Superfluid-Insulator transition of ultracold atoms in an optical lattice in the presence of a synthetic magnetic field

We study the Mott insulator-superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p/q (p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q=2,3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.