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

TL;DR

This paper provides an exact phase diagram for an ideal Bose gas in an optical cavity, revealing the interplay between Bose-Einstein condensation and self-organization, including effects of temperature and atomic-photon coupling.

Contribution

It offers a comprehensive analysis of the phase transitions and spectrum evolution in a coupled atom-cavity system, highlighting the bi-critical point and temperature-dependent behaviors.

Findings

Identification of a bi-critical point where phase transitions cross.

Suppression of BEC critical temperature due to density modulation.

Temperature-dependent evolution of the polariton spectrum.

Abstract

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. At low temperatures, the critical value of the Dicke-Hepp-Lieb transition decreases with temperature and thus thermal fluctuations can enhance the tendency to a periodic arrangement of the atoms.