Polaritons and Pairing Phenomena in Bose-Hubbard Mixtures

Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the two-band Bose-Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the interplay between Mott insulating behaviour and superfluidity. The model displays a $U(1)\times U(1)$ symmetry which supports the coexistence of Mott insulating and superfluid phases,and yields a rich phase diagram with multicritical points. This symmetry is shared by several other problems of current experimental interest, including two-component Bose gases in optical lattices, and the bosonic BEC-BCS crossover for atom-molecule mixtures induced by a Feshbach resonance. We corroborate our findings by numerical simulations. [M. J. Bhaseen, M. Hohenadler, A. O. Silver, and B. D. Simons, Phys. Rev. Lett. \textbf{102}, 135301 (2009)]