  We study the nonequilibrium dynamics of a Bose-Einstein condensate which is
split in a harmonic trap by turning up a periodic optical lattice potential. We
evaluate the dynamical evolution of the phase coherence along the lattice and
the number fluctuations in individual lattice sites within the stochastic
truncated Wigner approximation when several atoms occupy each site. We show
that the saturation of the number squeezing at high lattice strengths, which
was observed in recent experiments by Orzel et. al., can be explained by the
nonadiabaticity of the splitting.
