Anderson localization in an oscillating Rydberg-dressed condensate with random disorder

We numerically study the Anderson localization in an oscillating one-dimensional Rydberg-dressed Bose-Einstein condensate with weak random disorder in which the range of the interaction, the blockade radius Rc, is variable. Without disorder, the uniform system can undergo a superfluid-supersolid transition at Rc=lc≃1.7ζ0 with ζ0 the zero-range healing length. When ζ0 exceeds the disorder correlation length σD, we show that exponential localization occurs in the equilibrium condensate when Rc≤lc, while Gaussian localization occurs when Rc>lc. The latter suggests that the k wave for a long-ranged interacting system could decay Gaussianly with weak random disorder.