Counting statistics of the Dicke superradiance phase transition

Wassilij Kopylov, Clive Emary, and Tobias Brandes

Phys. Rev. A 87, 043840 – Published 26 April 2013

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 nontrivial in form and divergent around the quantum phase transition.