Stability analysis and attractor dynamics of 3D dark solitons with localized dissipation

TL;DR

This paper investigates how localized dissipation affects the stability and attractor dynamics of dark solitons in a 3D Bose-Einstein condensate, revealing conditions for stabilization and decay pathways.

Contribution

It provides a numerical analysis of dissipation-induced stabilization of dark solitons and identifies the dark soliton as the unique steady-state attractor under various initial conditions.

Findings

Dissipation suppresses snaking instability depending on strength.

Threshold dissipation stabilizes dark solitons.

Dark soliton is the unique steady-state attractor.

Abstract

We study the stability and the attractor dynamics of an elongated Bose-Einstein condensate with dark or grey kink solitons in the presence of localized dissipation. To this end, the 3D Gross-Pitaevskii equation with an additional imaginary potential is solved numerically. We analyze the suppression of the snaking instability in dependence of the dissipation strength and extract the threshold value for the stabilization of the dark soliton for experimentally realistic parameters. Below the threshold value, we observe the decay into a solitonic vortex. Above the stabilization threshold, we observe the attractor dynamics towards the dark soliton when initially starting from a grey soliton. We find that for all initial conditions the dark soliton is the unique steady-state of the system - even when starting from the BEC ground state.