Berry Phase and Fidelity in the Dicke model with $A^{2}$ term

TL;DR

This paper investigates the quantum-phase-like transition in the Dicke model with an A^2 term, analyzing how Berry phase and fidelity reveal instability, which persists even with strong atom-field interactions.

Contribution

It demonstrates that the inclusion of the A^2 term does not eliminate the instability in the Dicke model, contrasting with previous findings.

Findings

Discontinuous behavior of Berry phase and fidelity signals the transition.

Instability persists despite strong atom-field coupling when A^2 term is included.

The A^2 term does not suppress the quantum-phase-like transition.

Abstract

The instability, so-called the quantum-phase-like transition, in the Dicke model with a rotating-wave approximation for finite $N$ atoms is investigated in terms of the Berry phase and the fidelity. It can be marked by the discontinuous behavior of these quantities as a function of the atom-field coupling parameter. Involving an additional field $A^{2}$ term, it is observed that the instability is not eliminated beyond the characteristic atom-field coupling parameter even for strong interaction of the bosonic fields, contrarily to the previous studies.