-law decay in the behavior of the relative proportion of mixed eigenstates. Our findings shed more light on the properties of eigenstates in mixed-type many-body systems and suggest that the principle of uniform semiclassical condensation of Husimi functions should also be valid for many-body quantum systems.

Classical route to ergodicity and scarring in collective quantum systems

Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.

Analysis of chaos and regularity in the open Dicke model

We present an analysis of chaos and regularity in the open Dicke model, when dissipation is due to cavity losses. Due to the infinite Liouville space of this model, we also introduce a criterion to numerically find a complex spectrum which approximately represents the system spectrum. The isolated Dicke model has a well-defined classical limit with two degrees of freedom. We select two case studies where the classical isolated system shows regularity and where chaos appears. To characterize the open system as regular or chaotic, we study regions of the complex spectrum taking windows over the absolute value of its eigenvalues. Our results for this infinite-dimensional system agree with the Grobe-Haake-Sommers (GHS) conjecture for Markovian dissipative open quantum systems, finding the expected 2D Poisson distribution for regular regimes, and the distribution of the Ginibre unitary ensemble (GinUE) for the chaotic ones, respectively.

Nonequilibrium dynamics of the Jaynes-Cummings dimer

We investigate the nonequilibrium dynamics of a Josephson-coupled Jaynes-Cummings dimer in the presence of Kerr nonlinearity, which can be realized in the cavity and circuit quantum electrodynamics systems. The semiclassical dynamics is analyzed systematically to chart out a variety of photonic Josephson oscillations and their regime of stability. Different types of transitions between the dynamical states lead to the self-trapping phenomenon, which results in photon population imbalance between the two cavities. We also study the dynamics quantum mechanically to identify characteristic features of different steady states and to explore fascinating quantum effects, such as spin dephasing, phase fluctuation, and revival phenomena of the photon field, as well as the entanglement of spin qubits. For a particular "self-trapped" state, the mutual information between the atomic qubits exhibits a direct correlation with the photon population imbalance, which is promising for generating photon mediated entanglement between two non interacting qubits in a controlled manner. Under a sudden quench from stable to unstable regime, the photon distribution exhibits phase space mixing with a rapid loss of coherence, resembling a thermal state. Finally, we discuss the relevance of the new results in experiments, which can have applications in quantum information processing and quantum technologies.

Quantum Phase Transitions in a Generalized Dicke Model

We investigate a generalized Dicke model by introducing two interacting spin ensembles coupled with a single-mode bosonic field. Apart from the normal to superradiant phase transition induced by the strong spin-boson coupling, interactions between the two spin ensembles enrich the phase diagram by introducing ferromagnetic, antiferromagnetic and paramagnetic phases. The mean-field approach reveals a phase diagram comprising three phases: paramagnetic-normal phase, ferromagnetic-superradiant phase, and antiferromagnetic-normal phase. Ferromagnetic spin-spin interaction can significantly reduce the required spin-boson coupling strength to observe the superradiant phase, where the macroscopic excitation of the bosonic field occurs. Conversely, antiferromagnetic spin-spin interaction can strongly suppress the superradiant phase. To examine higher-order quantum effects beyond the mean-field contribution, we utilize the Holstein-Primakoff transformation, which converts the generalized Dicke model into three coupled harmonic oscillators in the thermodynamic limit. Near the critical point, we observe the close of the energy gap between the ground and the first excited states, the divergence of entanglement entropy and quantum fluctuation in certain quadrature. These observations further confirm the quantum phase transition and offer additional insights into critical behaviors.

Dynamical transition from localized to uniform scrambling in locally hyperbolic systems

Fast scrambling of quantum correlations, reflected by the exponential growth of out-of-time-order correlators (OTOCs) on short pre-Ehrenfest time scales, is commonly considered as a major quantum signature of unstable dynamics in quantum systems with a classical limit. In two recent works [Phys. Rev. Lett. 123, 160401 (2019)0031-900710.1103/PhysRevLett.123.160401] and [Phys. Rev. Lett. 124, 140602 (2020)10.1103/PhysRevLett.124.140602], a significant difference in the scrambling rate of integrable (many-body) systems was observed, depending on the initial state being semiclassically localized around unstable fixed points or fully delocalized (infinite temperature). Specifically, the quantum Lyapunov exponent λ_{q} quantifying the OTOC growth is given, respectively, by λ_{q}=2λ_{s} or λ_{q}=λ_{s} in terms of the stability exponent λ_{s} of the hyperbolic fixed point. Here we show that a wave packet, initially localized around this fixed point, features a distinct dynamical transition between these two regions. We present an analytical semiclassical approach providing a physical picture of this phenomenon, and support our findings by extensive numerical simulations in the whole parameter range of locally unstable dynamics of a Bose-Hubbard dimer. Our results suggest that the existence of this crossover is a hallmark of unstable separatrix dynamics in integrable systems, thus opening the possibility to distinguish the latter, on the basis of this particular observable, from genuine chaotic dynamics generally featuring uniform exponential growth of the OTOC.