The Holstein Primakoff transformation in the generation of a squeezed field by collective atomic states

Abstract

The Dicke hamiltonian of a single mode cavity interacting with a collective atomic state is here approximated by means of the Holstein Primakoff transformation. We thus obtain analytical solutions for the time evolution of the state and for the variances of the field which are valid in the lower range of energy. The squeezing obtained depends on the nature of the initial state (atomic or field coherent state). In both cases, for small times, it increases with time and exhibits oscillations which depend on the Rabi frequency. However only the initial field coherent state may generate a squeezed vacuum state.