Bose-Hubbard Model in the Rotating Frame of Reference

T.P. Polak Faculty of Physics, Adam Mickiewicz University of Poznań, Umultowska 85, 61-614 Poznań, Poland

and T.K. Kopeć Institute for Low Temperatures and Structure Research, Polish Academy of Sciences, POB 1410, 50-950 Wrocław 2, Poland

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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.

DOI: 10.12693/APhysPolA.118.279 PACS numbers: 05.30.Jp, 03.75.Lm, 03.75.Nt