Vorticity Knot in Two-component Bose-Einstein Condensates

TL;DR

This paper demonstrates the existence of helical vortex solutions in two-component Bose-Einstein condensates, interpreting knots as linked vorticity flux rings with topological stability, and estimates their energy.

Contribution

It introduces the concept of vorticity knots as linked vortex rings in two-component BECs, providing a new topological interpretation and stability analysis.

Findings

Helical vortex solutions exist in two-component BECs.

Knots can be viewed as linked vortex rings with fixed topology.

Estimated energy of the lightest knot is about 3×10^{-3} eV.

Abstract

We demonstrate the existence of the helical vortex solution in two-component Bose-Einstein condensates which can be identified as a twisted vorticity flux. Based on this we argue that the recently proposed knot in two-component Bose-Einstein condensates can be interpreted as a vorticity knot, a vortex ring made of the helical vortex. This picture shows that the knot is made of two quantized vorticity fluxes linked together, whose topology $\pi_3(S^2)$ is fixed by the linking number of two vorticity fluxes. Due to the helical structure the knot has both topological and dynamical stability. We estimate the energy of the lightest knot to be about $3\times 10^{-3} eV$.