Polaritons and Pairing Phenomena in Bose--Hubbard Mixtures

TL;DR

This paper explores a two-band Bose--Hubbard model coupled to quantum light, revealing complex phase behavior including coexistence of Mott insulator and superfluid phases, relevant to cold atomic gases and optical lattice experiments.

Contribution

It introduces a novel two-band Bose--Hubbard model with a U(1) x U(1) symmetry, demonstrating rich phase diagrams and multicritical points supported by numerical simulations.

Findings

Coexistence of Mott insulator and superfluid phases.

Presence of multicritical points in the phase diagram.

Relevance to experimental systems like cold atomic gases and optical lattices.

Abstract

Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the problem of a two-band Bose--Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the non-trivial interplay between Mott insulating behavior and superfluidity. The model displays a global U(1) X U(1) symmetry which supports the coexistence of Mott insulating and superfluid phases, and yields a rich phase diagram with multicritical points. This symmetry property is shared by several other problems of current experimental interest, including two-component Bose gases in optical lattices, and the bosonic BEC-BCS crossover problem for atom-molecule mixtures induced by a Feshbach resonance. We corroborate our findings by numerical simulations.