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arXiv:1205.6949 · Physical Review A

Visibility of ultracold Bose system in triangular optical lattices

Zhi Lin, Jun Zhang, Ying Yan Jiang

Published Sep 24, 2012• 6 citations
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Abstract

In this paper, by treating the hopping parameter in the Bose-Hubbard model as a perturbation, with the help of the resummed Green's function method and cumulant expansion, the momentum distribution function of an ultracold Bose system in a triangular optical lattice is calculated analytically. By its use, the time-of-flight absorption picture is plotted and the corresponding visibility is determined. A comparison between our analytical results and the experimental data of Becker et al. [New J. Phys. 12, 065025 (2010)] exhibits a qualitative agreement.

DOI
10.1103/physreva.86.033625

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In this paper, by treating the hopping parameter in the Bose-Hubbard model as a perturbation, with the help of the resummed Green's function method and cumulant expansion, the momentum distribution function of an ultracold Bose system in a triangular optical lattice is calculated analytically. By its use, the time-of-flight absorption picture is plotted and the corresponding visibility is determined. A comparison between our analytical results and the experimental data of Becker et al. [New J. Phys. 12, 065025 (2010)] exhibits a qualitative agreement.
By treating the hopping parameter as a perturbation, with the help of cumulant expansion and the re-summing technique, the one-particle Green's function of a spin-1 Bose system in a honeycomb optical lattice is calculated analytically. By the use of the re-summed Green's function, the quantum phase diagrams of the system in ferromagnetic cases as well as in antiferromagnetic cases are determined. It is found that in antiferromagnetic cases the Mott insulating states with even filling factor are more robust against the hopping parameter than that with odd filling factor, in agreement with results via other different approaches. Moreover, in order to illustrate the effectiveness of the re-summed Green's function method in calculating time-of-flight pictures, the momentum distribution function of a honeycomb lattice spin-1 Bose system in the antiferromagnetic case is also calculated analytically and the corresponding time-of-flight absorption pictures are plotted.
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 (±πa,±πa)\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)(±aπ​,±aπ​) 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 this letter, by the use of the generalized effective potential theory, with the help of the process chain approach under the framework of the Kato formulation of the perturbation expansion, we calculate out the quantum phase diagram up to the 8th order for an ultracold Bose system in a square optical superlattice. Based on these perturbative data, with the help of the linear fit extrapolation technique, more accurate results are obtained, which are in excellent agreement with recent Monte Carlo numerical results. Moreover, by employing the generalized re-summed Green's function method and cumulant expansion, the momentum distribution function of the system is also calculated analytically and the time-of-flight absorption pictures of the system are plotted.
We investigate the ground-state and finite-temperature properties of the Bose-Hubbard model using the standard basis operator method applied to the equation of motion for Green's functions. We show that by introducing the self-consistent approach, the theory goes significantly beyond the mean-field approximation, allowing more-precise description of quantum and thermal fluctuations. For optical lattice systems with ultracold bosons, we find relevant quantitative agreement with numerical and experimental data. In particular, the presented method reveals the importance of thermal fluctuations in time-of-flight experiments. For the most reliable fitting of the visibility analytical curve to the experimental data, the value of temperature is determined and proximity to the quantum regime is discussed. The problem of identification of the superfluid--Mott-insulator phase boundary from time-of-flight experiments is also considered.