  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 non-uniform 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 new zero-temperature phases,
including a localized and a quasi Bose-glass phase, and discuss prospects for
their experimental observation.
