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

The standard model introduced to describe the collective atomic recoil of an ensemble of atoms interacting with a strong electromagnetic field has been here extended by the inclusion of collisions with a buffer gas. As a result, we find that in the thermodynamic limit the coherent emission of radiation exhibits a continuous phase transition upon increasing the pump intensity. The output laser field is strictly larger than 0 only above a critical value. We find that the transition is not associated with the onset of spatial ordering but rather with the onset of a synchronization between the polarization phase and spatial position. A coherence parameter is introduced to characterize the phase transition.