  This paper presents a mean-field numerical analysis, using the full
three-dimensional time-dependent Gross-Pitaevskii equation (GPE), of an
experiment carried out by Orzel et al. [Science 291, 2386 (2001)] intended to
show number squeezing in a gaseous Bose-Einstein condensate in an optical
lattice. The motivation for the present work is to elucidate the role of
mean-field effects in understanding the experimental results of this work and
those of related experiments. We show that the non-adiabatic loading of atoms
into optical lattices reproduces many of the main results of the Orzel et al.
experiment, including both loss of interference patterns as laser intensity is
increased and their regeneration when intensities are lowered. The
non-adiabaticity found in the GPE simulations manifests itself primarily in a
coupling between the transverse and longitudinal dynamics, indicating that
one-dimensional approximations are inadequate to model the experiment.
