Dissipative quantum phase transition of light in a generalized Jaynes-Cummings-Rabi model

The mean-field steady states of a generalized model of $N$ two-state systems interacting with one mode of the radiation field in the presence of external driving and dissipation are surveyed as a function of three control parameters: one governs the interaction strength relative to the resonance frequency, thus accessing the Dicke quantum phase transition, a second the relative strength of counter-rotating to rotating-wave interactions, and a third the amplitude of an external field driving the cavity mode. We unify the dissipative extension of the Dicke quantum phase transition with the recently reported breakdown of photon blockade [H.~J.~Carmichael, Phys.\ Rev.\ X {\bf 5}, 031028 (2015)]; key to the unification is a previously unreported phase of the Dicke model and a renormalized critical drive strength in the breakdown of photon blockade. For the simplest case of one two-state system, we complement mean-field results with a full quantum treatment: we derive quasi-energies to recover the renormalized critical drive strength, extend the multi-photon resonances of photon blockade to a counter-rotating interaction, and explore quantum fluctuations through quantum trajectory simulations.