Beating dark-dark solitons in Bose-Einstein condensates

TL;DR

This paper investigates beating dark-dark solitons in two-component Bose-Einstein condensates, analyzing their properties, stability, and interactions, and connecting them to dark-bright solitons through SO(2) rotation.

Contribution

It identifies exact periodic orbits of beating dark-dark solitons in the Manakov limit and explores their persistence and dynamics under deviations and external trapping.

Findings

Beating dark-dark solitons are connected to dark-bright solitons via SO(2) rotation.

These solitons are exact periodic orbits in the Manakov limit with and without trapping.

The breathing states can break into dark-antidark solitons under large deviations.

Abstract

Motivated by recent experimental results, we study beating dark-dark solitons as a prototypical coherent structure that emerges in two-component Bose-Einstein condensates. We showcase their connection to dark- bright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating that this breathing state may be broken apart into dark-antidark soliton states. Finally, we consider the dynamics and interactions of two beating dark-dark solitons in the absence and in the presence of the trap, inferring their typically repulsive interaction.