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The criteria for validity of adiabaticity for nonlinear wave equations areconsidered within the context of atomic matter-waves tunneling frommacroscopically populated optical standing-wave traps loaded from aBose-Einstein condensate. We show that even when the optical standing wave isslowly turned on and the condensate behaves adiabatically during this turn-on,once the tunneling-time between wells in the optical lattice becomes longerthan the nonlinear time-scale, adiabaticity breaks down and a significantspatially varying phase develops across the condensate wave function from wellto well. This phase drastically affects the contrast of the fringe pattern inJosephson-effect interference experiments, and the condensate coherenceproperties in general.Comment: 5 pages, 3 figure

Bose-Einstein condensates in time-dependent light potentials: Adiabatic and nonadiabatic behavior of nonlinear wave equations