Superradiant transition and its classical analogue

Abstract

The two-level quantum model proposed by Preparata, according to which the interaction of a material system with a electromagnetic field can cause the loss of stability of the lower level, is examined. As a result of this instability, the role of the ground state is played by a periodic process generating superradiance (in contrast to laser radiation induced by overpopulation of the upper level). A classical analogue of a super-radiant quantum transition, a system of van der Pol-Duffing oscillators (generators) weakly coupled via a linear oscillator, is for the first time described. Such an analogue is a strongly modulated oscillatory process of almost complete periodic energy exchange between the generators. It is shown that a necessary condition for the transition to intense energy exchange in the classical system is the instability of one of the nonlinear normal modes, similar to how the condition for a superradiant transition to occur is the instability of the ground state of a two-level quantum system coupled with a resonant electromagnetic field.