Nonadiabatic dynamics of a Bose-Einstein condensate in an optical lattice

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.