Extended Bose-Hubbard model in a shaken optical lattice

Abstract

We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude $t_2$, which can be easily tuned via shaking amplitude. As $t_2$ increases, a $Z_2$-symmetry-breaking superfluid ($Z_2$SF) phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, $Z_2$SF, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.

6 pages, 6 figures

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