Bose-Hubbard Model in the Rotating Frame of Reference

Following a novel experimental arrangement which can rotate a two-dimensional optical lattice at frequencies up to several kilohertz we discuss the ground state of the two-dimensional Bose-Hubbard Hamiltonian, relevant for rotating gaseous Bose-Einstein condensates, by employing U(1) quantum rotor approach and the topologically constrained path integral. Ultracold atoms in such a rotating lattice can be used for the direct quantum simulation of strongly correlated systems under large effective magnetic fields. We derive an effective quantum action for the Bose-Hubbard model, which enables a non-perturbative treatment of the zero-temperature phase transition in the rotating frame. We calculate the ground-state phase diagram, analytically deriving maximum repulsive energy for several rational values of the frustration rotation parameter f = 0, 1/2, 1/3, 1/4, and 1/6 for the square and triangular lattice. Performed calculations revealed strong non-monotonical dependence of the critical ratio of the kinetic energy to the repulsive on-site energy, that separates the global coherent from the insulating state, on topology of the lattice.