Dicke phase transition without total spin conservation

TL;DR

This paper introduces a new fermionic path-integral formalism to analyze the Dicke phase transition in open, non-equilibrium systems without assuming total spin conservation, broadening understanding of experimental scenarios.

Contribution

The authors develop a general formalism that accounts for spin non-conservation in the Dicke model, extending previous theories to more realistic dissipative conditions.

Findings

Derived a general expression for the phase transition point.

Identified regimes with conserved and non-conserved spin.

Discovered non-monotonous transition dependence on bath parameters.

Abstract

We develop a new fermionic path-integral formalism to analyze the phase diagram of open nonequilibrium systems. The formalism is applied to analyze an ensemble of two-level atoms interacting with a single-mode optical cavity, described by the Dicke model. While this model is often used as the paradigmatic example of a phase transition in driven-dissipative systems, earlier theoretical studies were limited to the special case when the total spin of the atomic ensemble is conserved. This assumption is not justified in most experimental realizations. Our new approach allows us to analyze the problem in a more general case, including the experimentally relevant case of dissipative processes that act on each atom individually and do not conserve the total spin. We obtain a general expression for the position of the transition, which contains as special cases the two previously known regimes: i) non-equilibrium systems with losses and conserved spin and ii) closed systems in thermal equilibrium and with the Gibbs ensemble averaging over the values of the total spin. We perform a detailed study of different types of baths and point out the possibility of a surprising non-monotonous dependence of the transition on the baths' parameters.