Scattering of solitons in binary Bose-Einstein condensates with spin-orbit and Rabi couplings

TL;DR

This study investigates how solitons in binary Bose-Einstein condensates scatter under spin-orbit and Rabi couplings, revealing chaotic behavior, fractal structures, and the influence of coupling strength on critical velocities.

Contribution

It introduces a reduced ODE model for soliton scattering in spin-orbit coupled BECs and explores the chaotic and fractal nature of the dynamics through numerical simulations.

Findings

Final velocities are highly sensitive to initial conditions, indicating chaos.

Existence of fractal-like reflection and transmission windows.

Spin-orbit coupling affects critical velocities and the structure of soliton interactions.

Abstract

In this paper we study the scattering of solitons in a binary Bose-Einstein Condensate (BEC) including SO- and Rabi-couplings. To this end, we derive a reduced ODE model in view to provide a variational description of the collisional dynamics. Also, we assume negative intra- and inter-component interaction strengths, such that one obtains localized solutions even in absence of external potentials. By performing extensive numerical simulations of this model we observe that, for specific conditions, the final propagation velocity of the scattered solitons could be highly sensitive to small changes in the initial conditions, being a possible signature of chaos. Additionally, there are infinitely many intervals of regularity emerging from the obtained chaotic-like regions and forming a fractal-like structure of reflection/transmission windows. Finally, we investigate how the value of the spin-orbit coupling strength changes the critical velocities, which are minimum/maximum values for the occurrence of solitons bound-states, as well as the fractal-like structure.