Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

Abstract

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at $$\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)$$ in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.