Collective spontaneous emission from small assemblies of atoms

We study collective spontaneous emission from arbitrary distributions of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the average integrated intensity. We investigate the dependence of the angular distribution of emission on the geometry of the atomic distribution. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred to a few thousand atoms. In order to illustrate important differences between our model and single-mode models we consider shot-to-shot intensity fluctuations and angular correlations in the emitted intensity.