Localization of a matter wave packet in a disordered potential

TL;DR

This paper presents a theoretical model for Anderson localization of matter waves in disordered potentials, revealing complex localized density profiles and supporting findings with numerical simulations relevant to ultracold atom experiments.

Contribution

Develops an analytical model incorporating initial phase-space density and spectral broadening, providing new insights into localized density profiles beyond simple exponential decay.

Findings

Localized density profiles are more complex than simple exponential decay.

Numerical simulations confirm the analytical predictions.

Results are relevant for interpreting ultracold atom experiments.

Abstract

We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis.