Many-Body Quantum Optics with Decaying Atomic Spin States: ($\gamma$, $\kappa$) Dicke model

TL;DR

This paper develops a theoretical framework for the open Dicke model with atomic spin states experiencing spontaneous emission, analyzing steady states and implications for quantum magnetism and superradiant phase transitions.

Contribution

It introduces a comprehensive theory for the open Dicke model with internal atomic states and decay channels, applicable in the thermodynamic limit, relevant for experimental quantum optics.

Findings

Mean-field steady states characterized for spin and photon observables.

The solution remains exact in the thermodynamic limit despite non-conservation of total angular momentum.

Provides a foundation for exploring open quantum magnets with quantum light in experiments.

Abstract

We provide a theory for quantum-optical realizations of the open Dicke model with internal, atomic spin states subject to spontaneous emission with rate $\gamma$. This introduces a second decay channel for excitations to irreversibly dissipate into the environment, in addition to the photon loss with rate $\kappa$, which is composed of individual atomic decay processes and a collective atomic decay mechanism. The strength of the latter is determined by the cavity geometry. We compute the mean-field non-equilibrium steady states for spin and photon observables in the long-time limit, $t\rightarrow \infty$. Although $\gamma$ does not conserve the total angular momentum of the spin array, we argue that our solution is exact in the thermodynamic limit, for the number of atoms $N\rightarrow \infty$. In light of recent and upcoming experiments realizing superradiant phase transitions using internal atomic states with pinned atoms in optical lattices, our work lays the foundation for the pursuit of a new class of open quantum magnets coupled to quantum light.