The emergence of Anderson localization (AL) has been well studied both theoretically and experimentally in zero-range (or contact) interacting Bose-Einstein condensates (BEC). In this thesis, we theoretically study the expansion of an initially confined 1D Rydberg-dressed BEC in a weak random potential in which the range of the interaction, the blockade radius Rc, is tunable. The localization is studied where the zero-range limit (Rc →0) healing length ξ0 is set to be fixed and exceed the disorder correlation length σD. It is found that when Rc ≤ lc, in the short-range superfluid phase (SF) [lc ≃ 1.7 ξ0 is the critical range for the SF–supersolid (SS)transition], exponential localization occurs. In the opposite long-range SS phase, Rc> lc, it yields Gaussian localization. We have verified the results by numerically simulating the oscillating Rydberg-dressed BEC in a weak random potential.

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