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

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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 U₀ is explained both in smaller and larger U₀. For a smaller U₀, it comes from a second order correction. For a larger U₀, 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 U₀ determined by the single atom Wannier function and the effective on site interaction Uₑff for a multi-occupation per site.