  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 behaviour 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.
