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

doi:10.1007/s11467-018-0751-9

Front. Phys.

2018, Vol. 13

Issue (4) : 136401 https://doi.org/10.1007/s11467-018-0751-9

RESEARCH ARTICLE

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

Zhi Lin^1,²(

), Jun Zhang², Ying Jiang^2,^3,⁴

¹. Department of Physics, State Key Laboratory of Surface Physics and Laboratory of Advanced Materials, Fudan University, Shanghai 200433, China
². Department of Physics, Shanghai University, Shanghai 200444, China
³. Qian Weichang College, Shanghai University, Shanghai 200444, China
⁴. Key Lab for Astrophysics, Shanghai 200234, China

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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 (± $π a$ ,± $π a$ ) 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

Corresponding Author(s): Zhi Lin

Issue Date: 23 April 2018

Cite this article:

Zhi Lin,Jun Zhang,Ying Jiang. Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method[J]. Front. Phys. , 2018, 13(4): 136401.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-018-0751-9
https://academic.hep.com.cn/fop/EN/Y2018/V13/I4/136401

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