Splitting of two-component solitary waves from collisions with narrow potential barriers

TL;DR

This paper investigates how two-component bright solitons in a Bose-Einstein condensate interact with narrow potential barriers, combining analytical approximations and numerical simulations to understand splitting behavior and internal vibrations.

Contribution

It provides analytical and numerical analysis of soliton splitting in two-component BECs, including regimes with weak barriers and asymmetric nonlinearities, advancing understanding of soliton-interferometer design.

Findings

One component can be almost fully transmitted while the other is reflected.

Weak internal vibrations occur during high-quality splitting.

Analytical results agree with simulations in specific parameter regimes.

Abstract

We consider the interaction of two-component bright-bright solitons with a narrow potential barrier (splitter) in the framework of a system of two Gross-Pitaevskii (nonlinear-Schr\"{o}dinger) equations modeling a binary Bose-Einstein condensate, with self-attraction in each component and cross-attraction between them. The objective is to study splitting of composite solitons, which may be used in the design of two-component soliton-interferometer schemes. We produce approximate analytic results, assuming a weak barrier and applying the perturbation theory in the limit in which the system is integrable and the solitary waves may be considered as exact solitons. We do this in the case of negligible interspecies interactions, and also when the nonlinearities are strongly asymmetric, allowing one to neglect the self-interaction in one of the species. Then, we use systematic simulations to study the transmissions of both components in regions outside these approximations and, in particular, to compare numerical results with their analytical countertparts. We concluded that there is an appreciable parameter range where one component is almost entirely transmitted through the barrier, while the other one is reflected. Excitation of internal vibrations in the passing and rebounding solitons is explored too, with a conclusion that it is weak in the regime of high-quality splitting.