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

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 $w_r=(\mu /\hslash )\sqrt{(8/15)g_{12}/g}$. 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.

References in corpus (2)

• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Experimental observation of oscillating and interacting matter wave dark solitons

Cited by in corpus (9)

• Non-degenerate Bound State Solitons in Multi-component Bose-Einstein Condensates
• Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions
• Internal Oscillations of a Dark-Bright Soliton in a Harmonic Potential
• Spatial Phase Separation of a Binary Mixture in a Ring Trimer
• Quantum Monte Carlo-based density functional for one-dimensional Bose-Bose mixtures
• Bound solitonic states in trapped multidimensional Bose-Einstein condensates
• On-demand generation of dark-bright soliton trains in Bose-Einstein condensates
• Dynamical generation of dark-bright solitons through the domain wall of two immiscible Bose-Einstein condensates
• Solitons in a class of interacting scalar field theories without $SO(2)$ invariance