Collective dynamics of inhomogeneously broadened emitters coupled to an optical cavity with narrow linewidth

We study collective effects in an inhomogeneously broadened ensemble of two-level emitters coupled to an optical cavity with narrow linewidth. Using second-order mean-field theory we find that the emitters within a few times the cavity linewidth exhibit synchronous behavior and undergo collective Rabi oscillations. Under proper conditions, the synchronized oscillations give rise to a modulated intracavity field which can excite emitters detuned by many linewidths from the cavity resonance. To study the synchronization in further detail, we simplify the model and consider two ensembles and study steady-state properties when the emitters are subjected to an incoherent drive.