The same team who tied the first "quantum knots" in a superfluid several years ago have now discovered that the knots decay, or "untie" themselves, fairly soon after forming, before turning into a vortex. The researchers also produced the first "movie" of the decay process in action, and they described their work in a recent paper in Physical Review Letters.

A mathematician likely would define a true knot as a kind of pretzel shape, or a knotted circle. A quantum knot is a little bit different. It's composed of particle-like rings or loops that connect to each other exactly once. A quantum knot is topologically stable, akin to a soliton—that is, it's a quantum object that acts like a traveling wave that keeps rolling forward at a constant speed without losing its shape.

Physicists had long thought it should be possible for such knotted structures to form in quantum fields, but it proved challenging to produce them in the laboratory. So there was considerable excitement early in 2016 when researchers at Aalto University in Finland and Amherst College in the US announced they had accomplished the feat in Nature Physics. The knots created by Aalto's Mikko Möttönen and Amherst's David Hall resembled smoke rings.

Hall and Möttönen used a quantum state of matter known as a Bose-Einstein Condensate (BEC) as their medium—technically a superfluid. Then they "tied" the knots by manipulating magnetic fields. If you think of the quantum field as points in space that each have an orientation—like arrows all pointing up, for instance—the core of a quantum knot would be a circle where the arrows all point down, similar to a god's eye yarn pattern. “If you followed the magnetic field line, it would go toward the center, but at the last minute it would peel away into a perpendicular direction,” Hall told Gizmodo in 2016. “It’s a particular way of rotating these arrows that gives you this linked configuration.”

Eventually they got so good at making quantum knots that they were able to make little movies of the exotic structures. Yet it was still not clear what would happen to the quantum knots over time. Sure, they were topologically stable. But Hall and Möttönen thought the knots should shrink over time as a means of minimizing their energy, the same way a bubble naturally assumes a spherical shape, or a ball "wants" to roll down a hill, thereby minimizing its potential energy. In other words, quantum knots might not be dynamically stable, winking out of existence before their superfluid medium decays. If they can outlast their superfluid medium, they would be effectively stable.

The group has since gained even better control over the BEC medium, enabling them to detect the decay of the knots and the formation of a new type of topological defect (a vortex). After creating a knot via a carefully structured magnetic field, they "perturbed" the BEC by removing the field and imaging what happened next. The experiment showed two distinct stages of the decay process. At first, the knot remained stable, while several "ferromagnetic islands" developed in the (nonmagnetic) BEC. But then the knot dissolved after a few hundred milliseconds, and the ferromagnetic islands migrated to the edges of the BEC, leaving a nonmagnetic core at the center. Finally, a vortex of atomic spins formed between the two magnetic regions of the BEC.

"The fact that the knot decays is surprising, since topological structures like quantum knots are typically exceptionally stable," said co-author Tuomas Ollikainen. "It’s also exciting for the field because our observation that a three-dimensional quantum defect decays into a one-dimensional defect hasn’t been seen before in these quantum gas systems."

For now, at least, quantum knots remain a laboratory curiosity, but the research might have bearing on ongoing research into building topological quantum computers. Such a device would braid qubits in different topologically stable structures, making the computer more robust against errors. This latest finding indicates that time may be an important factor, given the knots' rate of decay.

"It would be great to see this technology being used some day in a practical application, which may well happen," said Möttönen. "Our latest results show that while quantum knots in atomic gases are exciting, you need to be quick to use them before they untie themselves. Thus the first applications are likely to be found in other systems."

DOI: Physical Review Letters, 2019. 10.1103/PhysRevLett.123.163003 (About DOIs).