Quantum phases in a resonantly interacting Boson-Fermion mixture

We consider a resonantly interacting boson-fermion mixture of K-40 and Rb-87 atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for K-40 and Rb-87 atoms, and K-40-Rb-87 molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.