Physicists cooled a ring of atoms and detected a quantum effect predicted a century ago

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• From Bethe’s calculation to atomic clusters
• How the experiment explored strings
• Short-lived states and next experiments

A laboratory experiment with ultracold atoms has produced indirect evidence that particles confined to a single line can bind into multi-particle clusters known as Bethe strings. Published Aug. 29 in Nature Communications, the work gives researchers a new, controllable platform to test how many-body quantum systems organize and evolve.

From Bethe’s calculation to atomic clusters

In 1931, Hans Bethe analyzed a simple model: a one-dimensional chain of electrons whose spins can be either up or down. His solution showed that when a few spins flip, those flipped excitations can move together as a collective object instead of separately.

Physicists later realized Bethe’s approach applies beyond spins to particles moving along a line. When particles attract one another, theory predicts they form bound groups called Bethe strings, each group behaving like a single quasiparticle.

How the experiment explored strings

The research team began by cooling tens of thousands of cesium atoms into a Bose-Einstein condensate, a quantum state in which many atoms share the same wavefunction. They then used laser beams to carve the condensate into thousands of very narrow tubes, each holding at most a few dozen atoms in one dimension.

At first the atoms repelled one another. The scientists tuned a magnetic field to reduce that repulsion to zero and then make the interactions attractive. Under those conditions, theory says atoms should bind into strings rather than clump in three dimensions.

The team could not image individual strings directly. Instead they released the atoms and compared how fast the clouds expanded when the atoms were allowed to move only along the tubes versus when they expanded in all three dimensions. In three dimensions, the clouds carried roughly three times more kinetic energy than in the one-dimensional channels, consistent with bound groups releasing binding energy when they broke apart.

From the difference in expansion the researchers estimated the bound groups contained at least six atoms in many cases. Their measurements also agreed closely with predictions from generalized hydrodynamics, a framework that treats the gas as a fluid made of many species, including strings of different sizes.

“That some theory fits to your data is not a proof that something exists,” said study co-author Hanns‑Christoph Nägerl, an experimental physicist at the University of Innsbruck, emphasizing the result is supportive but indirect.

Short-lived states and next experiments

The observed strings appear to be transient. Even inside the one-dimensional tubes, the atoms still experience three-dimensional effects at short range, and the bound states eventually decay into ordinary cesium molecules. In the coldest runs, the team lost about 40% of the atoms.

Still, the group is already considering ways to make the states longer lived. Nägerl suggested shielding ultracold molecules with microwaves to prevent short-range collisions; the idea remains untested. Another avenue is using quantum gas microscopy to image atoms individually, which could provide direct visual evidence of strings.

Longer term, Nägerl wants experiments that control both particle motion and spin flips, enabling researchers to assemble simple model materials atom by atom. His team has begun the next step by using lasers to manipulate atomic spins in the one-dimensional gas. He described Bethe strings as a minor detour, but added they are unavoidable whenever the atoms attract.