Phase transition in the multimode two- and three-level Dicke model (Green's function method)

Abstract

By using the thermodynamic Green's function method, the authors study the phase transition of a collection of two- as well as three-level atoms interacting with the electromagnetic field and contained within a volume much smaller than the smallest resonance wavelength (Dicke model). They show for the case of three-level atoms the existence of two critical temperatures where a second-order phase transition takes place. The upper critical temperature is determined by the largest of the three coupling constants in the three-level model, whereas the lower critical temperature is a function of the remaining two coupling constants. It is also shown that for a collection of two- as well as three-level atoms, the critical temperature depends upon the number of atoms contained within lambda r3 ( lambda r is a resonance wavelength) rather than the density as has previously been suggested. Also, using the Green's function method, we show the formal equivalence of the Dicke model in thermodynamic equilibrium with the BCS model of superconductivity.