Simulation of a stationary dark soliton in a trapped zero-temperature Bose-Einstein condensate

TL;DR

This paper presents a computational method to generate and analyze stationary dark solitons in trapped Bose-Einstein condensates using the Gross-Pitaevskii equation, demonstrating their stability and numerical generation.

Contribution

It introduces a novel numerical scheme for creating stationary dark solitons in BECs as eigenstates of the GP equation, applicable in various trapping potentials and interaction types.

Findings

Dark solitons are stationary eigenstates of the GP equation.

The method efficiently generates solitons as nonlinear continuations of vibrational states.

The scheme's stability is confirmed under different perturbations.

Abstract

We discuss a computational mechanism for the generation of a stationary dark soliton, or black soliton, in a trapped Bose-Einstein condensate using the Gross-Pitaevskii (GP) equation for both attractive and repulsive interaction. It is demonstrated that the black soliton with a "notch" in the probability density with a zero at the minimum is a stationary eigenstate of the GP equation and can be efficiently generated numerically as a nonlinear continuation of the first vibrational excitation of the GP equation in both attractive and repulsive cases in one and three dimensions for pure harmonic as well as harmonic plus optical-lattice traps. We also demonstrate the stability of this scheme under different perturbing forces.