  We use Quantum Monte Carlo simulations and exact diagonalization to explore
the phase diagram of the Bose-Hubbard model with an additional superlattice
potential. We first analyze the properties of superfluid and insulating phases
present in the hard-core limit where an exact analytic treatment is possible
via the Jordan-Wigner transformation. The extension to finite on-site
interaction is achieved by means of quantum Monte Carlo simulations. We
determine insulator/superfluid phase diagrams as functions of the on-site
repulsive interaction, superlattice potential strength, and filling, finding
that insulators with fractional occupation numbers, which are present in the
hard-core case, extend deep into the soft-core region. Furthermore, at integer
fillings, we find that the competition between the on-site repulsion and the
superlattice potential can produce a phase transition between a Mott insulator
and a charge density wave insulator, with an intermediate superfluid phase. Our
results are relevant to the behavior of ultracold atoms in optical
superlattices which are beginning to be studied experimentally.
