Physicists in Innsbruck realize a nearly century-old prediction by Hans Bethe in an ultracold gas.
Image Credit: University of Innsbruck / AI generated
Scientific Frontline: Extended "At a Glance" Summary: Bethe Strings
The Core Concept: Bethe strings are multi-particle bound states that form in specific one-dimensional quantum systems. They arise purely from the interactions between particles rather than from traditional chemical bonds.
Key Distinction/Mechanism: Unlike ordinary molecules held together by chemical bonds, Bethe strings exist exclusively in one dimension and rely solely on tunable interparticle attraction. When confined to a single dimension, they exhibit remarkable collisional stability and remain intact during collisions. However, if released into three-dimensional space, the strings instantly break apart, converting their binding energy into rapid kinetic motion.
Origin/History: Nobel laureate physicist Hans Bethe first predicted the existence of these strings in 1931 as part of a mathematical description of quantum many-body systems. Almost a century later, a collaborative team of researchers from the University of Innsbruck, the University of Amsterdam, and the Technical University of Munich successfully created and observed them in an ultracold atomic gas, publishing their findings in Nature Communications in 2026.
Major Frameworks/Components:
- Ultracold atomic gas: A cloud of cesium atoms cooled to a few billionths of a degree above absolute zero serves as the foundational experimental medium.
- One-dimensional confinement: The atomic cloud is divided into thousands of narrow tubes, strictly restricting particle movement to a single axis.
- Tunable interactions: Researchers modulate the interactions between atoms, shifting them from repulsive to attractive to induce the formation of multi-particle bound states.
- Expansion signatures: By comparing one-dimensional expansion (where strings survive) with three-dimensional expansion (where strings break and release measurable kinetic energy), scientists conclusively verify the presence of Bethe strings.
Branch of Science: Quantum Physics, Atomic Physics, and Condensed Matter Physics.
Future Application: This highly controllable ultracold gas platform opens new experimental pathways for manipulating collective quantum objects, studying their formation, and probing the complex interactions of quantum many-body systems.
Why It Matters: The observation validates a foundational, nearly century-old theoretical prediction within a novel laboratory setting. While previously observed in solid-state magnetic systems, realizing Bethe strings in an ultracold atomic gas allows for unprecedented precision in controlling system geometry, particle density, and atomic interactions.
Nearly a century after they were predicted by Nobel laureate Hans Bethe, a team led by quantum physicist Hanns-Christoph Nägerl has observed so-called Bethe strings in ultracold atoms. The ultracold gas provides an ideal platform for further investigation of these quantum many-body states.
In 1931, physicist Hans Bethe predicted that in certain one-dimensional quantum systems, particles can bind together to form multiparticle states known as Bethe strings. Unlike ordinary molecules, which are held together by chemical bonds, Bethe strings arise purely from the interactions between particles and exist only in one dimension. For decades, Bethe strings remained primarily a theoretical concept. Now, almost a century after Bethe’s prediction, researchers from the University of Innsbruck, in collaboration with theory teams from the Department of Experimental Physics at the University of Amsterdam and the Technical University of Munich, have created and observed these multiparticle bound states in an ultracold gas. Their findings are published in Nature Communications.
The experiment begins with a cloud of cesium atoms cooled to temperatures only a few billionths of a degree above absolute zero. The researchers then divide the cloud into several thousand narrow, one-dimensional tubes. Inside these tubes, the atoms can essentially move in only a single direction. The interactions between the atoms can be precisely controlled. By tuning the interactions between the atoms from repulsive to attractive, the researchers can cause the atoms to bind together. Instead of simply collapsing, the atoms form bound states of different sizes, including larger clusters containing six or more particles.
The researchers then asked a simple question: How can we tell that the particles are really bound together? “One of the simplest experiments was to let the strings expand,” says Milena Horvath, one of the lead authors. First, the researchers allow the atoms to expand while keeping them confined to their one-dimensional tubes. As they move, the strings collide but remain intact. “This is a remarkable feature of the strings: they can collide without breaking apart,” says Horvath. In a second step, the researchers remove the confinement and let the atoms expand freely in three dimensions. Because Bethe strings can exist only in one dimension, this sudden change causes the bound states to break apart. The energy that held the particles together is converted into motion, causing the atoms to fly apart more rapidly. The difference between the two expansions provides a clear signature of the Bethe strings. For unbound particles, as in the repulsive interaction regime, the two measurements give essentially the same energy. When strings are present, however, the three-dimensional expansion carries additional energy, which is released when the bound states break apart.
“Bethe strings were predicted almost a century ago as part of a beautiful mathematical description of quantum many-body systems,” says Sudipta Dhar, another lead author. “Now we can create them in the laboratory, manipulate them, make them collide, and probe their remarkable collisional stability.” Bethe strings have also been observed experimentally in solid-state magnetic systems. The present work brings these unusual quantum bound states into a different setting: an ultracold atomic gas, where the system geometry, density of particles, and interactions can be controlled with exceptional precision. “This opens new possibilities for studying how these collective quantum objects form and interact,” says lead theorist Alvise Bastianello.
Funding: The research has been funded by the Austrian Science Fund (FWF) through a Wittgenstein Prize grant, by the European Union through an ERC grant, and by the UK Engineering and Physical Sciences Research Council. Horvath is a member of the FWF doctoral program Atoms, Light, and Molecules (DK-ALM).
Published in journal: Nature Communications
Title: Probing Bethe strings in an attractive one-dimensional Bose gas
Authors: Milena Horvath, Alvise Bastianello, Sudipta Dhar, Rebekka Koch, Yanliang Guo, Jean-Sébastien Caux, Manuele Landini, and Hanns-Christoph Nägerl
Source/Credit: University of Innsbruck
Edited by: Scientific Frontline
Reference Number: qs091426_01
