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Recent experiments have shown a remarkable number of collapse-and-revivaloscillations of the matter-wave coherence of ultracold atoms in opticallattices [Will et al., Nature 465, 197 (2010)]. Using a mean-fieldapproximation to the Bose-Hubbard model, we show that the visibility ofcollapse-and-revival interference patterns reveal number squeezing of theinitial superfluid state. To describe the dynamics, we use an effectiveHamiltonian that incorporates the intrinsic two-body and induced three-bodyinteractions, and we analyze in detail the resulting complex pattern ofcollapse-and-revival frequencies generated by virtual transitions to higherbands, as a function of lattice parameters and mean-atom number. Our work showsthat a combined analysis of both the multiband, non-stationary dynamics in thefinal deep lattice, and the number-squeezing of the initial superfluid state,explains important characteristics of optical lattice collapse-and-revivalphysics. Finally, by treating the two- and three-body interaction strengths,and the coefficients describing the initial superposition of number states, asfree parameters in a fit to the experimental data it should be possible to gobeyond some of the limitations of our model and obtain insight into thebreakdown of the mean-field theory for the initial state or the role ofnonperturbative effects in the final state dynamics.

Collapse and revival dynamics of superfluids of ultracold atoms in optical lattices