Emission of Radiation from a System of Many Excited Atoms

Abstract

The Weisskopf-Wigner theory of the natural linewidth of a single isolated atom is extended to a system of $N(\ensuremath{\gg}1)$ identical nonoverlapping atoms which are all in the same excited state at time $t=0$. The positions ${\mathrm{X}}_{1}\ensuremath{\cdots}{\mathrm{X}}_{N}$ of the atoms are assumed to fill a volume $\mathcal{U}$ of given shape and size with macroscopically constant density. Emission of radiation from this system takes place only in the form of one narrow, but nonzero-width, bundle of nearly equal photons, which contains all the emitted radiation. If the density of atoms within $\mathcal{U}$ exceeds a certain threshold, the rate of emission of photons has the form of a typical spike. All effects depend sensitively on the shape and size of $\mathcal{U}$ and on the density of atoms within $\mathcal{U}$, and cannot be explained in conventional terms of spontaneous or stimulated emission of radiation.