Density-induced processes in quantum gas mixtures in optical lattices

Abstract

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

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

“…Those parameters are, as mentioned above, determined by the boson-fermion interaction strength. For too strong interactions one would have to consider higher bands [44,45] not included in our model.…”

“…[38][39][40] (for the analogous effects with Bose-Bose mixtures and tightly trapped bosons, see [41,42]), could not be explained with this simple description. It has soon been realized that density-dependent tunneling terms as well as contributions coming from higher Bloch bands are necessary to describe the systems in question [43][44][45][46], whenever the interspecies interaction becomes strong enough. As a consequence, for bosons interacting with immobile fermionic impurities the disorder affects also the tunneling.…”

Observation of Density-Induced Tunneling

“…It originates from the two-body interaction operator and represents the dominant off-site contribution for neutral atoms in optical lattices [7][8][9]. Its amplitude…”

“…The experimental data points pinpoint the dependence on the interaction strength as discussed above and agree well with the generalized model including density-induced tunneling. Note that the interaction-induced admixture of higher-bands will lead to a slightly modified rate for the total tunneling [7][8][9]19].…”

“…In optical lattices, density-induced tunneling [5][6][7][8][9] is even more pronounced due to the characteristic shape of the Wannier functions [7]. Several indications for density-induced tunneling have been found: It has a strong influence on the superfluid to Mottinsulator transition in bosonic [7,10,11] and multicomponent systems such as Bose-Fermi mixtures of atoms [6,8,[12][13][14][15]. As a tunneling process, it also modifies the effective band structure, which has also been observed in a Bose-Fermi mixture [16].…”