We investigate the superfluid-insulator transition of one-dimensional interacting bosons in both deep and shallow periodic potentials. We compare a theoretical analysis based on quantum Monte Carlo simulations in continuum space and Luttinger liquid approach with experiments on ultracold atoms with tunable interactions and optical lattice depth. Experiments and theory are in excellent agreement. Our study provides a quantitative determination of the critical parameters for the Mott transition and defines the regimes of validity of widely used approximate models, namely, the Bose-Hubbard and sine-Gordon models.
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 Schr\"odinger 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.