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

Abstract

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 ${R}_{\mathrm{c}}$, is variable. Without disorder, the uniform system can undergo a superfluid-supersolid transition at ${R}_{\text{c}}={l}_{\mathrm{c}}\ensuremath{\simeq}1.7{\ensuremath{\xi}}_{0}$ with ${\ensuremath{\xi}}_{\text{0}}$ the zero-range healing length. When ${\ensuremath{\xi}}_{0}$ exceeds the disorder correlation length ${\ensuremath{\sigma}}_{\mathrm{D}}$, we show that exponential localization occurs in the equilibrium condensate when ${R}_{\mathrm{c}}\ensuremath{\le}{l}_{\mathrm{c}}$, while Gaussian localization occurs when ${R}_{\mathrm{c}}g{l}_{\mathrm{c}}$. The latter suggests that the $k$ wave for a long-ranged interacting system could decay Gaussianly with weak random disorder.