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

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Abstract
The criteria for validity of adiabaticity for nonlinear wave equations are considered within the context of atomic matter waves tunneling from macroscopically populated optical standing-wave traps loaded from a Bose-Einstein condensate. We show that, even when the optical standing wave is slowly turned on and the condensate behaves adiabatically during this turn-on, once the tunneling time between wells in the optical lattice becomes longer than the nonlinear time scale, adiabaticity breaks down and a significant spatially varying phase develops across the condensate wave function from well to well. This phase drastically affects the contrast of the fringe pattern in Josephson-effect interference experiments, and the condensate coherence properties in general.
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