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

Adiabatic and nonadiabatic behavior of nonlinear wave equations was studied within the context of atomic matter waves tunneling from macroscopically populated optical standing-wave traps loaded from a Bose-Einstein condensate. Bose-Einstein condensed Rb87atoms in the hyperfine state confined in an array of optical traps in a gravitational field were considered. Results indicated that the spatially varying phase of the solution to the Gross-Pitaevskii equation was large when the tunneling time between wells in the optical lattice was comparable to or larger than the nonlinear time scale.