In a breakthrough discovery detailed in a paper in the journal Nature Physics, a team of physicists from Finland and the United States has found a way to create knotted solitary waves, or knot solitons, in a quantum-mechanical field.
Topological structure of a quantum-mechanical knot soliton: the white ring is the core of the soliton (field pointing down), and the surrounding colored bands define a set of nested tori that illustrate the linked structure of its field lines. The boundary of the knot lies near the dark grey lines (field pointing up). Image credit: David Hall.
Scientists have long predicted the possibility of tying knots in quantum fields. But no one has been able to make or observe a 3D quantum knot, until now.
“For decades, physicists have been theoretically predicting that it should be possible to have knots in quantum fields, but nobody else has been able to make one,” said co-author Prof. Mikko Möttönen, of Aalto University.
“Now that we have seen these exotic beasts, we are really excited to study their peculiar properties,” he added.
“Importantly, our discovery connects to a diverse set of research fields including cosmology, fusion power, and quantum computers.”
To make this discovery, Prof. Möttönen and his colleagues from Amherst College and Aalto University exposed a rubidium condensate to rapid changes of a specifically tailored magnetic field, tying the knot in less than a thousandth of a second.
“First we cooled a gas of rubidium atoms down to billionths of a degree above zero, at which point it became a superfluid – a tiny, well-ordered environment in which these particle-like objects can exist,” explained Prof. David Hall of Amherst College, who is the lead author on the study.
“Then we exposed the superfluid to a rapid change of a specifically tailored magnetic field, which tied the knot in less than a thousandth of a second.”
Knots are defined mathematically as closed curves in 3D space. A knot soliton consists of an infinite number of rings, each linked with all of the others to generate a toroidal structure.
Previous experiments have identified solitons in one and two dimensions, but the knot solitons created by the team exist in all three spatial dimensions.
“What we’re seeing is a true 3D object,” Prof. Hall said.
The knots exist within a tiny droplet of superfluid that is just barely visible to the human eye. The knot itself is less than 10 microns across.
“The next step is to see what these quantum knots can do. Now that we’ve created these particles, we can begin experimenting with them and studying their properties,” Prof. Hall said.
“This is the beginning of the story of quantum knots. It would be great to see even more sophisticated quantum knots to appear such as those with knotted cores,” Prof. Möttönen added.
“Also it would be important to create these knots in conditions where the state of the quantum matter would be inherently stable. Such system would allow for detailed studies of the stability of the knot itself.”
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D.S. Hall et al. Tying quantum knots. Nature Physics, published online January 18, 2016; doi: 10.1038/nphys3624
