Cesium atoms trapped in one-dimensional tubes bind into the Bethe strings predicted in 1931

The release's summary says the strings were "created and directly observed" ^[15]. What the team measured is a difference in energy, and the design of that measurement is the strongest part of the work. Bethe strings can exist only in one dimension, held together by the particles' interactions with no chemical bond involved ^[2]. Taking the atoms out of their tubes therefore has a predictable effect on any string present, and the energy it frees can be measured ^[11].

The control is the repulsive gas. When the atoms push each other away, nothing binds, and expansion inside the tubes and expansion into three dimensions gave essentially the same energy ^[12]. That rules out the possibility that removing the confinement adds energy on its own ^[12]. Only with attractive interactions did the three-dimensional release carry an excess ^[12]. Because the interaction strength is adjustable ^[6], the bound and unbound runs use the same atoms, cooled to within a few billionths of a degree of absolute zero, in the same set of tubes ^[5].

The collision result came from the in-tube expansion. "One of the simplest experiments was to let the strings expand," said Milena Horvath, one of the lead authors ^[8]. As the strings spread along their tubes they ran into one another, and the bound structures held ^[9]. "This is a remarkable feature of the strings: they can collide without breaking apart," Horvath said ^[10].

The release does not give the size of the energy excess, or explain how the team established that some clusters held six or more particles ^[7]. Readers will have to go to the Nature Communications paper for those details ^[3].

Bethe's prediction was 95 years old when the release came out ^[17]. The experiment was led by Hanns-Christoph Nägerl ^[4]. Sudipta Dhar, another lead author, described what the gas adds. "Bethe strings were predicted almost a century ago as part of a beautiful mathematical description of quantum many-body systems," Dhar said. "Now we can create them in the laboratory, manipulate them and make them collide and probe their remarkable collisional stability." ^[13]