Superradiance and subradiance

The paper is the third in a theoretical study of subradiance, and is devoted to the problem of the cooperative spontaneous emission of atomic samples with linear dimensions much smaller than the wavelength of the emitted light. The treatment corroborates the results obtained in a semiclassical treatment by Friedberg and Hartmann (1974, Opt. Commun. 10, 298). Starting from a master equation describing both the cooperative spontaneous emission and the dipole-dipole interaction, a statistical treatment of the latter is introduced and the corresponding symmetry relaxation is studied. The evolution of the atoms is described in three typical cases that correspond to different sample geometries and/or atomic distributions. In one of these cases, in particular, the symmetry is first conserved and the atoms follow Dicke's predictions for a time, and then a 'retarded' symmetry breaking occurs suddenly, near the zero value of the collective energy. With regard to the further evolution of the atoms in this case, which cannot be studied in a semiclassical model, it is shown that the decay rate quickly becomes much smaller than the incoherent decay rate. An unquestionable subradiance phenomenon is thus predicted in this case. (author)