Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice

By direct numerical simulation and variational solution of the Gross-Pitaevskii equation, we studied the stationary and dynamic characteristics of a cigar-shaped, localized, collisionally inhomogeneous Bose-Einstein condensate trapped in a one-dimensional bichromatic quasi-periodic optical-lattice potential, as used in a recent experiment on the localization of a Bose-Einstein condensate [Roati et al., Nature (London) {\bf 453}, 895 (2008)]. The effective potential characterizing the spatially modulated nonlinearity is obtained. It is found that the collisional inhomogeneity has influence not only on the central region but also on the tail of the Bose-Einstein condensate. The influence depends on the sign and value of the spatially modulated nonlinearity coefficient. We also demonstrate the stability of the stationary localized stat$ performing a standard linear stability analysis. Where possible, the numerical results are shown to be in good agreement with the variational results.