Deviation from one-dimensionality in stationary properties and collisional dynamics of matter-wave solitons

TL;DR

This paper investigates how residual three-dimensional effects influence the behavior and collisions of matter-wave solitons in a Bose-Einstein condensate, using an effective 1D model with additional nonlinear terms.

Contribution

It introduces an effective 1D Gross-Pitaevskii equation with a quintic term, finds exact soliton solutions, and analyzes their stability and collision dynamics, including symmetry breaking effects.

Findings

Stable soliton family despite collapse risk in 1D model

Existence of a critical velocity for soliton merger

Symmetry breaking in soliton collisions with phase difference

Abstract

By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective 1D Gross-Pitaevskii equation that includes an additional quintic self-focusing term, generated by the tight transverse confinement, we find a family of exact one-soliton solutions and demonstrate stability of the entire family, despite the possibility of collapse in the 1D equation with the quintic self-focusing nonlinearity. Simulating collisions between two solitons in the same setting, we find a critical velocity, $V_{c}$, below which merger of identical in-phase solitons is observed. Dependence of $V_{c} $ on the strength of the transverse confinement and number of atoms in the solitons is predicted by means of the perturbation theory and investigated in direct simulations. Symmetry breaking in collisions of identical solitons with a nonzero phase difference is also shown in simulations and qualitatively explained by means of an analytical approximation.