Anyone for Anyons?

Researchers have demonstrated that a strange type of quantum particle called the anyon, believed to exist in only two dimensions, can also be created in one dimension. Further studies exploring different types of one-dimensional anyons could bring scientists one step closer to using the particles as a fundamental unit of memory in a quantum computer.

A team led by Harvard scientists Joyce Kwan and Markus Greiner and which includes Alexey Gorshkov, a theoretical physicist at the National Institute for Standards and Technology (NIST), reported the discovery in the November 29, 2024, issue of Science. Gorshkov is also a fellow at the Joint Center for Quantum Information and Computer Science (QUICS) and the Joint Quantum Institute (JQI), research partnerships between NIST and the University of Maryland. 

Anyons, whose existence was predicted four decades ago but were only experimentally discovered in 2020, are the mavericks among quantum particles. Although all elementary particles belong to one of two families – bosons and fermions – anyons exhibit behavior that defies either classification. 

Fermions, which include electrons, protons, and neutrons, obey a statistical rule: If two identical fermions trade places, the wavefunction that describes them inverts, or rotates by 180 degrees, so that the crests of the wave become troughs and the troughs become crests. (This also implies that two identical fermions can never occupy the same quantum state at the same time.)

In contrast, bosons, which include photons, obey a different rule. When two identical bosons switch places, their wavefunction does not rotate, remaining as it was. (This allows bosons to clump together, occupying the same quantum state.)

Anyons, however, don’t follow either rule. When they trade places, the phase of their wavefunction rotates by a fractional amount that varies with the type of anyon. In two dimensions, that strange behavior manifests itself in a curious but important way: When one anyon makes a complete circle around another, it retains memory of that motion in its wavefunction. Scientists are exploring ways to harness that memory for quantum computers.

When Harvard researchers Kwan, Greiner and their colleagues began studying anyons, they were, in part, inspired to try to produce them in one dimension after reading a journal article Gorshkov and his collaborators had published in 2018. The article described a key test to determine whether some particles confined to one dimension could qualify as anyons.

In the team’s experiment, which Gorshkov helped analyze, the scientists chilled rubidium-87 atoms and trapped them in an optical lattice – an array of peaks and valleys of light intensity created by interfering lasers. The rubidium atoms tended to reside in the valleys.

Like all atoms, the trapped rubidium atoms initially acted as bosons, not anyons. But the researchers elicited a different behavior when they manipulated the atoms, encouraging them to hop from one trough to the next by switching on a magnetic field and varying both the intensity and frequency of the laser light. Under those conditions, the team found that when two of the rubidium atoms swapped places, their wavefunction rotated by a fractional amount – the hallmark of anyons. 

The type of one-dimensional anyons found by the team could not serve as memory for quantum computing. But other researchers are finding hints that other types of one-dimensional anyons may have properties similar to those in two dimensions that could be used for quantum memory, Kwan said.

Paper: J. Kwan , P. Segura , Y. Li , S. Kim, A.V. Gorshkov , A. Eckardt , B. Bakkali-Hassani , and M. Greiner. Realization of one-dimensional anyons with arbitrary statistical phase. Science. Published online Nov. 28, 2024. DOI: 10.1126/science.adi3252