Rotational pendulum dynamics of a vortex molecule in a channel geometry

TL;DR

This paper studies the complex dynamics of vortex molecules in coupled superfluids within channel geometries, revealing internal rotations, boundary effects, and stability characteristics through theoretical modeling and simulations.

Contribution

It introduces an extended point vortex model combined with Gross-Pitaevskii simulations to analyze vortex molecule dynamics in confined geometries, highlighting new internal behaviors and boundary interactions.

Findings

Vortex molecules exhibit rotation and pendulum-like dynamics.

Trajectories can lead to boundary-induced break-up.

Stable and unstable fixed points are classified.

Abstract

A vortex molecule is a topological excitation in two coherently coupled superfluids consisting of a vortex in each superfluid connected by a domain wall of the relative phase, also known as a Josephson vortex. We investigate the dynamics of this excitation in a quasi-two-dimensional geometry with slab or channel boundary conditions using an extended point vortex framework complemented by Gross-Pitaevskii simulations. Apart from translational motion along the channel, the vortex molecule is found to exhibit intriguing internal dynamics including rotation and rotational-pendulum-like dynamics. Trajectories leading to a boundary-induced break-up of the vortex molecule are also described qualitatively by the simplified model. We classify the stable and unstable fixed points as well as separatrices that characterize the vortex molecule dynamics.