Coherent structures in quantum optical models with dissipation

We have used an approximate dynamical symmetry of the Dicke model (quantum field interacting with the two-level atoms) to find an analytical solution in the presence of dissipation, see Eqs. (5.9)-(5.11) above. This solution reveals that some kind of coherent structure survives under dissipation. Namely, if the atoms are initially prepared in their semiclassical states, the state of the total system remains approximately factorized into the field and atomic parts (and thus keeps its purity). The evolution of the field part of the wave function recalls evolution of the Glauber coherent state interacting with the thermal bath at zero temperature. The evolution of an arbitrary initial atomic state can be completely described in terms of semiclassical atomic states