Physicists find evidence of weird quantum ‘Bethe strings’ nearly 100 years after they were predicted
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“Necklaces” of ultracold atoms have provided new evidence to support a nearly 100-year-old quantum theory.
In 1931, physicists were trying to use quantum mechanics to explain why some materials are magnetic. Then, a young physicist named Hans Bethe looked at a single row of electrons. Each electron’s spin can point up or down. Bethe worked out the math for how such a row behaves and found that if a few spins in the row flip, they can stick together and travel down the row as a single unit.
Decades later, physicists found that Bethe’s method also works for larger particles moving along a line, such as atoms. If those particles attract each other, the math predicts they will bind into clusters called Bethe strings.
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Now, physicists have found evidence of these clusters in a line of ultracold atoms. The findings were published Aug. 29 in the journal Nature Communications.
The discovery may not create new gadgets, but it addresses a fundamental mystery in physics. Everything around us, from magnets to phone chips, consists of countless interacting particles. This makes their behavior difficult to predict. Ultracold atoms serve as a clear and adjustable way to study these complex systems.
A “necklace” of atoms
Researchers have spotted small Bethe strings before, in magnetic crystals and superconducting quantum circuits — but those experiments captured strings one at a time.
Theory predicts that crowds of strings, in many sizes, can change how an entire system behaves, and studying that idea requires making many strings at once. That has been hard to do with atoms. Atoms that attract each other usually collapse into a clump. But this time, the team appears to have made many strings of different sizes at once, including some with more than six atoms.
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To make the “necklace” the researchers had to create a Bose-Einstein condensate, a special phase of matter.
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It’s tricky to get atoms to attract each other. In three dimensions, a gas made of attracting atoms tends to collapse as the atoms clump together and form molecules. That process releases energy that kicks atoms out of the experiment, so the gas quickly collapses and disappears. But when they’re in a single line, the atoms behave differently.
“They are really a bit like pearls on a string, right? Like on a necklace, they cannot go past,” study co-author Hanns-Christoph Nägerl, an experimental physicist at the University of Innsbruck, told Live Science. “In 3D, everything would collapse. But in 1D, it does not collapse.”
To build their “necklaces,” the team started with tens of thousands of cesium atoms cooled into a Bose-Einstein condensate — a state of matter in which atoms chilled to near absolute zero share a single quantum state. Laser beams then divided the condensate into thousands of thin tubes, each of which held up to a few dozen atoms in a line.
At first, the atoms repelled each other. The researchers used a magnetic field to gradually turn that repulsion down to zero, and then turned it into attraction.
The team couldn’t see the strings directly. Instead, they let the atoms go and measured how fast the cloud spread. When the atoms could expand only along their tubes, any strings stayed intact. When the atoms were freed in all three dimensions, the strings broke apart and released their binding energy as motion. The researchers found that the 3D clouds spread with about three times as much energy as the one-dimensional ones did.
From that difference, the team estimated how tightly the atoms had been bound. The answer pointed to strings of at least six atoms. The measurements also closely matched predictions from a theory called generalized hydrodynamics, which describes a gas like this one as a fluid made of many kinds of particles, including strings of different sizes. It also tracks how each kind flows over time rather than following every atom.
Nägerl was careful not to call this proof. “That some theory fits to your data is not a proof that something exists,” he said; it’s just more evidence to support it.
A short-lived state
The strings likely don’t survive long. Up close, the atoms still feel the three-dimensional world, and the strings eventually decay into ordinary cesium molecules. In the coldest runs, the team lost about 40% of the atoms.
“Transiently you create these Bethe string states,” Nägerl said. “But I don’t think they are long-lived.”
He has an idea for future experiments. Physicists recently learned to shield ultracold molecules with microwaves, which keeps the molecules from colliding at close range. Strings made from shielded molecules might last long enough to be studied directly. But Nägerl stressed that the idea is untested. “I’ve had nobody do a theory check on my claims now, but I think intuitively this should work,” he said.
Another option is quantum gas microscopy, which images atoms one at a time and could offer more direct evidence of individual strings.
For Nägerl, Bethe strings are one step in understanding how quantum systems with many particles behave and settle down over time. His long-term goal is an experiment in which physicists control both how every particle moves and how its spin flips, letting them assemble model materials piece by piece, “like a LEGO type,” he said. His team has begun the next step: using lasers to control the spins of the atoms in its one-dimensional gas. He described Bethe strings as “a little diversion.” But because the strings form whenever the atoms attract, they can’t be ignored.
Horvath, M., Bastianello, A., Dhar, S., Koch, R., Guo, Y., Caux, J.-S., Landini, M., & Nägerl, H.-C. (2026). Probing Bethe strings in an attractive one-dimensional Bose gas. Nature Communications, 17, 10330. https://doi.org/10.1038/s41467-026-76018-0
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