Dissipative Dicke model with collective atomic decay: Bistability, noise-driven activation, and the nonthermal first-order superradiance transition

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 nonthermal Markovian noise. The interplay between dissipative and coherent elements leads to a genuine nonequilibrium dynamics in the bistable regime, which is expressed via a nonconservative 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 the inclusion of fluctuation corrections with O(1/N) for finite N < infinity to locate the nonthermal first-order phase transition between the superradiant and the empty cavity.