A Peculiar Protected Structure Links Viking knots With Quantum Vortices

Researchers have demonstrated how three vortices can be linked to prevent them from being dismantled. The structure of the links resembles a pattern used by Vikings and other old cultures. However, this research focused on vortices in a special way of matter known as a Bose-Einstein condensate. The findings have implications for quantum computers, particle physics, and other fields.

The study is released in the journal Communications Physics

Postdoctoral scientist Toni Annala utilizes strings and water vortices to describe the phenomenon: “If you make a link framework out of, state, three unbroken strings in a circle, you can not unravel it because the string can not go through another cord. If, on the other hand, the same circular framework is made in water, the water vortices could collide and merge if they are not protected.”

” In a Bose-Einstein condensate, the link framework is somewhere between both,” states Annala, who started working on this in Prof. Mikko Möttönen’s research team at Aalto College prior to moving back to the College of British Columbia and then to the Institute for Advanced Study in Princeton. Roberto Zamora-Zamora, a postdoctoral researcher in Möttönen’s team, was also involved in the research.

The scientists mathematically showed the existence of a structure of linked vortices that can not break apart because of their fundamental properties. “The new element here is that we could mathematically construct 3 different flow vortices that were linked but might not pass through each other without topological consequences. If the vortices interpenetrate each other, a string would form at the intersection that binds the vortices together and consumes energy. This means that the framework can not easily break down,” says Möttönen.

From antiquity to cosmic strands

The framework is conceptually similar to the Borromean rings, a pattern of 3 interlinked circles which has been widely utilized in symbolism and as a coat of arms. A Viking symbol associated with Odin has 3 triangles interlocked similarly. If one of the circles or triangles is removed, the whole pattern dissolves because the remaining two are not directly connected. Each element thus links its 2 partners, stabilizing the framework as a whole.

The mathematical analysis in this research demonstrates how similarly robust frameworks could exist between knotted or linked vortices. Such frameworks may be observed in specific kinds of liquid crystals or condensed matter systems and might affect how those systems act and develop.

“To our surprise, these topologically protected links and also knots had not been invented before. This is probably because the link framework requires vortices with 3 distinct kinds of flow, that is much more complex than the before considered 2-vortex systems,” states Möttönen.

These findings may one day aid in making quantum computing more accurate. In topological quantum computers, the logical operations would be carried out by braiding distinct kinds of vortices around each other in several ways. “In normal liquids, knots unravel; however, in quantum fields, there could be knots with topological protection, as we are currently discovering,” says Möttönen.

Annala includes that “the same theoretical model can be utilized to describe structures in many different systems, such as cosmic strings in cosmology.” The topological frameworks used in the study also correspond to the vacuum frameworks in quantum field theory. The results may likewise have implications for particle physics.

Next, the researchers plan to theoretically show the presence of a knot in a Bose-Einstein condensate which would be topologically protected against dissolving in an experimentally feasible scenario. “The presence of topologically protected knots is one of the essential questions of nature. After a mathematical evidence, we can move on to simulations and experimental research,” states Möttönen.

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