Dissipative Dicke Model with Collective Atomic Decay: Bistability, Noise-Driven Activation and Non-Thermal First Order Superradiance Transition

TL;DR

This paper investigates the dissipative Dicke model with collective atomic decay, revealing bistability, noise-driven transitions, and a non-thermal first-order superradiance transition in a non-equilibrium setting.

Contribution

It introduces a comprehensive many-body master equation including collective decay and analyzes its dynamics, uncovering bistability and non-thermal phase transitions in the dissipative Dicke model.

Findings

Collective atomic decay induces bistability between empty and superradiant states.

Transitions are driven by non-thermal, Markovian noise.

Finite-size effects are crucial for locating the non-thermal first-order phase transition.

Abstract

The Dicke model describes the coherent interaction of a laser-driven ensemble of two level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to e.g. atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced, collective decay of an excitation that is shared by $N$ atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by non-thermal, markovian noise. The interplay between dissipative and coherent elements leads to a genuine non-equilibrium dynamics in the bistable regime, which is expressed via a non-conservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke Model become exact in the large-$N$-limit. The absence of an effective free energy functional, however, necessitates to include fluctuation corrections with $\mathcal{O}(1/N)$ for finite $N<\infty$ to locate the non-thermal first-order phase transition between the superradiant and the empty cavity.