Quantum Chaos in the Extended Dicke Model

TL;DR

This paper investigates how atomic interactions influence quantum chaos in the extended Dicke model by analyzing spectral statistics and eigenstates, revealing that atomic interactions amplify the transition from integrability to chaos.

Contribution

It provides a systematic analysis of chaos signatures in the extended Dicke model, highlighting the role of atomic interactions in enhancing quantum chaos.

Findings

Atomic interactions strengthen spectral chaos signatures.

The integrability-to-chaos transition is amplified by atomic interactions.

Spectral statistics are more affected by atomic interactions than eigenstate structures.

Abstract

We systematically study the chaotic signatures in a quantum many-body system consisting of an ensemble of interacting two-level atoms coupled to a single-mode bosonic field, the so-called extended Dicke model. The presence of the atom-atom interaction also leads us to explore how the atomic interaction affects the chaotic characters of the model. By analyzing the energy spectral statistics and the structure of eigenstates, we reveal the quantum signatures of chaos in the model and discuss the effect of the atomic interaction. We also investigate the dependence of the boundary of chaos extracted from both eigenvalue-based and eigenstate-based indicators on the atomic interaction. We show that the impact of the atomic interaction on the spectral statistics is stronger than on the structure of eigenstates. Qualitatively, the integrablity-to-chaos transition found in the Dicke model is amplified when the interatomic interaction in the extended Dicke model is switched on.