The production of single photons using rephased amplified spontaneous
emission is examined. This process produces single photons on demand with high
efficiency by detecting the spontaneous emission from an atomic ensemble, then
applying a population-inverting pulse to rephase the ensemble and produce a
photon echo of the spontaneous emission events. The theoretical limits on the
efficiency of the production are determined for several variants of the scheme.
For an ensemble of uniform optical density, generating the initial spontaneous
emission and its echo using transitions of different strengths is shown to
produce single photons at 70% efficiency, limited by reabsorption. Tailoring
the spatial and spectral density of the atomic ensemble is then shown to
prevent reabsorption of the rephased photon, resulting in emission efficiency
near unity