Analyzing superradiant emission by partially inverted atomic ensembles

Superradiance occurs in atomic ensembles due to an exchange of photonic excitations leading to constructive interference of emitted photons. The interacting, many-body nature of superradiance in an atomic ensemble causes the Hilbert space's dimensionality to scale exponentially, increasing the problem's analytical complexity. Previous models have attempted to simplify the system by working with size-constrained Dicke states or by considering only singly-excited states, or by using quantum jumps. However, these approaches are unable to reveal much about the superradiant burst or the late time dynamics of the ensemble. This research builds on the work of Ma et al. 2022, who use an integrated method with two probe atoms to obtain a non-linear two-atom master equation which captures the dynamics of the whole system. However, this model yields unphysical results for initially partially inverted ensembles among other issues. This research attempts to modify the aforementioned model to avoid apparent unphysical changes to the average upper state population and the cooperative decay rate. This is accomplished by both brute force - applying direct constraints and modifications to the cooperative decay rate - and analytic - improving theoretical approximations and imposing energy conservation - approaches.