Dark soliton in a disorder potential

TL;DR

This paper investigates the deformation and quantum localization of dark solitons in a Bose-Einstein condensate subjected to weak disorder, revealing that solitons can exhibit Anderson localization with long lifetimes.

Contribution

It provides a combined analytical and numerical study of dark soliton deformation and demonstrates the potential for Anderson localization in disordered Bose-Einstein condensates.

Findings

Good agreement between linear response analysis and numerical simulations.

Dark solitons can exhibit Anderson localization in disorder.

Localized solitons have lifetimes longer than typical condensate lifetimes.

Abstract

We consider dark soliton in a Bose-Einstein condensate in the presence of a weak disorder potential. Deformation of the soliton shape is analyzed within the Bogoliubov approach and by employing expansion in eigenstates of the P\"oschl-Teller Hamiltonian. Comparison of the results with the numerical simulations indicates that the linear response analysis reveals good agreement even if the strength of the disorder is of the order of the chemical potential of the system. In the second part of the paper we concentrate on quantum nature of the dark soliton and demonstrate that the soliton may reveal Anderson localization in the presence of a disorder. The Anderson localized soliton may decay due to quasi-particle excitations induced by the disorder. However, we show that the corresponding lifetime is much longer than condensate lifetime in a typical experiment.