Stimulated emission from single quantum dipoles
Whereas the basic features of stimulated emission are easily seen to hold true for ensembles of dipoles, the same is not always true for a single dipole system. For example, symmetry requires that well localized, bound dipoles emit a dipole field which is isotropic in the plane defined by the dipole vector. Indeed, for this case, nothing in the interaction between the dipole and the field contains information on the propagation direction of the field. These observations seem at odds with the highly directional nature of stimulated emission. The authors therefore test for stimulated emission by an explicit calculation considering both a single Rabi type dipole and a damped dipole whose centre-of-mass coordinates are fixed at a point. Remarkably, despite the symmetrical dipole radiation pattern, stimulated emission into the original stimulating wave is shown to occur exactly. An explanation of this effect is then considered by investigating dipoles whose centre-of-mass coordinates are allowed to vary. In this case, photon recoil of the dipole introduces a directional sense to the interaction. In the extreme opposite and trivial case of a highly delocalized dipole (centre-of-mass momentum eigenstates) stimulated emission again occurs exactly. In all intermediate cases, however, stimulated emission occurs only partially or approximately. A condition imposed on a dipole's spatial extent is established for stimulated emission to occur approximately. Finally, the original bound and localized dipole is seen to be a special limiting case of recoiling dipoles for which stimulated emission occurs exactly.