  We investigate the phase diagram of a two-species Bose-Hubbard model
including a conversion term, by which two particles from the first species can
be converted into one particle of the second species, and vice-versa. The model
can be related to ultra-cold atom experiments in which a Feshbach resonance
produces long-lived bound states viewed as diatomic molecules. The model is
solved exactly by means of Quantum Monte Carlo simulations. We show than an
"inversion of population" occurs, depending on the parameters, where the second
species becomes more numerous than the first species. The model also exhibits
an exotic incompressible "Super-Mott" phase where the particles from both
species 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.
