Thermodynamics and Electrodynamics of Superradiant Phase

TLDR: In this paper, a mean field approach and random phase approximation was used to obtain the equilibrium properties of the superradiant phase with infinite number of modes of radiation field and without trancation to a single rotating field, which is shown to be exact in the limit of large n.

Abstract: The thermodynamics and electrodynamics of the superradiant phase are analyzed on the basis of the Emeljanov·Klimontovich model by means of a mean field approach and random phase approximation. The model considers infinite modes of radiation field. The superradiant phase is characterized by a static and homogeneous Bose condensation of the transverse collective mode with zero wave vector. The thermodynamic Quantities and the dispersion relations for the collective mode are obtained in closed forms. While the thermodynamic properties of the present model are the same as those of the Dicke model, the electrodynamics differs in form from the latter. A softening of the lower branch of the collective mode behaves as (T- Te)l/2 for T> Te, whereas for T< Te it obeys a law Te- T or (Tc- T)I/2 according to the different regions of temperature and the polarizations. A light velocity is renormalized with an anisotropic constant. Properties of a system of n identical atoms with two levels interacting with a radiation field are now widely investigated. In the most of the works a simplification that takes account of only a single rotating field has been made. Within this simplified model it is shown that a mean field treatment is sufficient to obtain the equilibrium properties, which is shown to be exact in the limit of large n. I)~6) It was predicted that if the coupling between the two subsystems- the atoms and the radiation field-is sufficiently strong, the system exhibits a phase transition to an ordered state called a superradiant phase. In spite of this success, however, up to the present time a natural problem of infinite number of modes of the radiation field and without trancation to a single rotating field has been remained less clear. Emeljanov and Klimontovich 8