Quantum bright soliton in a disorder potential

TL;DR

This paper investigates the quantum motion of a bright soliton in a disordered potential, showing that it can exhibit Anderson localization with a potentially observable large localization length.

Contribution

It develops a non-perturbative Bogoliubov approach to analyze the quantum center of mass motion of bright solitons in disordered environments.

Findings

Quantum motion can exhibit Anderson localization.

Localization length can be much larger than soliton size.

Potential for experimental observation of localization effects.

Abstract

At very low temperature, a quasi-one-dimensional ensemble of atoms with attractive interactions tend to form a bright soliton. When exposed to a sufficiently weak external potential, the shape of the soliton is not modified, but its external motion is affected. We develop in detail the Bogoliubov approach for the problem, treating, in a non-perturbative way, the motion of the center of mass of the soliton. Quantization of this motion allows us to discuss its long time properties. In particular, in the presence of a disordered potential, the quantum motion of the center of mass of a bright soliton may exhibit Anderson localization, on a localization length which may be much larger than the soliton size and could be observed experimentally.