Dissipative Effects on the Superfluid to Insulator Transition in Mixed-dimensional Optical Lattices

We study the superfluid to Mott insulator transition of a mixture of heavy bosons and light fermions loaded in an optical lattice. We focus on the effect of the light fermions on the dynamics of the heavy bosons. It is shown that, when the lattice potential is sufficiently deep to confine the bosons to one dimension but allowing the fermions to freely move in three dimensions (i.e. a mixed-dimensionality lattice), the fermions act as an ohmic bath for bosons leading to screening and dissipation effects on the bosons. Using a perturbative renormalization-group analysis, it is shown that the fermion-induced dissipative effects have no appreciable impact on the transition from the superfluid to the Mott-insulator state at integer filling. On the other hand, dissipative effects are found to be very important in the half-filled case near the critical point. In this case, in the presence of a finite incommensurability that destabilizes the Mott phase, the bosons can still be localized by virtue of dissipative effects.