Solitons and vortices in nonlinear potential wells

TL;DR

This paper explores the formation, stability, and dynamics of topological modes such as solitons and vortices in nonlinear potential wells modeled by the nonlinear Schrödinger equation, with potential applications in optics and Bose-Einstein condensates.

Contribution

It extends previous studies by analyzing multi-dimensional topological modes in single- and double-well nonlinear potentials, including symmetry breaking and mode interactions.

Findings

Identification of stable 2D vortex and dipole modes

Observation of Rabi oscillations in rocking potential wells

Diverse topological states in double-well configurations

Abstract

We consider self-trapping of topological modes governed by the one- and two-dimensional (1D and 2D) nonlinear-Schrodinger/Gross-Pitaevskii equation with effective single- and double-well (DW) nonlinear potentials induced by spatial modulation of the local strength of the self-defocusing nonlinearity. This setting, which may be implemented in optics and Bose-Einstein condensates, aims to extend previous studies, which dealt with single-well nonlinear potentials. In the 1D setting, we find several types of symmetric, asymmetric and antisymmetric states, focusing on scenarios of the spontaneous symmetry breaking. The single-well model is extended by including rocking motion of the well, which gives rise to Rabi oscillations between the fundamental and dipole modes. Analysis of the 2D single-well setting gives rise to stable modes in the form of ordinary dipoles, vortex-antivortex dipoles (VADs), and vortex triangles (VTs), which may be considered as produced by spontaneous breaking of the axial symmetry. The consideration of the DW configuration in 2D reveals diverse types of modes built of components trapped in the two wells, which may be fundamental states and vortices with topological charges m = 1 and 2, as well as VADs (with m = 0) and VTs (with m = 2).