Under strong magnetic fields, electrons that are confined to two spatial dimensions can exhibit a fractional quantum Hall state where the elementary quasiparticles carry only a fraction of the electron charge. These exotic excitations, called anyons, moreover behave under the interchange of two individuals neither as fermions nor as bosons but are characterized instead by a non-trivial exchange phase. The experimental proof of these anyons and their exchange phase was performed only recently, in 2020. Recent experiments have notably demonstrated that a quantum point contact on the edge channels of a fractional quantum Hall (Laughlin) state is able to reveal the anyonic phase from noise measurements.
After introducing anyons in the fractional quantum Hall effect, we will explore their imprint along the edge of the system and their manipulation using quantum constrictions. Focusing on the tunneling of anyons at a quantum point contact, we will show how this process is partly governed by a 1+1 space-time braiding mechanism between anyons. This mechanism mirrors the conventional anyonic braiding observed when a quasiparticle adiabatically encircles another. The braiding phase can then be extracted from correlated noise measurements at the output of series of quantum point contacts where the non-linearity of tunneling also plays a significant role. We shall also discuss Andreev tunneling at a quantum constriction, which involves the conversion of anyons to electrons or between different types of anyons. This process leaves a distinctive signal on the cross-correlation, and has also received experimental confirmation.
