Anyon collisions and fractional statistics

Abstract

Quantum statistics refers to the properties of the wavefunction under the exchange of two particles. In three dimensions, there are two categories of particles depending on the value of the phase φ acquired by the wavefunction in the exchange process: bosons satisfy φ = 0 and fermions φ = π. In contrast, two-dimensional systems can host quasiparticles called anyons that obey intermediate, or fractional, statistics between fermions and bosons, with 0 ≤ φ ≤ π. As a result, and contrary to fermions and bosons, anyons have non trivial braiding properties. It means that the phase factor e2iφ accumulated by the wavefunction when one anyon encircles another one is different from 1. The fractional quantum Hall effect, which occurs in high mobility two-dimensional electron gases placed in a strong perpendicular magnetic field, is one of the systems which hosts anyons. They carry a fractional charge and obey fractional statistics. The fractional charge of anyons was measured in the 1990s from the noise generated by partitioning an anyon beam at a beam splitter. We discuss here the recent demonstration of their fractional statistics in an anyon collider at the filling factor ν = 1/3 of the fractional quantum Hall effect. In anyon collision experiments, two dilute beams of anyons generated randomly by two anyon sources collide on a beam splitter. For comparison with the anyon case, we present first bosonic and fermionic collisions. They are governed by boson bunching and fermion antibunching between two particles colliding simultaneously at the splitter. In the anyon case, specific mechanisms for charge transfer at the beam splitter occur, which are governed by the anyon braiding factor e2iφ. In these mechanisms, a single anyon emitted at the splitter input may trigger the bunching of another anyon in the same output, leaving a hole in the other output. We discuss in this manuscript how these specific anyon transfer mechanisms, which lead to strong negative cross-correlations of the current fluctuations at the splitter output, are used to distinguish anyon collisions from the bosonic and fermionic cases. We also discuss how the dependence of the noise correlations in the anyon braiding phase is used to quantitatively investigate the fractional exchange phase φ of anyons in colliders.