Dynamical evolution of correlated spontaneous emission of a single photon from a uniformly excited cloud of N atoms

TL;DR

This paper investigates how a dense atomic cloud's collective spontaneous emission dynamics depend on the interplay between the effective Rabi frequency and the photon flight time, revealing regimes of exponential decay and oscillatory behavior.

Contribution

It introduces a detailed analysis of the decay dynamics of a uniformly excited atomic cloud, highlighting the transition between exponential decay and oscillations based on system parameters.

Findings

Decay rate depends on the ratio of Rabi frequency times cloud size to light speed.

In one regime, the state decays exponentially with a rate proportional to Omega^2 R/c.

In the other regime, the system exhibits oscillations at frequency Omega with decay rate c/R.

Abstract

We study the correlated spontaneous emission from a dense spherical cloud of N atoms uniformly excited by absorption of a single photon. We find that the decay of such a state depends on the relation between an effective Rabi frequency Omega, which is proportional to sqrt{N}, and the time of photon flight through the cloud R/c. If Omega*R/c < 1 the state exponentially decays with rate Omega^{2}*R/c and the state life time is greater then R/c. In the opposite limit Omega*R/c >> 1, the coupled atom-radiation system oscillates between the collective Dicke state (with no-photons) and the atomic ground state (with one photon) with frequency Omega while decaying at a rate c/R.