Collective quantum features of the relaxation of nonlinear polariton excitations

A closed system of equations of the second - moments approximation for the average values and correlation functions of the atomic operators is obtained neglecting the mutual effect of quantum fluctuations of the populations in different atoms. The nonlinearity in these equations is introduced solely by the populations via the diagonal part of the correlation matrix of the atoms. For the case of a rarefied gas a complete investigation of the dynamics of spontaneous superradiation without a phenomenological simplification of the problem of the geometry of the medium is given, i.e., on the basis of an analysis of the collective matrix of the propagation of the excitation. The complete coherence of the superradiation for small Fresnel numbers is established and the coherence is estimated in the general case; the excitation of a very large number of modes and the presence of stochastic intermode beats due to collective frequency shifts which are different for different modes is explained, the dependence of the intensity on the concentration, which is nonquadratic with deviations from quadratic of <10%, and the delay time of the pulse, are refined.