We consider $N$ driven two-level atoms interacting with a structured reservoir. By dressing the collective operators within a semiclassical approach, we derive a master equation and a mean-field single-particle effective Hamiltonian. This Hamiltonian describes the optical bistability phenomenon occurring in the relation between an input electromagnetic field and the effective output generated by the $N$ atoms. The dissipative part of the master equation and the effective single-particle Hamiltonian contain new terms due the reservoir structure of modes. In plotting the output field amplitude and phase, for a structured reservoir, as a function of the input amplitude, one verifies the bistable behavior in both. We illustrate our results for two structured reservoirs: one having a Lorentzian shape for the distribution of modes, and the second is modeled as a photonic band-gap structure.

• Received 18 September 2012

DOI:https://doi.org/10.1103/PhysRevA.87.043831