The method of two-time temperature-depe ndent Green's functions is used to obtain the conversion time for a macroscopic system of two-level radiators interacting with the electromagnetic field with allowance for the motion of the centers of mass of the radiators. The influence of direct dipole-dipole interaction on the conversion time is investigated.

Abstract

The adequate description of the dynamic properties of macroscopic two-level systems interacting with the electromagnetic field is of particular interest in connection with the problem of choosing the working regime and active medium for the realization of single-pass resonator-free superradiative lasers. Since the derivation of an exact kinetic equation for such systems is a very complicated mathematical problem, different simplifying assumptions of physical nature are generally employed. There is, for example, the approach based on a Markov master equation developed in a series of papers by Bonifacio et al. [1-6]. The dynamics of the photon system with allowance for processes of incoherent pumping was studied on the basis of Zwanzig's approach [7] by Haake and Mandel [8, 9]. The Bogolyubov-Krylo v method of solution of nonlinear equations was used by Willis [10J. Some important estimates for the conversion times and other physical characteristics relating to the problem of creating a gamma laser were obtained by Khokhlov et al. [11-14] (see also the review [15]). Recently, exploitation of the deep analogies in the mathematical formulation of the model problems in the theory of superradiance and in polaron theory made it possible to obtain an exact generalization of the kinetic equation for superradiative systems [161 on the basis of the method of eliminating the boson variables developed in [17, 18]. It proved possible to obtain a number of physical results, in particular, to determine the magnitudes of the constant and collective frequency shift in the presence of inhomogeneous Lorentz broadening under conditions of cooperative spontaneous radiation. In following papers [19, 20], which were based on the generalized kinetic equation of [16], an equation for the single-particle distribution function was constructed. Comparison of this equation with Pauli's master equation made it possible to determine the characteristic relaxation times. There is however a simpler and more direct way of determining the probability F_ of transition of a radiator to an excited state with absorption of a photon and the probability F+ of transition to the de-excited state with emission of a photon (x~-F~ -', z are the characteristic relaxation times). It is associated with the use of the method of two-time temperature-depe ndent Green's functions. This method, which was introduced into statistical mechanics by Bogolyubov and Tyablikov [21], plays an important part in the theory of nonequilibrium processes (see, for example, [22, 23]). In the present paper, we investigate the dynamical properties of superradiative systems by means of two-time temperature-depe ndent Green's functions and, in particular, we obtain relations for the characteristic relaxation times. For clarity~ we consider the simplest model, characterized by the Hamiltonian