Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice

TL;DR

This paper studies the stability of dark solitons in a Bose-Einstein condensate within an optical lattice, revealing that instabilities are weak and influenced by lattice parameters, with oscillatory behavior observed over time.

Contribution

It provides a combined analysis using the Gross-Pitaevskii equation and a tight-binding model to understand dark soliton stability in optical lattices.

Findings

Dark solitons exhibit weak instabilities influenced by lattice period and amplitude.

Instabilities develop at large times with quasi-periodic oscillations.

Stability analysis applies to both continuous and discrete models.

Abstract

We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis is based on both the full Gross-Pitaevskii equation and its tight-binding approximation counterpart (discrete nonlinear Schr{\"o}dinger equation). We find that DSs are subject to weak instabilities with an onset of instability mainly governed by the period and amplitude of the OL. The instability, if present, sets in at large times and it is characterized by quasi-periodic oscillations of the DS about the minimum of the parabolic trap.