Large-N limit of spontaneous superradiance

TL;DR

This paper derives an exact expression for the density matrix of large-N Dicke superradiance in the thermodynamic limit, providing a precise analytical solution that improves upon previous numerical approximations and includes incoherent decay effects.

Contribution

It presents an exact analytical solution for the large-N limit of superradiance, including effects of incoherent decay, advancing theoretical understanding of collective emission phenomena.

Findings

Derived an exact density matrix expression for large N

Proved the solution's accuracy in the thermodynamic limit

Included incoherent decay effects in the model

Abstract

We investigate the thermodynamic limit of Dicke superradiance. We find an expression for the system's density matrix that we can prove is exact in the limit of large atom numbers N. This is in contrast to previously known solutions whose accuracy has only been established numerically and that are valid only for a range of times. We also introduce an asymptotically exact solution when the system is subject to additional incoherent decay of excitations as this is a common occurrence in experiment.