Counting statistics of the Dicke superradiance phase transition

TL;DR

This paper analyzes the photon counting statistics of a driven Dicke model near its quantum phase transition, revealing a Poissonian macroscopic component and complex fluctuation behavior that diverges at criticality.

Contribution

It derives the cumulant generating function for emitted photons in a dissipative Dicke model, highlighting the statistical signatures of the quantum phase transition.

Findings

Photon emission follows a Poissonian distribution with a rate linked to the order parameter.

Fluctuations in photon emission are non-trivial and diverge at the phase transition.

The cumulant generating function captures both macroscopic and fluctuation contributions.

Abstract

We consider a driven single mode Dicke-Hamiltonian coupled to a dissipative zero-temperature bath. We derive the cumulant generating function for emitted photons of this quantum-critical system by using a $P$-representation of the master equation in the thermodynamic limit. This cumulant generating function is shown to consist of two parts: a macroscopic component, which is Poissonian in nature with characteristic rate proportional to the order parameter of the system; and a part describing fluctuations which is non-trivial in form and divergent around the quantum phase transition.