Short-range coherence of a lattice Bose atom gas in the Mott insulating phase

We study the short-range coherence of ultracold lattice Bose gases in the Mott insulating phase. We calculate the visibility of the interference pattern and the results agree quantitatively with the recent experimental measurement [Phys. Rev. Lett. 95, 050404 (2005)]. The visibility deviation from the inversely linear dependence on the bare on-site interaction U_0 is explained both in smaller and larger U_0. For a smaller U_0, it comes from a second order correction. For a larger U_0, except the breakdown of adiabaticity as analyzed by Gerbier et al, there might be another source to cause this deviation, which is the diversity between $U_0$ determined by the single atom Wannier function and the effective on site interaction U_eff for a multi-occupation per site.