Theoretical study of early time superradiance for atom clouds and arrays

TL;DR

This paper provides a theoretical framework for understanding early-time superradiance in atom clouds and arrays, analyzing conditions for superradiance through photon emission rate expansions and offering algorithms for large systems.

Contribution

It introduces a method to determine superradiance conditions at early times for various atomic configurations, including arrays and multilevel atoms, with an efficient evaluation algorithm.

Findings

Superradiance occurs when the photon emission rate increases at early times.

Conditions for superradiance depend on atomic arrangement and initial inversion.

Algorithms enable analysis of large atom arrays for superradiance.

Abstract

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 have calculated 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 $t=0$, we also give equations for partially inverted two level atoms and for fully inverted multilevel atoms. We give an algorithm for efficiently evaluating these equations for atom arrays and determine superradiance conditions for large atom number.