Vector solitons in nearly-one-dimensional Bose-Einstein condensates

TL;DR

This paper derives a simplified model for two-component Bose-Einstein condensates in a cigar-shaped trap, constructs vector soliton solutions, and investigates their inelastic collisions and potential collapse.

Contribution

It introduces a nonpolynomial Schrödinger equation system for binary BECs and explores the dynamics and collisions of vector solitons within this framework.

Findings

Collisions are inelastic, causing vibrations and orthogonal components.

Collisions can trigger collapse depending on mass and velocity.

A family of vector soliton solutions was constructed.

Abstract

We derive a system of nonpolynomial Schroedinger equations (NPSEs) for one-dimensional wave functions of two components in a binary self-attractive Bose-Einstein condensate loaded in a cigar-shaped trap. The system is obtained by means of the variational approximation, starting from the coupled 3D Gross-Pitaevskii equations and assuming, as usual, the factorization of 3D wave functions. The system can be obtained in a tractable form under a natural condition of symmetry between the two species. A family of vector (two-component) soliton solutions is constructed. Collisions between orthogonal solitons (ones belonging to the different components) are investigated by means of simulations. The collisions are essentially inelastic. They result in strong excitation of intrinsic vibrations in the solitons, and create a small orthogonal component ("shadow") in each colliding soliton. The collision may initiate collapse, which depends on the mass and velocities of the solitons.