Superradiant Peierls transition in a multi-mode optical cavity

The strong matter-light coupling attainable in optical cavities has been employed with remarkable success to study quantum systems. It has facilitated the realization of many exciting phenomena from superradiance and self organization of matter to exciton-polaritons condensates. We consider such a system in which a one dimensional interacting Bose gas is loaded into a multi-mode optical cavity and subject to a pump field. Focusing on the steady state properties of the system we find that for sufficiently strong repulsive interactions a superradiant transition takes place which is accompanied by a metal insulator transition in the atomic system. In the limit of infinite repulsion this is attributable to the Peierls instability. Away from this special point we show that this still occurs however the nature of the transition changes and upon further reducing the interaction strength the system undergoes a transition to a gapless normal state.