Researchers have shown a method of connecting three vortices that prevents them from unraveling. The structure of the links is similar to a pattern used by the Vikings and other ancient cultures. However, this study focused on vortices in a special type of matter called a Bose-Einstein condensate. Quantum computing, particle physics, and other disciplines may all benefit from these insights.

Toni Annala, a postdoctoral researcher, explains the phenomenon with the help of strings and water vortices. “If you make a link structure out of, say, three unbroken strings in a circle, you can’t unravel it because the string can’t go through another string. If, on the other hand, the same circular structure is made in water, the water vortices can collide and merge if they are not protected.”

According to Annala, who started working on this in Professor Mikko Möttönen’s research group at Aalto University before returning to the University of British Columbia and then moving to the Institute for Advanced Study in Princeton, “In a Bose-Einstein condensate, the link structure is somewhere between the two.” The study also included Roberto Zamora-Zamora, a postdoctoral researcher in Möttönen’s lab.

The researchers used mathematics to prove the existence of a network of interconnected vortices that, due to their intrinsic features, cannot be dismantled. ­ 

“The new element here is that we were able to mathematically construct three different flow vortices that were linked but could not pass through each other without topological consequences. If the vortices interpenetrate each other, a cord would form at the intersection, which binds the vortices together and consumes energy. This means that the structure cannot easily break down,” adds Möttönen.

The Borromean rings, a design of three interconnected circles that has been extensively employed in symbolism and as a coat of arms, are theoretically related to the structure. Three triangles are similarly linked in a Viking sign for Odin. The whole pattern disintegrates if one of the circles or triangles is removed since the two that remain are not related in any way. Thus, each element forms a connection between its two partners, stabilizing the whole structure.

The mathematical analysis used in this study demonstrates how knotted or connected vortices might have comparable resilient structures. These structures may be seen in certain liquid crystal or condensed matter systems and may have an impact on the behavior and growth of such systems.

“To our surprise, these topologically protected links and knots had not been invented before. This is probably because the link structure requires vortices with three different types of flow, which is much more complex than the previously considered two-vortex systems,” remarks Möttönen.

These discoveries could one day contribute to the accuracy of quantum computing. In topological quantum computing, logical operations would be done by weaving different kinds of vortices around each other in different ways. According to Möttönen, “In normal liquids, knots unravel, but in quantum fields there can be knots with topological protection, as we are now discovering.”

The same theoretical model, according to Annala, may be used to explain structures in several other systems, such as cosmic strings in cosmology. The study’s topological structures match those found in quantum field theory’s vacuum structures. Therefore, the findings could possibly have an impact on particle physics.

Next, the researchers want to show theoretically that there is a knot in a Bose-Einstein condensate that is protected from dissolving by its topology in a way that could be tested. 

“The existence of topologically protected knots is one of the fundamental questions of nature. After a mathematical proof, we can move on to simulations and experimental research,” adds Möttönen.

Source: 10.1038/s42005-022-01071-2