  We study the ground-state phase diagram of spinless and spin-1 bosons in
optical superlattices using a Bose-Hubbard Hamiltonian that includes
spin-dependent interactions. We decouple the unit cells of the superlattice via
a mean-field approach and take into account the dynamics within the unit cell
exactly. The system supports Mott-insulating as well as superfluid phases. The
transitions between these phases are second-order for spinless bosons and
second- or first-order for spin-1 bosons. Anti-ferromagnetic interactions
energetically penalize high-spin configurations and elongate all Mott lobes,
especially the ones corresponding to an even atom number on each lattice site.
We find that the quadratic Zeeman effect lifts the degeneracy between different
polar superfluid phases leading to additional metastable phases and first-order
phase transitions. Finally, we show that an energy offset between the two sites
of the unit cell induces a staircase of single-atom tunneling resonances which
surprisingly survives well into the superfluid regime.
