Collisions between solitary waves of three-dimensional Bose-Einstein condensates

TL;DR

This paper investigates the behavior and collisions of bright solitary waves in three-dimensional trapped Bose-Einstein condensates, revealing stability thresholds, collision outcomes, and phase effects consistent with experiments.

Contribution

It identifies a lower stability cutoff for solitary waves and analyzes collision dynamics, including phase effects and stability conditions, in 3D Bose-Einstein condensates.

Findings

Existence of a lower cut-off for stable solitary waves.

Collision outcomes include elastic, inelastic, and collapse.

π-phase difference promotes elastic collisions and matches experimental results.

Abstract

We study bright solitary waves of three dimensional trapped Bose-Einstein condensates and their collisions. For a single solitary wave, in addition to an upper critical number, we also find a {\em lower} cut-off, below which no stable state can be found. Collisions between solitary waves can be elastic, inelastic with either reduced or increased outgoing speed, or completely unstable due to a collapse instability. A $\pi$-phase difference between the waves promotes elastic collisions, and gives excellent agreement with recent experimental results over long timescales.