In one minute

Piazza, Strack and Zwerger solve exactly how Bose-Einstein condensation competes with the Dicke-Hepp-Lieb self-organisation transition for an ideal Bose gas in a single-mode optical cavity driven by a transverse laser. An effective action approach gives the full phase diagram at any temperature, with a bicritical point where the two transitions cross. They compute the atoms' dynamically generated band structure and the resulting drop in the condensation temperature once the density becomes periodically modulated. The polariton spectrum near the transition behaves quite differently above and below the condensation temperature. At low temperature the critical value for self-organisation falls as temperature rises, so thermal fluctuations can strengthen the atoms' tendency to arrange periodically.

Bose-Einstein condensation versus Dicke-Hepp-Lieb transition in an optical cavity