  In this paper, by treating the hopping parameter in Bose-Hubbard model as a
perturbation, with the help of the re-summed Green's function method and
cumulants expansion, the momentum distribution function of the ultra-cold Bose
system in triangular optical lattice is calculated analytically. By utilizing
it, the time-of-flight absorption picture is plotted and the corresponding
visibility is determined. The comparison between our analytical results and the
experimental data from Ref.[4] exhibits a qualitative agreement.
