Theoretical study of early time superradiance for atom clouds and arrays*

We present results from a recent publication where we explore conditions for Dicke superradiance in a cloud of atoms by examining the Taylor series expansion of the photon emission rate at t=0. By defining superradiance as an increasing photon emission rate for $t\sim 0$, we calculate the conditions for superradiance for a variety of cases. We investigate superradiance as defined for photon emission into all angles as well as directional superradiance where the photon emission is only detected in a particular direction. Although all of the examples are for two level atoms that are fully inverted at t=0, the publication contains equations for partially inverted two level atoms and for fully inverted multilevel atoms. The publication also contains an algorithm for efficiently evaluating these equations for atom arrays and uses this algorithm to determine superradiance conditions for large atom number, N → ∞. The method used to explore this system was inspired by S. J. Masson and A. Asenjo-Garcia, "Universality of Dicke superradiance in atomic arrays," arXiv preprint arXiv:2106.02042 (2021).