Physicist Hans Bethe proposed Bethe strings in 1931, and researchers at the University of Innsbruck finally created them. By cooling cesium atoms near absolute zero in narrow tubes, the team formed these unique quantum states. Milena Horvath said, "This is a remarkable feature of the strings: they can collide without breaking."
In 1931, physicist Hans Bethe proposed that particles in certain quantum systems restricted to one dimension could join together into collective states now called Bethe strings. These structures differ fundamentally from familiar molecules. Rather than being connected through chemical bonds, the particles remain bound because of their interactions with one another, and the resulting states can exist only in one dimension.
For much of the past century, Bethe strings were primarily a theoretical idea. Researchers at the University of Innsbruck have now created and detected these multiparticle bound states in an ultracold gas, working with theory teams from the Department of Experimental Physics at the University of Amsterdam and the Technical University of Munich. The results were published in Nature Communications.
Creating Bethe Strings Near Absolute Zero
To produce the unusual quantum states, the researchers started with a cloud of cesium atoms cooled to within only a few billionths of a degree above absolute zero. They then separated the cloud into several thousand extremely narrow tubes.
Within each tube, the atoms are effectively restricted to moving along a single direction, creating the one-dimensional environment required for Bethe strings to exist. The researchers can also precisely adjust how strongly the atoms interact.
By changing those interactions from repulsive to attractive, the team caused the atoms to bind together. Rather than simply collapsing into one group, the atoms formed bound states of several different sizes. Some of the larger clusters contained six or more particles.
Watching Quantum Strings Collide
The next challenge was demonstrating that these particles were truly bound together.
"One of the simplest experiments was to let the strings expand," says Milena Horvath, one of the lead authors.
The researchers first allowed the atoms to spread out while keeping them trapped inside their one-dimensional tubes. During this expansion, the strings encountered one another and collided, yet the bound structures survived.
"This is a remarkable feature of the strings: they can collide without breaking apart," says Milena Horvath.
The scientists then performed a second version of the experiment in which they removed the confinement and allowed the atoms to expand freely through three-dimensional space. Because Bethe strings can exist only in one dimension, releasing the atoms into three dimensions caused the bound states to fall apart.
The energy that had kept the particles bound was then transformed into motion, making the atoms spread apart faster. Comparing the two types of expansion gave the researchers a clear way to identify the presence of Bethe strings.
When the particles were unbound, as they were when the interactions were repulsive, both expansion measurements produced essentially the same energy. When Bethe strings were present, however, the three-dimensional expansion contained extra energy released as the bound states broke apart.
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. "Now we can create them in the laboratory, manipulate them and make them collide and probe their remarkable collisional stability."
Bethe strings have previously been detected experimentally in solid-state magnetic systems. The new work places these unusual quantum bound states in a very different environment: an ultracold atomic gas where researchers can control the system's geometry, particle density, and interactions with exceptional precision.
"This opens new possibilities for studying how these collective quantum objects form and interact," says lead theorist Alvise Bastianello.
The research was funded by the Austrian Science Fund FWF through a Wittgenstein Prize grant, the European Union through an ERC grant, and the UK Engineering and Physical Sciences Research Council. Milena Horvath is a member of the FWF doctoral program Atoms, Light and Molecules (DK-ALM).