Do Vortices Entangle?

TL;DR

This paper proposes an experiment to create and detect topologically entangled states of superconducting vortices, predicting how vortex behavior changes with geometry and providing experimental signatures for entanglement and cutting.

Contribution

It introduces a feasible experimental setup for directly constructing and probing vortex entanglement in superconductors, with theoretical predictions on vortex stability and signatures.

Findings

Vortices approach each other as the pitch increases.

Entangled vortex states become unstable beyond a maximum pitch.

Predicted experimental signatures for vortex entanglement and cutting.

Abstract

We propose an experiment for directly constructing and locally probing topologically entangled states of superconducting vortices which can be performed with present-day technology. Calculations using an elastic string vortex model indicate that as the pitch (the winding angle divided by the vertical distance) increases, the vortices approach each other. At values of the pitch higher than a maximum value the entangled state becomes unstable to collapse via a singularity of the model. We provide predicted experimental signatures for both vortex entanglement and vortex cutting. The local probe we propose can also be used to explore a wide range of other quantities.