Observing one-dimensional anyons: Exotic quasiparticles in the coldest corners of the universe

Nature categorizes particles into two fundamental types: fermions and bosons. While matter-building particles such as quarks and electrons belong to the fermion family, bosons typically serve as force carriers -- examples include photons, which mediate electromagnetic interactions, and gluons, which govern nuclear forces. When two fermions are exchanged, the quantum wave function picks up a minus sign, i.e., mathematically speaking, a phase of pi. This is totally different for bosons: Their phase upon exchange is zero. This quantum statistical property has drastic consequences for the behaviour of either fermionic or bosonic quantum many-body systems. It explains why the periodic table is built up the way it is, and it is at the heart of superconductivity.

However, in low-dimensional systems, a fascinating new class of particles emerges: anyons -- neither fermions nor bosons, with exchange phases between zero and pi. Unlike traditional particles, anyons do not exist independently but arise as excitations within quantum states of matter. This phenomenon is akin to phonons, which manifest as vibrations in a string yet behave as distinct "particles of sound." While anyons have been observed in two-dimensional media, their presence in one-dimensional (1D) systems has remained elusive -- until now.

A study published in Nature reports the first observation of emergent anyonic behaviour in a 1D ultracold bosonic gas. This research is a collaboration between Hanns-Christoph Nägerl's experimental group at the University of Innsbruck (Austria), theorist Mikhail Zvonarev at Université Paris-Saclay, and Nathan Goldman's theory group at Université Libre de Bruxelles (Belgium) & Collège de France (Paris). The research team achieved this remarkable feat by injecting and accelerating a mobile impurity into a strongly interacting bosonic gas, meticulously analysing its momentum distribution. Their findings reveal that the impurity enables the emergence of anyons in the system.

"What's remarkable is that we can dial in the statistical phase continuously, allowing us to smoothly transition from bosonic to fermionic behavior," says Sudipta Dhar, one of the leading authors of the study. "This represents a fundamental advance in our ability to engineer exotic quantum states." The theorist Botao Wang agrees: "Our modelling directly reflects this phase and allows us to capture the experimental results very well in our computer simulations."

This elegantly simple experimental framework opens new avenues for studying anyons in highly controlled quantum gases. Beyond fundamental research, such studies are particularly exciting because certain types of anyons are predicted to enable topological quantum computing -- a revolutionary approach that could overcome key limitations of today's quantum processors.

This discovery marks a pivotal step in the exploration of quantum matter, shedding new light on exotic particle behaviour that may shape the future of quantum technologies.