In a laboratory at the University of Innsbruck, cesium atoms cooled to a few billionths of a degree above absolute zero suddenly formed unusual bound states — Bethe strings. These quantum clusters, predicted by Hans Bethe back in 1931, existed for nearly a century only on paper and in indirect observations in magnetic materials.
Scientists led by Hanns-Christoph Nägerl split a cloud of atoms into thousands of narrow one-dimensional tubes. Inside each tube, the atoms could move only along a single line. The researchers then smoothly changed the interaction between the atoms — from repulsive to attractive. Instead of the expected collapse of the gas, bound groups of particles of various sizes appeared, including clusters of six or more atoms.
Unlike ordinary molecules, in which particles are held together by chemical bonds, Bethe strings arise exclusively from quantum interactions and exist only in one dimension. Their stability was tested in two ways: in the one-dimensional tubes the clusters survived even collisions, while when the confinement was removed and they expanded into three-dimensional space, they fell apart, releasing binding energy.
Measurements of the binding energy, the momentum distribution and the Tan contact confirmed the presence of large strings. The results matched the predictions of generalized hydrodynamics precisely. The experiment showed that in a controlled environment of an ultracold gas, complex quantum states inaccessible in other systems can be created and studied.
The discovery opens the way to investigating quantum coherence, nonlinear dynamics and thermalization in strongly interacting one-dimensional systems. Physicists will now be able to manipulate these states, collide them and test their stability under laboratory conditions.
