Phase diagram of bosonic atoms in two-color superlattices

We investigate the zero-temperature phase diagram of a gas of bosonic atoms in one- and two-color standing-wave lattices in the framework of the Bose-Hubbard model. We first introduce some relevant physical quantities; superfluid fraction, condensate fraction, quasimomentum distribution, and matter-wave interference pattern. We then discuss the relationships between them on the formal level and show that the superfluid fraction, which is the relevant order parameter for the superfluid to Mott-insulator transition, cannot be probed directly via the matter-wave interference patterns. The formal considerations are supported by exact numerical solutions of the Bose-Hubbard model for uniform one-dimensional systems. We then map out the phase diagram of bosons in nonuniform lattices. The emphasis is on optical two-color superlattices which exhibit a sinusoidal modulation of the well depth and can be easily realized experimentally. From the study of the superfluid fraction, the energy gap, and other quantities, we identify additional zero-temperature phases, including a localized and a quasi-Bose-glass phase, and discuss prospects for their experimental observation