Directed spontaneous emission from an extended ensemble of N atoms: timing is everything

A collection of static atoms is fixed in a crystal at a low temperature and prepared by a pulse of incident radiation of wave vector . The atoms are well described by an entangled Dicke-like state, in which each atom carries a characteristic phase factor exp(ik0.r(j)), where is the atomic position in the crystal. It is shown that a single photon absorbed by the N atoms will be followed by spontaneous emission in the same direction. Furthermore, phase matched emission is found when one photon is absorbed by N atoms followed by two-photon down-conversion.