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We investigate the phase diagram of a two-species Bose-Hubbard modelincluding a conversion term, by which two particles from the first species canbe converted into one particle of the second species, and vice-versa. The modelcan be related to ultra-cold atom experiments in which a Feshbach resonanceproduces long-lived bound states viewed as diatomic molecules. The model issolved exactly by means of Quantum Monte Carlo simulations. We show than an"inversion of population" occurs, depending on the parameters, where the secondspecies becomes more numerous than the first species. The model also exhibitsan exotic incompressible "Super-Mott" phase where the particles from bothspecies can flow with signs of superfluidity, but without global supercurrent.We present two phase diagrams, one in the (chemical potential, conversion)plane, the other in the (chemical potential, detuning) plane.

Quantum phases of mixtures of atoms and molecules on optical lattices