Cooperativity of a few quantum emitters in a single-mode cavity

We theoretically investigate the emission properties of a single-mode cavity coupled to a mesoscopic number of incoherently pumped quantum emitters. We propose an operational measure for the medium cooperativity, valid both in the bad and in the good cavity regimes. We show that
the opposite regimes of subradiance and superradiance correspond to negative and positive cooperativity,
respectively. The lasing regime is shown to be characterized by nonnegative cooperativity.
In the bad cavity regime we show that the cooperativity denes the transitions from subradiance to superradiance. In the good cavity regime it helps to dene the lasing threshold, also providing distinguishable signatures indicating the lasing regime. Increasing the quality of the cavity mode
induces a crossover from the solely superradiant to the lasing regime. Furthermore, we verify that lasing is manifested in a wide range of positive cooperative behavior, showing that stimulated emission and superradiance can coexist. The robustness of the cooperativity is studied with respect to
experimental imperfections, such as inhomogeneous broadening and pure dephasing.