  We examine spinor Bose-Einstein condensates in optical superlattices
theoretically using a Bose-Hubbard Hamiltonian that takes spin effects into
account. Assuming that a small number of spin-1 bosons is loaded in an optical
potential, we study single-particle tunneling that occurs when one lattice site
is ramped up relative to a neighboring site. Spin-dependent effects modify the
tunneling events in a qualitative and quantitative way. Depending on the
asymmetry of the double well different types of magnetic order occur, making
the system of spin-1 bosons in an optical superlattice a model for mesoscopic
magnetism. We use a double-well potential as a unit cell for a one-dimensional
superlattice. Homogeneous and inhomogeneous magnetic fields are applied and the
effects of the linear and the quadratic Zeeman shifts are examined. We also
investigate the bipartite entanglement between the sites and construct states
of maximal entanglement. The entanglement in our system is due to both orbital
and spin degrees of freedom. We calculate the contribution of orbital and spin
entanglement and show that the sum of these two terms gives a lower bound for
the total entanglement.
