Cooperative Spontaneous Emission as a Many Body Eigenvalue Problem

TL;DR

This paper provides an exact analytical solution for the eigenvalues and eigenstates of cooperative spontaneous emission in a spherical atomic cloud, revealing states with vastly different decay rates and significant frequency shifts in small clouds.

Contribution

It introduces an exact analytical framework for many-body cooperative emission, highlighting the diverse decay behaviors and frequency shifts in atomic ensembles.

Findings

Some states decay faster than single-atom rate

Other states are trapped with slow decay

Large frequency shifts occur in small clouds

Abstract

We study emission of a single photon from a spherically symmetric cloud of N atoms (one atom is excited, N-1 are in ground state) and present an exact analytical expression for eigenvalues and eigenstates of this many body problem. We found that some states decay much faster then the single-atom decay rate, while other states are trapped and undergo very slow decay. When size of the atomic cloud is small compared with the radiation wave length we found that the radiation frequency undergoes a large shift.