Dark-dark-soliton dynamics in two density-coupled Bose-Einstein condensates

TL;DR

This paper investigates the dynamics of dark-dark solitons in two coupled Bose-Einstein condensates, revealing attractive interactions, oscillatory behaviors, and stability phenomena influenced by interparticle interactions and trapping.

Contribution

It introduces an adiabatic perturbation theory for dark-dark solitons in coupled BECs, uncovering attractive interactions and complex stability behaviors not previously detailed.

Findings

Soliton interactions are attractive when inter-condensate interactions are repulsive.

Relative soliton motion exhibits harmonic oscillations with frequency depending on interaction parameters.

Resonance effects lead to alternating stability and instability fringes in finite systems.

Abstract

We study the 1D dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate ($g>0$). By using an adiabatic perturbation theory in the parameter $g_{12}/{g}$, we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive $g_{12}>0$. As a result, the relative motion of dark solitons with equal chemical potential $\mu$ is well approximated by harmonic oscillations of angular frequency $w_r=(\mu/\hbar)\sqrt{({8}/{15}){g_{12}}/{g}}$. We also show that in finite systems, the resonance of this anomalous excitation mode with the spin density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter. In the presence of harmonic trapping (with angular frequency $\Omega$) the solitons are driven by the superposition of two harmonic motions at a frequency given by $w^2=(\Omega/\sqrt{2})^2+w_r^2$. When $g_{12}<0$, these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them.