Researchers at the University of Innsbruck have experimentally created and detected Bethe strings, unusual quantum structures predicted by Nobel laureate Hans Bethe in 1931. These multiparticle bound states had remained largely theoretical throughout the past century. The findings, conducted in collaboration with theory teams from the University of Amsterdam and the Technical University of Munich, were published in Nature Communications.
The experimental team produced Bethe strings by cooling cesium atoms to within billionths of a degree above absolute zero and separating them into several thousand narrow one-dimensional tubes. This geometry confined the atoms to movement along a single direction, creating the essential one-dimensional environment necessary for Bethe strings to form. Researchers achieved the binding of atoms by precisely adjusting their interactions from repulsive to attractive forces, resulting in bound states of varying sizes, with some clusters containing six or more particles.
To confirm the existence of these bound structures, scientists conducted collision experiments within the one-dimensional tubes, observing that the strings remained intact even when encountering each other. In a second experimental approach, researchers released the atoms into three-dimensional space, where Bethe strings cannot exist. This comparison revealed that the energy released from breaking the bound states caused faster particle dispersal in three dimensions compared to expansion within the confined tubes, providing clear evidence of the strings’ presence.
This work represents the first creation of Bethe strings in ultracold atomic gases, a system offering researchers unprecedented control over geometry, particle density, and interaction parameters. Previous experimental detections of Bethe strings had occurred only in solid-state magnetic systems. The new platform opens possibilities for deeper investigation into the formation and interactions of these collective quantum objects. Funding was provided through grants from the Austrian Science Fund, the European Union, and the UK Engineering and Physical Sciences Research Council.
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