Quantum chaos and thermalization in the two-mode Dicke model

TL;DR

This paper investigates how quantum chaos and thermalization emerge in the two-mode Dicke model, revealing insights into phase transitions, out-of-time-order correlators, and the system's approach to equilibrium.

Contribution

It provides a detailed analysis of quantum chaos indicators and thermalization processes in the two-mode Dicke model, highlighting the behavior of fidelity correlators and collective spin observables.

Findings

Exponential growth of out-of-time-order correlator not linked to classical unstable points.

Collective spin saturates to long-time average, matching microcanonical predictions.

System exhibits thermalization with fluctuations decreasing as system size increases.

Abstract

We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model, which describes the dipolar interaction between an ensemble of spins and two bosonic modes. The two-mode Dicke model exhibits normal to superradiant quantum phase transition with spontaneous breaking either of a discrete or continuous symmetry. We study the behaviour of the fidelity out-of-time-order correlator derived from the Loschmidt echo signal in the quantum phases of the model and show that its exponential growth cannot be related to a classical unstable point in the general case. Moreover, we find that the collective spin observable in the two-mode Dicke model quickly saturates to its long-time average value, and shows very good agreement between its diagonal ensemble average and microcanonical average even for a small number of spins. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size, which leads to thermalization of the spin system.