Analytical Mean-Field Approach to the Phase Diagram of Ultracold Bosons in Optical Superlattices

We report a multiple-site mean-field analysis of the zero-temperature phase diagram for ultracold bosons in realistic optical superlattices. The system of interacting bosons is described by a Bose-Hubbard model whose site-dependent parameters reflect the nontrivial periodicity of the optical superlattice. An analytic approach is formulated based on an analysis of the stability of a fixed point of the map defined by the self-consistency condition inherent in the mean-field approximation. The experimentally relevant case of the two-period one-dimensional superlattice is briefly discussed. In particular, it is shown that, for a special choice of the superlattice parameters, the half-filling insulator domain features an unusual loophole shape that the single-site mean-field approach fails to capture.