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

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.