Phase Transitions in Open Dicke Model: a degenerate perturbation theory approach

TL;DR

This paper investigates how local dephasing and decay influence the superradiant phase transition in the open Dicke model, using a degenerate perturbation theory approach to analyze steady states and spin distributions.

Contribution

It introduces a degenerate perturbation theory framework to analyze the impact of dephasing and decay on the phase transition in the open Dicke model, connecting quantum Rabi and Dicke physics.

Findings

Superradiant phase transition occurs only for spin S>S_c above a threshold.

Weak dephasing and decay induce mixing between S-subspaces, affecting steady states.

The spin distribution width scales as 1/√N, simplifying analysis.

Abstract

We study the steady-state behavior of the open Dicke model, which describes the collective interaction of $N$ spin-$1/2$ particles with a lossy, quantized cavity mode and exhibits a superradiant phase transition above a critical light-matter coupling. While the standard model conserves total spin, Kirton and Keeling \cite{PhysRevLett.118.123602} demonstrated that even infinitesimal homogeneous local dephasing destroys this phase transition, and that local atomic decay can restore it. We analyze this interplay using degenerate perturbation theory across subspaces of fixed total spin, $S$. For coupling strengths above the threshold, there exists a critical spin value $S_c$ such that the superradiant phase transition occurs only for $S>S_c$. The perturbative approach captures how weak dephasing and decay induce mixing between different $S$-subspaces, yielding a steady-state spin distribution whose width scales as $1/\sqrt{N}$. This framework requires only the first and second moments and can be implemented via different methods that can yield these two moments (for example, the 2nd-cumulant approach), circumventing the need for full density matrix calculations. These results bridge the quantum Rabi model and Dicke physics, elucidate the roles of dephasing and decay in collective quantum effects, and apply broadly to open quantum systems with degenerate steady states.