Frontiers of Physics

, 13:136401 | Cite as

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

  • Zhi Lin
  • Jun Zhang
  • Ying Jiang
Research article


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.


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

PACS numbers

03.75.Hh 64.70.Tg 67.85.Hj 03.75.Lm 



Y.J. acknowledges Axel Pelster for his stimulating and fruitful discussions. Z.L. acknowledges inspiring discussions with Yan Chen. This work was supported by the National Natural Science Foundation of China [Grant Nos. 11074043 (Z.L.), 11274069 (Z.L.) and 11275119 (Y.J.)] and by the State Key Programs of China (Grant Nos. 2012CB921604 and 2009CB929204) (Z.L.). This work was also supported by Ph.D. Programs Foundation of Ministry of Education of China under Grant No. 20123108110004 (Y.J.).


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics, State Key Laboratory of Surface Physics and Laboratory of Advanced MaterialsFudan UniversityShanghaiChina
  2. 2.Department of PhysicsShanghai UniversityShanghaiChina
  3. 3.Qian Weichang CollegeShanghai UniversityShanghaiChina
  4. 4.Key Lab for AstrophysicsShanghaiChina

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