Few emitters in a cavity: From cooperative emission to individualization

We study the temporal correlations of the field emitted by an electromagnetic resonator coupled to a mesoscopic number of two-level emitters that are incoherently pumped by a weak external drive. We solve the master equation of the system for increasing number of emitters and as a function of the cavity quality factor, and we identify three main regimes characterized by well distinguished statistical properties of the emitted radiation. For small cavity decay rate, the emission events are uncorrelated and the number of photons in the emitted field becomes larger than one, resembling the build-up of a laser field inside the cavity. At intermediate decay rates (as compared to the emitter-cavity coupling) and for few emitters, the statistics of the emitted radiation is bunched and strikingly dependent on the parity of the number of emitters. The latter property is related to the cooperativity of the emitters mediated by their coupling to the cavity mode, and its connection with steady state subradiance is discussed. Finally, in the bad cavity regime the typical situation of emission from a collection of individual emitters is recovered. We also analyze how the cooperative behavior evolves as a function of pure dephasing, which allows to recover the case of a classical source made of an ensemble of independent emitters, similar to what is obtained for a very leaky cavity. State-of-art techniques of Q-switch of resonant cavities, allied with the recent capability to tune single emitters in and out of resonance, suggest this system as a versatile source of different quantum states of light.