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 (±\frac{\mathrm{\pi }}{a},±\frac{\mathrm{\pi }}{a}) 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.

Keywords

ultracold Bose gases / quantum phase transition / bipartite optical lattice / generalized / Green’s function method / time-of-flight absorption picture

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[58] Disgusting ghost peaks are well known in cubic lattice systems [15]. Our method shows the existence of ghost peaks in square lattice when J/U>(J/U)_c, but no ghost peak in triangular [16] and hexagonal lattice for arbitrary J/U. Thus, the existence of disgusting ghost peaks is not only due to the divergence of re-summed Green’ function, but also depends on the lattice structure or some unknown reasons. At the critical point (V ˜0= V ˜0c ), the ground state of the system is neither localized phases (MI or CDW) nor compressible phases (SS or SF), but it includes characteristic fingerprints of the physical properties of both localized and compressible phases. At V ˜0c , some tiny satellite peaks appear in ‘SS’ phase but not in ‘SF’ phase. The appearance of those tiny peaks can be deemed to be an evidence of ‘SS’ phase, since it coincides with the feature of ‘SS’ phase. In the case of J/U>(J/U)_c, our theory may not be exactly solid, but it is available for triangular [16] and hexagonal systems. The above-mentioned argument indicates that when J/U>(J/U)_c, if these satellite peaks appear in SS phase, these are real peaks; but they should be taken as ghost peaks in SF phases if existing, since there is no such peaks at the critical point where our theory is valid and it also does not coincide with the features of SF phase.

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