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

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-Schrodinger) 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 counterparts. We conclude that there is an appreciable parameter range where one component is almost entirely transmitted through the barrier, while the other one is reflected. The excitation of internal vibrations in the passing and rebounding solitons is explored as well, with a conclusion that it is weak in the regime of high-quality splitting.