Fusion and Fission of Particle-like Chiral Nematic Vortex Knots

TL;DR

This paper demonstrates the creation, stability, and reversible fusion and fission of topologically protected vortex knots in chiral nematic liquid crystals, revealing physical realizations of knot theory concepts with potential applications in optics.

Contribution

It introduces a new class of stable, topologically protected vortex knots in liquid crystals that can be controllably fused and split using electric pulses, illustrating knot theory in a physical system.

Findings

Vortex knots remain stable and topologically protected in chiral nematic liquid crystals.

Fusion and fission of vortex knots can be reversibly controlled by electric pulses.

The process embodies knot theory concepts like connected sums in a physical medium.

Abstract

Vortex knots have been seen decaying in many physical systems. Here we describe topologically protected vortex knots, which remain stable and undergo fusion and fission while conserving a topological invariant analogous to that of baryon number. While the host medium, a chiral nematic liquid crystal, exhibits intrinsic chirality, cores of the vortex lines are structurally achiral regions where twist cannot be defined. We refer to them as "dischiralation" vortex lines, in analogy to dislocations and disclinations in ordered media where, respectively, positional and orientational order is disrupted. Fusion and fission of these vortex knots, which we reversibly switch by electric pulses, vividly reveal the physical embodiments of knot theory's concepts like connected sums of knots. Our findings provide insights into related phenomena in fields ranging from cosmology to particle physics and can enable applications in electro-optics and photonics, where such fusion and fission processes can be used for controlling light.