Dynamics of Vector Solitons in Bose-Einstein Condensates

TL;DR

This paper investigates the dynamics of dark-bright vector solitons in Bose-Einstein condensates using variational approximation, deriving analytical and numerical results on their oscillation modes, stability, and experimental observability.

Contribution

It introduces a variational approach to analyze two-component vector solitons in BECs, providing new insights into their oscillation behavior and stability conditions.

Findings

Oscillation frequency range 90-405 Hz for $^{87}$Rb BECs.

Internal oscillation eigenmode exists when bright density is less than dark density.

Numerical demonstration of soliton breakup and unbinding phenomena.

Abstract

We analyze the dynamics of two-component vector solitons, namely bright-in-dark solitons, via the variational approximation in Bose-Einstein condensates. The system is described by a vector nonlinear Schr\"odinger equation appropriate to multi-component Bose-Einstein condensates (BECs). The variational approximation is based on hyperbolic secant (hyperbolic tangent) for the bright (dark) component, which leads to a system of coupled ordinary differential equations for the evolution of the ansatz parameters. We obtain the oscillation dynamics of two-component dark-bright vector solitons. Analytical calculations are performed for same-width components in the vector soliton and numerical calculations extend the results to arbitrary widths. We calculate the binding energy of the system and find it proportional to the intercomponent coupling interaction, and numerically demonstrate the break up or unbinding of a dark-bright soliton. Our calculations explore observable eigenmodes, namely the internal oscillation eigenmode and the Goldstone eigenmode. We find analytically that the density of the bright component is required to be less than the density of the dark component in order to find the internal oscillation eigenmode of the vector soliton and support the existence of the dark-bright soliton. This outcome is confirmed by numerical results. Numerically, we find that the oscillation frequency is amplitude independent. For dark-bright vector solitons in $^{87}$Rb we find that the oscillation frequency range is 90 to 405 Hz, and therefore observable in multi-component BEC experiments.