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Laser Physics

Quantum phase diagrams and time-of-flight pictures of spin-1 Bose systems in honeycomb optical lattices

Jun Zhang, Ying Yan Jiang

Published Jun 29, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1054-660x/26/9/095501

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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 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.
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.
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 paper, we present a generalized Green's function method which can be used to investigate the quantum phase transitions analytically in a systematic way for ultracold Bose systems in bipartite optical lattices. As an example, to the lowest order, we calculate the quantum phase boundaries of the localized states (Mott insulator or charge density wave) of an ultracold Bose system in a ddd-dimensional hypercubic optical lattice with nearest-neighbor repulsive interactions. Due to the inhomogeneity of the system, in the generalized Green's function method, cumuants on different sublattices are calculated separately, together with re-summed Green's function technique, the analytical expression of the phase boundaries of the localized phases in the system is presented.
We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence of the Green function leads to non-perturbative results for the boundary between the superfluid and the Mott phase for finite temperatures. Whereas the first-order calculation reproduces the seminal mean-field result, the second order goes beyond and shifts the phase boundary in the immediate vicinity of the critical parameters determined by the latest high-precision Monte-Carlo simulations of the Bose-Hubbard model. In addition, our Green's function approach allows for calculating the excitation spectrum at finite temperature and for determining the effective masses of particles and holes.
In this paper, we investigate systematically the quantum phase transition between the Mott-insulator and superfluid states of the Jaynes–Cummings Hubbard model in triangular, square, honeycomb and kagomé lattices. With the help of Green's function method, by treating the hopping term in the Jaynes–Cummings Hubbard model as perturbation, we calculate the phase boundaries of Jaynes–Cummings Hubbard models on different geometrical lattices analytically up to second order for both detuning and . It is shown that the Mott phase becomes more unstable when increasing the polariton number n . Meanwhile, the Mott lobe of n = 0 is enlarged while other Mott lobes shrink as the detuning parameter increases.