  Recent experiments have shown a remarkable number of collapse-and-revival
oscillations of the matter-wave coherence of ultracold atoms in optical
lattices [Will et al., Nature 465, 197 (2010)]. Using a mean-field
approximation to the Bose-Hubbard model, we show that the visibility of
collapse-and-revival interference patterns reveal number squeezing of the
initial superfluid state. To describe the dynamics, we use an effective
Hamiltonian that incorporates the intrinsic two-body and induced three-body
interactions, and we analyze in detail the resulting complex pattern of
collapse-and-revival frequencies generated by virtual transitions to higher
bands, as a function of lattice parameters and mean-atom number. Our work shows
that a combined analysis of both the multiband, non-stationary dynamics in the
final deep lattice, and the number-squeezing of the initial superfluid state,
explains important characteristics of optical lattice collapse-and-revival
physics. Finally, by treating the two- and three-body interaction strengths,
and the coefficients describing the initial superposition of number states, as
free parameters in a fit to the experimental data it should be possible to go
beyond some of the limitations of our model and obtain insight into the
breakdown of the mean-field theory for the initial state or the role of
nonperturbative effects in the final state dynamics.
