Solitons and solitary vortices in "pancake"-shaped Bose-Einstein condensates

TL;DR

This paper investigates solitons and vortices in pancake-shaped Bose-Einstein condensates using an effective 2D equation derived from the 3D Gross-Pitaevskii equation, revealing new stable vortex dynamics.

Contribution

It introduces a nonpolynomial Schrödinger equation for 2D BECs that accurately models 3D behavior, including vortex stability and novel vortex splitting phenomena.

Findings

Effective 2D NPSE matches 3D GPE results

Identifies stable vortex splitting and recombination

Describes density profiles in various traps

Abstract

We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates (BECs) subject to strong confinement along the axial direction. Starting from the three-dimensional (3D) Gross-Pitaevskii equation (GPE), we proceed to an effective 2D nonpolynomial Schroeodinger equation (NPSE) derived by means of the integration over the axial coordinate. Results produced by the latter equation are in very good agreement with those obtained from the full 3D GPE, including cases when the formal 2D equation with the cubic nonlinearity is unreliable. The 2D NPSE is used to predict density profiles and dynamical stability of repulsive and attractive BECs with zero and finite topological charge in various planar trapping configurations, including the axisymmetric harmonic confinement and 1D periodic potential. In particular, we find a stable dynamical regime that was not reported before, viz., periodic splitting and recombination of trapped vortices with topological charge 2 or 3 in the self-attractive BEC.