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We study the splitting of a harmonically trapped atomic Bose-Einsteincondensate when we continuously turn up an optical lattice (or a double-well)potential. As the lattice height is increased, quantum fluctuations of atomsare enhanced. The resulting nonequilibrium dynamics of the fragmentationprocess of the condensate, the loss of the phase coherence of atoms along thelattice, and the reduced atom number fluctuations in individual lattice sitesare stochastically studied within the truncated Wigner approximation. Weperform a detailed study of the effects of temperature and lattice height onatom dynamics, and investigate the validity of the classical Gross-Pitaevskiiequation in optical lattices. We find the atom number squeezing to saturate indeep lattices due to nonadiabaticity in turning up of the lattice potentialthat is challenging to avoid in experiments when the occupation number of thelattice sites is large, making it difficult to produce strongly number squeezed(or the Mott insulator) states with large filling factors. We also investigatesome general numerical properties of the truncated Wigner approximation.Comment: 17 page

Quantum dynamics in splitting a harmonically trapped Bose-Einstein condensate by an optical lattice: Truncated Wigner approximation