Density-induced processes in quantum gas mixtures in optical lattices

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We show that off-site processes and multi-orbital physics have a crucial impact on the phase diagram of quantum gas mixtures in optical lattices. In particular, we discuss Bose-Fermi mixtures where the intra- and interspecies interactions induce competing density-induced hopping processes, the so-called bond-charge interactions. Furthermore, higher bands strongly influence tunneling and on-site interactions. We apply a multi-orbital interaction-induced dressing of the lowest band which leads to renormalized hopping processes. These corrections give rise to an extended Hubbard model with intrinsically occupation-dependent parameters. The resulting decrease of the tunneling competes with a decrease of the total on-site interaction energy both affecting the critical lattice depth of the superfluid to Mott insulator transition. In contrast to the standard Bose-Fermi-Hubbard model, we predict a large shift of the transition to shallower lattice depths with increasing Bose-Fermi attraction. The applied theoretical model allows an accurate prediction of the modified tunneling amplitudes and the critical lattice depth both recently observed experimentally.