Bose-Einstein Condensation versus Dicke-Hepp-Lieb Transition in an Optical Cavity

Understand

We provide an exact solution for the interplay between Bose-Einstein condensation and the Dicke-Hepp-Lieb self-organization transition of an ideal Bose gas trapped inside a single-mode optical cavity and subject to a transverse laser drive.

• Based on an effective action approach, we determine the full phase diagram at arbitrary temperature, which features a bi-critical point where the transitions cross.
• We calculate the dynamically generated band structure of the atoms and the associated supression of the critical temperature for Bose-Einstein condensation in the phase with a spontaneous periodic density modulation.
• Moreover, we determine the evolution of the polariton spectrum due to the coupling of the cavity photons and the atomic field near the self-organization transition, which is quite different above or below the Bose-Einstein condensation temperature.