“Necklaces” of ultracold atoms have provided new evidence supporting 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 observed a single row of electrons. The spin of each electron can point up or down. Bethe calculated how such a row behaves and discovered that if some spins in the row change, they can stay together and travel down the row as a single unit. Decades later, physicists discovered that Bethe’s method also works for larger particles that move along a line, such as atoms. If those particles attract each other, mathematics predicts that they will stick together, forming clumps called Bethe strings. Latest videos from Live Science Now, physicists have found evidence of these clusters in a line of ultracold atoms. The findings were published August 29 in the journal Nature Communications. The discovery may not create new devices, but it addresses a fundamental mystery in physics. Everything around us, from magnets to phone chips, is made up of countless interacting particles. This makes their behavior difficult to predict. Ultracold atoms serve as a clear and tunable way to study these complex systems. You may like A “necklace” of atoms. Researchers have detected small Bethe strings before, in magnetic crystals and superconducting quantum circuits, but those experiments captured the strings one at a time. Theory predicts that multitudes of strings, of many sizes, can change the behavior of an entire system, and studying that idea requires making many strings at once. That has been difficult to do with atoms. Atoms that are attracted to each other usually collapse, forming a group. But this time, the team appears to have created many chains of different sizes at once, including some with more than six atoms. Get the world’s most fascinating discoveries delivered straight to your inbox. To make the “necklace,” the researchers had to create a Bose-Einstein condensate, a special phase of matter. (Image credit: blackdovfx via Getty Images) It’s tricky to get atoms to attract each other. In three dimensions, a gas made up of atoms that attract each other tends to collapse as the atoms group together and form molecules. This process releases energy that expels the atoms from the experiment, so the gas collapses and quickly disappears. But when they are in a single line, the atoms behave differently. “They’re actually a bit like pearls on a string, right? Like on a necklace, they can’t get through,” study co-author Hanns-Christoph Nägerl, an experimental physicist at the University of Innsbruck, told LiveScience. “In 3D, everything would collapse. But in 1D, it doesn’t collapse.” To build their “necklaces,” the team started with tens of thousands of cesium atoms cooled in a Bose-Einstein condensate, a state of matter in which atoms cooled to near absolute zero share a single quantum state. The laser beams then split the condensate into thousands of thin tubes, each containing up to a few dozen atoms in a line. What to read next At first, atoms repelled each other. The researchers used a magnetic field to gradually reduce that repulsion to zero and then converted it to attraction. The team could not see the ropes directly. Instead, they released the atoms and measured the speed at which the cloud spread. When atoms could only expand along their tubes, the strings remained intact. When the atoms were released into three dimensions, the strings broke and released their binding energy in the form of movement. The researchers found that 3D clouds propagated with about three times more energy than one-dimensional ones. From that difference, the team estimated how closely the atoms had bonded. The answer pointed to chains of at least six atoms. The measurements also closely matched the predictions of a theory called generalized hydrodynamics, which describes a gas like this as a fluid made up of many types of particles, including chains of different sizes. It also tracks how each type flows over time rather than following each atom. Nägerl was careful not to call this a test. “Just because some theory fits your data is not proof that something exists,” he said; It’s just more evidence to support it. A short-lived state The strings probably won’t survive for long. Up close, the atoms still sense the three-dimensional world and the strings eventually decay into ordinary cesium molecules. In the coldest tests, the team lost about 40% of the atoms. “These Bethe chain states are created transiently,” Nägerl said. “But I don’t think they will last.” You have an idea for future experiments. Physicists recently learned to shield ultracold molecules with microwaves, which prevents the molecules from colliding at close range. Strings made from protected molecules could last long enough to be studied directly. But Nägerl stressed that the idea has not yet been tested. “No one has done a theoretical verification of my claims now, but I think intuitively this should work,” he said. Another option is quantum gas microscopy, which images atoms one by one and could offer more direct evidence of individual strings. For Nägerl, Bethe strings are a step in understanding how quantum systems with many particles behave and settle over time. His long-term goal is an experiment in which physicists control how each particle moves and how its spin changes, allowing them to assemble model materials piece by piece, “like a LEGO guy,” he said. His team has taken the next step: using lasers to control the spins of atoms in their one-dimensional gas. He described Bethe’s strings as “a little fun.” But since strings form whenever atoms attract each other, they cannot be ignored. Horvath, M., Bastianello, A., Dhar, S., Koch, R., Guo, Y., Caux, J.-S., Landini, M. and Nägerl, H.-C. (2026). Probing Bethe’s strings in attractive one-dimensional Bose gas. Nature Communications, 17, 10330. https://doi.org/10.1038/s41467-026-76018-0
