# Atom-only descriptions of the driven-dissipative Dicke model

## TL;DR

This paper derives a Redfield master equation to accurately describe the dissipative dynamics of atoms in the driven-dissipative Dicke model, surpassing standard approximations and correctly predicting phase transitions and damping.

## Contribution

It introduces a Redfield master equation that goes beyond common approximations for the driven-dissipative Dicke model, enabling accurate analysis of atomic dynamics.

## Key findings

- Standard secular approximation fails to predict the Dicke transition.
- Large detuning approximation is inadequate for damping rates.
- Full Redfield theory accurately predicts phase transition and damping.

## Abstract

We investigate how to describe the dissipative spin dynamics of the driven-dissipative Dicke model, describing $N$ two-level atoms coupled to a cavity mode, after adiabatic elimination of the cavity mode. To this end, we derive a Redfield master equation which goes beyond the standard secular approximation and large detuning limits. We show that the secular (or rotating wave) approximation and the large detuning approximation both lead to inadequate master equations, that fail to predict the Dicke transition or the damping rates of the atomic dynamics. In contrast, the full Redfield theory correctly predicts the phase transition and the effective atomic damping rates. Our work provides a reliable framework to study the full quantum dynamics of atoms in a multimode cavity, where a quantum description of the full model becomes intractable.