Dissipation in collective interactions

An approximate solution is given for the interaction of a set of A two-level atoms with a single mode of a quantized radiation field when the field is damped by a reservoir at zero temperature. Assuming that the average photon number is much larger than the number of atoms, we study the influence of dissipation on the approximate factorization of the density matrix. For realistic values of the parameters, the factorization survives under the presence of field damping. The main effect of dissipation is an exponential decay of the average photon number and a loss of coherence among the different factorized states. The influence of field dissipation on the atomic inversion, purity, and field squeezing are studied