Ultracold bosons in a synthetic periodic magnetic field: Mott phases and reentrant superfluid-insulator transitions

We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength p and a period l=qa, where q is an integer and a is the lattice spacing. We show that the Schrodinger equation for the noninteracting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields q energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying p for a given q. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the p and q dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several reentrant field-induced SI transitions for any fixed period q. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity q (q/2) in real space for odd (even) q and suggest experiments to test our theory.