Characterizing the dynamical phase diagram of the Dicke model via classical and quantum probes

TL;DR

This paper explores the dynamical phase diagram of the Dicke model using classical and quantum analyses, revealing new critical points and the persistence of quantum signatures of chaos, with implications for quantum simulators.

Contribution

It provides a comprehensive characterization of the dynamical phases of the Dicke model, highlighting differences from equilibrium transitions and validating mean-field predictions in quantum regimes.

Findings

Dynamical critical points are distinct from equilibrium transitions.

Mean-field dynamics remain valid in quantum regimes.

Quantum effects can sustain signatures of chaos and dynamical phases.

Abstract

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 distinct from previously investigated excited-state equilibrium transitions. 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.