We investigate the stochastic initiation of superradiant emission from a collection of excited two-state atoms coupled through a low-Q cavity mode. Noncollective emission into other modes of the electromagnetic field is included, allowing us to describe the transition from predominantly noncollective to collective behavior as the number of atoms is increased. We examine the dependence of the photon statistics on the number of atoms and the ratio of collective to noncollective decay rates. Numerical results for a few to
106 atoms are obtained using an approximation scheme developed within the framework of quantum trajectory theory. Results are compared with those for a pure collective emission process and an earlier treatment of noncollective effects.
Superradiance is a quantum phenomenon in which coherence between emitters results in enhanced and directional radiative emission. Many quantum optical phenomena can be characterized by the two-time quantum correlation function
g(2)(t,τ), which describes the photon statistics of emitted radiation. However, the critical task of determining
g(2)(t,τ) becomes intractable for large emitter ensembles due to the exponential scaling of the Hilbert space dimension with the number of emitters. Here, we analyse and benchmark two approximate numerical sampling methods applicable to emitter arrays embedded within electromagnetic environments, which generally provide upper and lower bounds for
g(2)(t,0). We also introduce corrections to these methods (termed offset corrections) that significantly improve the quality of the predictions. The optimal choice of method depends on the total number of emitters, such that taken together, the two approaches provide accurate descriptions across a broad range of important regimes. This work therefore provides new theoretical tools for studying the well-known yet complex phenomenon of superradiance in large ensembles of quantum emitters.