Universal Critical Behavior in the Dicke Model

TL;DR

This paper investigates the critical behavior of the Dicke model, using semiclassical and exact quantum methods to determine phase transitions and universal parametric curves for key observables.

Contribution

It introduces a combined semiclassical and quantum approach to identify phase transitions and universal behavior in the Dicke model.

Findings

Universal parametric curves for expectation values are obtained.

Semiclassical and exact solutions agree in the thermodynamic limit.

Critical coupling values are determined for finite atom numbers.

Abstract

The critical value of the atom-field coupling strength for a finite number of atoms is deter- mined by means of both, semiclassical and exact solutions. In the semiclassical approach we use a variational procedure with coherent and symmetry-adapted states, while for the exact quantum solution the concept of fidelity is employed. These procedures allow for the determination of the phase transitions in the model, and coincide in the thermodynamic limit. For the three cases men- tioned above, universal parametric curves are obtained for the expectation values of both the first quadrature of the electromagnetic field, and the atomic relative population, as implicit functions of the atom-field coupling parameter, valid for the ground- and first-excited states.