Internal Oscillations of a Dark-Bright Soliton in a Harmonic Potential

TL;DR

This paper studies the internal oscillations of dark-bright solitons in harmonic traps within Bose-Einstein condensates, revealing how trap strength influences the coupling between internal modes and center of mass motion.

Contribution

It introduces a combined analytical and numerical approach to analyze the internal and external dynamics of dark-bright solitons in harmonic potentials, highlighting the coupling effects.

Findings

Internal modes are nearly independent of center of mass in weak traps.

Strong traps cause coupling between internal modes and center of mass.

Results are robust against initial condition noise.

Abstract

We investigate the dynamics of a dark-bright soliton in a harmonic potential using a mean-field approach via coupled nonlinear Schr\"odinger equations appropriate to multicomponent Bose-Einstein condensates. We use a modified perturbed dynamical variational Lagrangian approximation, where the perturbation is due to the trap, taken as a Thomas-Fermi profile. The wavefunction ansatz is taken as the correct hyperbolic tangent and secant solutions in the scalar case for the dark and bright components of the soliton, respectively. We also solve the problem numerically with psuedo-spectral Runge-Kutta methods. We find, analytically and numerically, for weak trapping the internal modes are nearly independent of center of mass motion of the dark-bright soliton. In contrast, in tighter traps the internal modes couple strongly to the center of mass motion, showing that for dark-bright solitons in a harmonic potential the center of mass and relative degrees of freedom are not independent. This result is robust against noise in the initial condition and should, therefore, be experimentally observable.