Atom-only theories for U(1) symmetric cavity-QED models

TL;DR

This paper develops an atom-only effective theory for a U(1) symmetric cavity-QED model, revealing the limitations of standard Redfield theory and emphasizing the importance of higher-order corrections to capture phase transitions.

Contribution

It introduces a method to derive atom-only theories for models with continuous symmetry, demonstrating the necessity of higher-order corrections beyond Redfield theory.

Findings

Redfield theory fails to describe the superradiant transition

Higher-order corrections recover the phase transition

Effective theories must adapt for models with continuous symmetry

Abstract

We consider a generalized Dicke model with U(1) symmetry, which can undergo a transition to a superradiant state that spontaneously breaks this symmetry. By exploiting the difference in timescale between atomic and cavity dynamics, one may eliminate the cavity dynamics, providing an atom-only theory. We show that the standard Redfield theory cannot describe the transition to the superradiant state, but including higher-order corrections does recover the transition. Our work reveals how the forms of effective theories must vary for models with continuous symmetry, and provides a template to develop effective theories of more complex models.