Quantum phases of Fermi-Fermi mixtures in optical lattices

The ground state phase diagram of Fermi-Fermi mixtures in optical lattices is analyzed as a function of interaction strength, population imbalance, filling fraction and tunneling parameters. It is shown that population imbalanced Fermi-Fermi mixtures reduce to strongly interacting Bose-Fermi mixtures in the molecular limit, in sharp contrast to homogeneous or harmonically trapped systems where the resulting Bose-Fermi mixture is weakly interacting. Furthermore, insulating phases are found in optical lattices of Fermi-Fermi mixtures in addition to the standard phase-separated or coexisting superfluid/excess fermion phases found in homogeneous systems. The insulating states can be a molecular Bose-Mott insulator (BMI), a Fermi-Pauli insulator (FPI), a phase-separated BMI/FPI mixture or a Bose-Fermi checkerboard (BFC).