January 18, 2016
By Rachel Rogol

quantum knot illustration

This figure illustrates part of the peculiar structure of the quantum knot. There are actually an infinite number of rings, each linked with all of the others exactly once. Image credit: Allen Li '15

AMHERST, Mass.—Physicists have long predicted the possibility of tying knots in quantum fields. But no one has been able to make or observe a three-dimensional quantum knot, until now. 

In a breakthrough discovery explored in a paper published in Nature Physics, one of the most prestigious journals in physics, a scientific team led by Amherst Physics Professor David S. Hall ’91 and Aalto University (Finland) Professor Mikko Möttönen have found a way to create knotted solitary waves in a quantum-mechanical field. 

The discovery builds on their recent work on Dirac monopoles and isolated monopoles, and is yet another extraordinary step forward in understanding the nature of quantum fluids. The isolated monopole research in particular, Hall says, led to the quantum knot discovery.

“The creation of isolated monopoles made us realize that we also had the technology to create quantum knots,” Hall says. “Since they had never before been realized, we knew this could be a remarkable achievement.”

The scientific team created the quantum knots, also known as knot solitons, in Hall’s lab at Amherst College. “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,” Hall says. “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 three-dimensional space. A knot soliton consists of an infinite number of rings, each linked with all of the others to generate a toroidal (donut-like) structure. Previous experiments have identified solitons in one and two dimensions, but the knot solitons created in Hall’s lab exist in all three spatial dimensions. “What we’re seeing is a true three-dimensional object,” Hall says.

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 in across, or approximately 10 times smaller than the thickness of a human hair.

Co-author and Amherst graduate Andrei-Horia Gheorghe ’15 assisted Hall and Möttönen as part of his senior thesis. Now a graduate student at Harvard University, Gheorghe explored the knot structure in depth for his thesis. Working with undergraduates on complex and often groundbreaking research is “part of the beauty of our liberal arts curriculum,” Hall says. "I can't wait to bring these results into the classroom, and my class into the laboratory."  

For Hall, the next step is to see what these quantum knots can do. “Now that we’ve created these particles,” he says, “we can begin experimenting with them and studying their properties.” 

Though it’s too soon to tell what could come of this discovery, Hall says this kind of fundamental research often has the potential to revolutionize people’s lives in ways that are impossible to predict now. “We don’t know what this particular discovery might lead to, but the possibilities are exciting,” Hall says. “When scientists invented lasers, they certainly weren’t thinking about grocery store scanners.”

This material is based upon work supported by the National Science Foundation under Grant No. PHY-1205822, the Academy of Finland (grant nos. 251748,284621,135794, and 272806), Finnish Doctoral Programme in Computational Sciences, and the Magnus Ehrnrooth Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

The article

D. S. Hall, M. W. Ray, K. Tiurev, E. Ruokokoski, A. H. Gheorghe, and M. Möttönen
Tying Quantum Knots” 
Nature Physics, DOI:10.1038/NPHYS3624

See also the previous work of the team:



About Amherst College

Founded in 1821, Amherst is a highly selective, coeducational liberal arts college with 1,800 students from most of the 50 states and more than 30 other countries. Considered one of the nation’s best educational institutions, Amherst awards the B.A. degree in 38 fields of study. Sixty percent of Amherst students receive need-based financial aid.