Bright-Dark Soliton Complexes in Spinor Bose-Einstein Condensates

TL;DR

This paper derives and analyzes approximate bright-dark vector solitons in spinor Bose-Einstein condensates, demonstrating their stability, collision properties, and oscillations within a trapping potential through analytical and numerical methods.

Contribution

It introduces a multiscale expansion approach to reduce the complex GPE system to an integrable model, providing new approximate solutions for vector solitons in spinor BECs.

Findings

Solitons propagate undistorted and undergo quasi-elastic collisions.

Bright components are guided by dark components in a trap, performing harmonic oscillations.

Deviations from harmonic oscillations increase with soliton depth and interaction strength.

Abstract

We present bright-dark vector solitons in quasi-one-dimensional spinor (F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations (GPEs) to a completely integrable Yajima-Oikawa system. In this way, we obtain approximate solutions for small-amplitude vector solitons of dark-dark-bright and bright-bright-dark types, in terms of the $m_{F}=+1,-1,0$ spinor components, respectively. By means of numerical simulations of the full GPE system, we demonstrate that these states indeed feature soliton properties, i.e., they propagate undistorted and undergo quasi-elastic collisions. It is also shown that, in the presence of a parabolic trap of strength $\omega $, the bright component(s) is (are) guided by the dark one(s), and, as a result, the small-amplitude vector soliton as a whole performs harmonic oscillations of frequency $\omega/ \sqrt{2}$ in the shallow soliton limit. We investigate numerically deviations from this prediction, as the depth of the solitons is increased, as well as when the strength of the spin-dependent interaction is modified.