Phase transition in a radiation-matter interaction with recoil and collisions

The standard model introduced to describe the collective atomic recoil of a n ensemble of atoms interacting with a strong electromagnetic field has bee n hen extended by the inclusion of collisions with a buffer gas. As a resul t, we find that in the thermodynamic limit the coherent emission of radiati on exhibits a continuous phase transition upon increasing the pump intensit y. The output laser field is strictly larger than 0 only above a critical v alue. We find that the transition is not associated with the onset of spati al ordering but rather with the onset of a synchronization between the pola rization phase and spatial position. A coherence parameter is introduced to characterize the phase transition.