Matter-wave localization in a weakly perturbed optical lattice

TL;DR

This paper investigates how weak perturbations in optical lattices can induce localization of Bose-Einstein condensates, analyzing stability and dynamics through numerical and variational methods.

Contribution

It introduces a study of localization in BECs caused by weak perturbations in optical lattices, combining numerical solutions and variational approximation.

Findings

Weak perturbations induce localization in optical lattices.

Localized states remain stable under certain dynamics.

Perturbations remove lattice periodicity, leading to localization.

Abstract

By numerical solution and variational approximation of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly-interacting Bose-Einstein condensate in a weakly perturbed optical lattice in one and three dimensions. The perturbation achieved through a weak delocalizing expulsive or a linear potential as well as a weak localizing harmonic potential removes the periodicity of the optical lattice and leads to localization. We also studied some dynamics of the localized state confirming its stability.