Physicists find evidence of weird quantum ‘Bethe strings’ nearly 100 years after they were predicted

“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.

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A “necklace” of atoms

“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.

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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

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