Nearly a century after Nobel laureate Hans Bethe first predicted their theoretical existence, scientists have successfully created and observed unusual quantum structures known as "Bethe strings" using ultracold atoms. The breakthrough experiment, led by quantum physicist Hanns-Christoph Nägerl and detailed in a newly published study, provides researchers with an unprecedentedly controllable way to explore these extraordinary quantum many-body states in a laboratory setting.
In 1931, the renowned physicist Hans Bethe proposed that particles within specific quantum systems restricted to a single spatial dimension could join together into collective states that are now referred to as Bethe strings. These remarkable structures differ fundamentally from the familiar molecules encountered in standard chemistry. Rather than being connected through traditional chemical bonds, the constituent particles remain bound together purely because of their quantum mechanical interactions with one another. Furthermore, these unique states are strictly confined to existence in one dimension, making them exceptionally difficult to isolate and study.
For much of the past century, Bethe strings remained largely a theoretical concept, fascinating mathematicians and physicists alike as part of a sophisticated framework for understanding quantum mechanics. Now, a collaborative team of researchers at the University of Innsbruck has successfully created and detected these multiparticle bound states within an ultracold gas. The experimental breakthrough was achieved in close partnership with theory teams from the Department of Experimental Physics at the University of Amsterdam and the Technical University of Munich. The significant findings of this international collaboration have been officially published in the scientific journal Nature Communications.
Creating Bethe Strings Near Absolute Zero
To produce these unusual quantum states in the laboratory, the research team began with a dense cloud of cesium atoms. Using sophisticated laser-cooling and trapping techniques, they cooled this atomic cloud down to within only a few billionths of a degree above absolute zero, bringing the thermal motion of the particles almost to a complete standstill. Once the atoms were sufficiently chilled, the researchers separated the cloud into several thousand extremely narrow, parallel tubes.
Within the confines of each individual tube, the cesium atoms are effectively restricted to moving back and forth along a single spatial direction, thereby establishing the strict one-dimensional environment that is fundamentally required for Bethe strings to form and persist. Additionally, the experimental setup grants the research team the ability to precisely adjust how strongly the atoms interact with one another in real time.
By dynamically changing these atomic interactions from a repulsive state to an attractive one, the team successfully caused the atoms to bind together. Rather than simply collapsing inward into a single, unstructured clump, the atoms organized themselves into stable bound states comprising several different sizes. Some of the larger clusters observed during the experiment contained six or more particles linked together through their mutual quantum interactions.
Watching Quantum Strings Collide
Once the bound states were successfully formed, the next major challenge for the research team was demonstrating definitively that these particles were truly bound together rather than merely passing close to one another by coincidence.
"One of the simplest experiments was to let the strings expand," says Milena Horvath, one of the lead authors of the research study.
To execute this, the researchers first allowed the atoms to spread out while carefully maintaining their confinement inside their respective one-dimensional tubes. During this controlled expansion, the individual Bethe strings encountered one another and frequently collided, yet the delicate bound structures remarkably survived the impacts without breaking apart.
"This is a remarkable feature of the strings: they can collide without breaking apart," notes Milena Horvath, highlighting the unexpected robustness of these quantum objects.
Following the constrained expansion tests, the scientists performed a second version of the experiment in which they completely removed the spatial confinement. This allowed the atoms to expand freely outward through three-dimensional space. Because the foundational physics dictating Bethe strings dictates that they can only exist within a strictly one-dimensional environment, releasing the atoms into three dimensions caused the bound states to immediately fall apart.
The internal binding energy that had previously kept the individual particles locked together was suddenly transformed into kinetic motion, causing the released atoms to spread apart noticeably faster. Comparing the data from the two distinct types of expansion gave the researchers a clear, quantitative way to identify and confirm the presence of Bethe strings within the gas.
When the particles were unbound—such as during phases of the experiment when the atomic interactions were kept strictly repulsive—both expansion measurements produced essentially the same underlying energy profile. However, when Bethe strings were actively present in the system, the subsequent three-dimensional expansion contained distinct extra energy that was released as the complex bound states dissolved.
A New Laboratory for Quantum Many-Body Physics
"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 of the study. "Now we can create them in the laboratory, manipulate them and make them collide and probe their remarkable collisional stability."
While Bethe strings have occasionally been detected in previous experiments involving solid-state magnetic systems, this new body of work places these unusual quantum bound states into a completely different physical environment: an ultracold atomic gas. This gaseous platform offers researchers unprecedented experimental advantages, allowing them to control the system’s overall geometry, local particle density, and internal interactions with exceptional precision.
"This opens new possibilities for studying how these collective quantum objects form and interact," explains lead theorist Alvise Bastianello, emphasizing the broad implications of the research for the broader physics community.
The successful realization and study of Bethe strings marks a significant milestone in modern quantum physics, bridging a nearly hundred-year gap between theoretical prediction and laboratory observation. By offering a clean, highly tunable platform for investigating complex many-body states, the work paves the way for deeper explorations into the fundamental laws governing quantum matter.
The international research project received substantial funding and support from several major scientific organizations, including the Austrian Science Fund FWF through a prestigious Wittgenstein Prize grant, the European Union through an advanced ERC grant, and the UK Engineering and Physical Sciences Research Council. Furthermore, lead author Milena Horvath participates as an active member of the FWF doctoral program known as Atoms, Light and Molecules, reflecting the collaborative and academic depth supporting the discovery.
