Effects of Atom-Atom Interaction on Localization and Adiabaticity of BEC in One-Dimensional Disorder Optical Lattice

We numerically simulate the dynamical behavior of BEC in one-dimensional incommensurable optical lattice by split-step Fourier method in a time-dependent one-dimensional Gross-Pitaevskii equation. It is indicated that the atom-atom interaction will weaken the localization and broaden the wave function, and it will destroy the adiabaticity of the ramped loading process in both single lattice and incommensurate lattice due to the broadening effect. A band structure model can interpret the difference of the adiabatic condition with non-interacting BEC in these optical lattices.