Scientists have shown how three vortices can be connected in a way that prevents their dismantling. The bond structure resembles a pattern used by the Vikings and other ancient cultures, although this study focused on vortices in a special form of matter known as a Bose-Einstein condensate. The findings have implications for quantum computing, particle physics and other fields.
The study is published in the journal Physics of communications.
Postdoctoral researcher Toni Annala uses ropes and vortices of water to explain the phenomenon: “If you create a link structure from, say, three unbroken ropes in a circle, you can’t untangle it because the rope doesn’t cannot cross another rope. If, on the other hand, the same circular structure is made in water, the water vortices can collide and merge if not protected.”
“In a Bose-Einstein condensate, the link structure is somewhere in between,” says Annala, who started working on it in Professor Mikko Möttönen’s research group at Aalto University before returning. at the University of British Columbia, then at the Institute for Advanced Studies in Princeton. Roberto Zamora-Zamora, a postdoctoral researcher in Möttönen’s group, also participated in the study.
The researchers have mathematically demonstrated the existence of a structure of bound vortices that cannot separate due to their fundamental properties. “The novel thing here is that we were able to mathematically construct three different flow vortices that were linked but could not cross each other without topological consequences. If the vortices interpenetrated, a chord would form at the intersection, which links swirls together and consumes energy. This means that the structure cannot easily break down,” explains Möttönen.
From antiquity to cosmic strands
The structure is conceptually similar to the Borromean rings, a pattern of three interconnected circles that has been widely used in symbolism and as a coat of arms. A Viking symbol associated with Odin has three similarly interlocking triangles. If one of the circles or triangles is removed, the entire pattern dissolves because the other two are not directly connected. Each element thus connects its two partners, stabilizing the entire structure.
The mathematical analysis of this research shows how such robust structures could exist between knotted or bound eddies. Such structures could be observed in certain types of liquid crystal or condensed matter systems and could affect the way these systems behave and grow.
“To our surprise, these topologically protected links and nodes had not been invented before. This is probably because the bond structure requires vortices with three different flow types, which is much more complex than the previously considered two-vortex systems,” says Möttönen. .
These discoveries could one day help make quantum computing more precise. In topological quantum computing, logical operations would be performed by braiding different types of vortices around each other in different ways. “In normal liquids knots unravel, but in quantum fields there can be knots with topological protection, as we are now discovering,” says Möttönen.
Annala adds that “the same theoretical model can be used to describe structures in many different systems, such as cosmic strings in cosmology”. The topological structures used in the study also correspond to vacuum structures in quantum field theory. The results could therefore also have implications for particle physics.
Next, the researchers plan to theoretically demonstrate the existence of a node in a Bose-Einstein condensate that would be topologically protected against dissolution in an experimentally feasible scenario. “The existence of topologically protected nodes is one of the fundamental questions in nature. After a mathematical proof, we can move on to simulations and experimental investigations,” says Möttönen.
Toni Annala et al, topologically protected vortex nodes and links, Physics of communications (2022). DOI: 10.1038/s42005-022-01071-2. www.nature.com/articles/s42005-022-01071-2
Provided by Aalto University
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