The Buck-Sukumar model described in terms of su(2) x su(1, 1) coherent states

The Buck-Sukumar model, which describes an assembly of A identical two-level atoms in interaction with a monochromatic radiation field, is investigated using su(2) x su(1, 1) coherent states, in the framework of conventional mean-field many-body approaches. In particular, the super-radiant phase transition is studied. We find that results based on the mean-field method compare favorably with exact results. We also find that the results are much improved if the constant of motion of the model is implemented exactly, with the help of appropriate projection techniques, instead of being implemented only in the average. Since the Hamiltonian of the Buck-Sukumar model is unbounded from below, i.e., it lacks a ground state, a stabilized version of the model is also studied