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.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.

Frontiers of PhysicsMar 22, 20182 citations

Ultracold Atoms and Bose-Einstein Condensates in Optical Lattices

O. Morsch, E. Arimondo

arXiv:cond-mat/0209034Lecture notes in physicsJan 1, 200219 citations

Ultracold atomic Bose and Fermi spinor gases in optical lattices

K. Eckert, Łukasz Zawitkowski, M. J. Leskinen +2 more

We investigate magnetic properties of Mott-insulating phases of ultracold Bose and Fermi spinor gases in optical lattices. We consider in particular the F = 2 Bose gas, and the F = 3/2 and 5/2 Fermi gases. We derive effective spin Hamiltonians for one and two atoms per site and discuss the possibilities of manipulating the magnetic properties of the system using optical Feshbach resonances. We discuss low temperature quantum phases of a Rb-87 gas in the F = 2 hyperfine state, as well as possible realizations of high spin Fermi gases with either Li-6 or Cs-132 atoms in the F = 3/2 state, and with Yb-173 atoms in the F = 5/2 state.We investigate magnetic properties of Mott-insulating phases of ultracold Bose and Fermi spinor gases in optical lattices. We consider in particular the F = 2 Bose gas, and the F = 3/2 and 5/2 Fermi gases. We derive effective spin Hamiltonians for one and two atoms per site and discuss the possibilities of manipulating the magnetic properties of the system using optical Feshbach resonances. We discuss low temperature quantum phases of a Rb-87 gas in the F = 2 hyperfine state, as well as possible realizations of high spin Fermi gases with either Li-6 or Cs-132 atoms in the F = 3/2 state, and with Yb-173 atoms in the F = 5/2 state.

Jan 1, 200714 citations

\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.