Dynamics of Vector Solitons in Bose-Einstein Condensates

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 Schrödinger 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.

11 pages, 9 figures, 1 table, 1 appendix

References in corpus (6)

• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Generation of dark-bright soliton trains in superfluid-superfluid counterflow
• Soliton trains in Bose-Fermi mixtures
• Formation and Transformation of Vector-Solitons in Two-Species Bose-Einstein Condensates with Tunable Interaction
• Interaction of dark-bright solitons in two-component Bose-Einstein condensates
• Fluctuation and interaction induced instability of dark solitons in single and binary condensates

Cited by in corpus (11)

• Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions
• Beating Effects of Vector Solitons in Bose-Einstein Condensate
• AC Oscillation of a Spin Soliton Driven by a Constant Force
• Flemish Strings of Magnetic Solitons and a Non-Thermal Fixed Point in a One-Dimensional Antiferromagnetic Spin-1 Bose Gas
• Dark-bright soliton pairs: bifurcations and collisions
• A direct derivation of the dark soliton excitation energy
• Mixed Bubbles in a one-dimensional Bose-Bose mixture
• Scattering of a dark-bright soliton by an impurity
• Internal Oscillations of a Dark-Bright Soliton in a Harmonic Potential
• Novel soliton in dipolar BEC caused by the quantum fluctuations
• Spin Solitons in Spin-1 Bose-Einstein Condensates