Dissipative quantum phase transitions 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 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 quasienergies to recover the renormalized critical drive strength, extend the multiphoton resonances of a photon blockade to a counter-rotating interaction, and explore quantum fluctuations through quantum trajectory simulations.