  We analyze theoretically the experiment reported in [F. Gerbier et al,
cond-mat/0503452], where the interference pattern produced by an expanding
atomic cloud in the Mott insulator regime was observed. This interference
pattern, indicative of short-range coherence in the system, could be traced
back to the presence of a small amount of particle/hole pairs in the insulating
phase for finite lattice depths. In this paper, we analyze the influence of
these pairs on the interference pattern using a random phase approximation, and
derive the corresponding visibility. We also account for the inhomogeneity
inherent to atom traps in a local density approximation. The calculations
reproduce the experimental observations, except for very large lattice depths.
The deviation from the measurement in this range is attributed to the
increasing importance of non-adiabatic effects.
