Localization from quantum interference in one-dimensional disordered potentials

TL;DR

This paper analyzes how quantum wave packets localize in one-dimensional disordered potentials, showing that their density tails can be described by eigenstate projections, with implications for understanding Anderson localization in ultracold atoms.

Contribution

It introduces a simplified approach to describe localized quantum states in disordered potentials using eigenstate projections, validated by numerical simulations.

Findings

Density tails are well described by eigenstate projections.

Phase randomization of interference terms is a valid approximation.

Results are consistent with experimental observations of Anderson localization.

Abstract

We show that the tails of the asymptotic density distribution of a quantum wave packet that localizes in the the presence of random or quasiperiodic disorder can be described by the diagonal term of the projection over the eingenstates of the disordered potential. This is equivalent of assuming a phase randomization of the off-diagonal/interference terms. We demonstrate these results through numerical calculations of the dynamics of ultracold atoms in the one-dimensional speckle and quasiperiodic potentials used in the recent experiments that lead to the observation of Anderson localization for matter waves [Billy et al., Nature 453, 891 (2008); Roati et al., Nature 453, 895 (2008)]. For the quasiperiodic case, we also discuss the implications of using continuos or discrete models.