In 1931, physicist Hans Bethe proposed that particles in certain one-dimensional quantum systems could bind into collective states. Nearly a century later, researchers at the University of Innsbruck have created and directly observed these "Bethe strings" in an ultracold gas of cesium atoms. The results were published in Nature Communications.
The team cooled cesium atoms to within a few billionths of a degree above absolute zero and split the cloud into thousands of extremely narrow tubes, effectively restricting the atoms to one dimension. By tuning the interactions from repulsive to attractive, they made the atoms bind into clusters of different sizes, some with six or more particles. Unlike ordinary molecules, these clusters are not held together by chemical bonds but by the particles' mutual interactions, and they can exist only in one dimension.
To show the clusters were truly bound, the researchers let the strings expand while still confined in the tubes. The strings collided with one another and survived intact. In a second experiment, they removed the confinement and let the atoms expand freely in three dimensions. Because Bethe strings cannot exist in 3D, the bound states fell apart, and the energy that had held them together was converted into motion, making the atoms spread faster. Comparing the two expansion measurements gave a clear signature of the strings.
Bethe strings had previously been detected in solid-state magnetic systems, but the new experiment places them in a highly controllable ultracold atomic gas. Researchers can adjust the system's geometry, particle density, and interactions with exceptional precision. As lead theorist Alvise Bastianello put it, "This opens new possibilities for studying how these collective quantum objects form and interact."