Spatial tuning of Bose-Einstein condensations

We briefly review our recent work on spatial tuning of Bose-Einstein condensation (BEC). We first study spatially periodic tuning of the s-wave scattering length for controlling the propagation of a BEC matter wave, and find matter wave limiting processing and bistability. Second, we show that a stable BEC with natural attractive interaction could be formed by tuning the s-wave scattering length with a Gaussian optical field, but the condensed atom number should be less than a critical value. Further, we apply Thomas-Fermi approximation to obtain a formula for this critical value.