Excited-state phase transition leading to symmetry-breaking steady states in the Dicke model

TL;DR

This paper explores the phase diagram of the Dicke model, revealing an excited-state phase transition that leads to symmetry-breaking steady states, with implications for experimental exploration of the model's spectral phases.

Contribution

It uncovers an excited-state phase transition in the Dicke model and links symmetry-breaking steady states to the energy spectrum's phases, providing new insights into the model's behavior.

Findings

Identification of a critical coupling constant $$ for phase transition.

Existence of two spectral phases separated by a critical energy $E_c$.

Steady states' symmetry depends on their energy relative to $E_c$.

Abstract

We study the phase diagram of the Dicke model in terms of the excitation energy and the radiation-matter coupling constant $\lambda$. Below a certain critical value $\lambda_c$ of the coupling constant $\lambda$ all the energy levels have a well-defined parity. For $\lambda > \lambda_c$ the energy spectrum exhibits two different phases separated by a critical energy $E_c$ that proves to be independent of $\lambda$. In the upper phase, the energy levels have also a well defined parity, but below $E_c$ the energy levels are doubly degenerated. We show that the long-time behavior of appropriate parity-breaking observables distinguishes between the different phases of the energy spectrum of the Dicke model. Steady states reached from symmetry-breaking initial conditions restore the symmetry only if their expected energies are above the critical. This fact makes it possible to experimentally explore the complete phase diagram of the excitation spectrum of the Dicke model.