A peculiar protected structure links Viking knots with quantum vortices
In Borromean rings, each circle holds the pattern together by passing through the other two circles. Credit: Alexandr Kakinen / Aalto University

Scientists have shown how they can be linked together to prevent them from being dismantled. The structure of the links is similar to the one used by Vikings and other ancient cultures. Implications for quantum computing and other fields can be found in the findings.

The study is in a journal.

If you make a link structure out of three strings in a circle, you can't untangle it because the string can't go through another string If the same structure is made in water, the water can cause problems if it's not protected.

Annala started working on this in Professor Mikko Mttnen's research group at the University of British Columbia before moving to the Institute for Advanced. A researcher in Mttnen's group was involved in the study.

The researchers showed the existence of a structure that cannot be broken apart because of their fundamental properties. There is a new element that we were able to construct three different flow vortices that were linked but could not pass through each other. A cord would be formed at the intersection if the vortices interpenetrate each other. Mttnen says that the structure can't easily be broken down.

From the beginning to the end.

The Borromean rings are a pattern of three circles which have been used in symbolism and as a coat of arms. There is a viking symbol with three triangles interlocked. The entire pattern will collapse if one of the circles or triangles is taken away. The elements link their partners, stabilizing the structure as a whole.

The mathematical analysis shows how strong the structures could be if they were tied together. Liquid crystals or Condensed Matter systems could be affected by such structures.

We were surprised that these topologically protected links and knots hadn't been invented before. According to Mttnen, the link structure requires three different types of flow, which is much more complex than the two-vortex system.

It is possible that these findings will help make quantum computing more accurate. The logical operations are carried out by braiding different types of vortices around each other. Mttnen said that there can be knots in quantum fields.

The same theoretical model can be used to describe structures in a variety of systems. The structure used in the study is similar to the structure used in quantum field theory. There are implications for particle physics from the results.

The researchers plan to demonstrate the existence of a knot in a Bose-Einstein condensate that would be protected against dissolution. One of nature's fundamental questions is the existence of protected knots. Mttnen says that after a mathematical proof, we can move on to simulations and experiments.

There is more information about the topologically protected vortex knots and links. www.nature.com/articles/s42005

Journal information: Communications Physics