Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier

TL;DR

This paper explores how a potential barrier can suppress transverse instability in dark solitons within 2D Bose-Einstein condensates and optical waveguides, enabling control over vortex nucleation and stability.

Contribution

It introduces a method using external barriers to stabilize dark-soliton stripes and control vortex nucleation, supported by analytical and numerical validation.

Findings

Barrier potential reduces the MI wavenumber band.

Dark-soliton stripe can be made completely stable.

Number of vortices nucleated per perturbation period can be controlled.

Abstract

We study possibilities to suppress the transverse modulational instability (MI) of dark-soliton stripes in two-dimensional (2D) Bose-Einstein condensates (BECs) and self-defocusing bulk optical waveguides by means of quasi-1D structures. Adding an external repulsive barrier potential (which can be induced in BEC by a laser sheet, or by an embedded plate in optics), we demonstrate that it is possible to reduce the MI wavenumber band, and even render the dark-soliton stripe completely stable. Using this method, we demonstrate the control of the number of vortex pairs nucleated by each spatial period of the modulational perturbation. By means of the perturbation theory, we predict the number of the nucleated vortices per unit length. The analytical results are corroborated by the numerical computation of eigenmodes of small perturbations, as well as by direct simulations of the underlying Gross-Pitaevskii/nonlinear Schr\"{o}dinger equation.