Statistics of Anyons in quantum Hall conductors – ANY-HALL

Exchange statistics are related to the phase f accumulated by the wavefunction describing the state of an ensemble of undistinguishable particles when two particles are exchanged. In the three-dimensional world, particles are divided between bosons, which obey f=0 and tend to bunch together, and fermions, for which f=p and which exclude each other via the Pauli exclusion principle. The situation is different in two-dimensional systems which allow the existence of quasiparticles called anyons with intermediate statistics between fermions and bosons, leading to intermediate degrees of bunching and exclusion. The strongly correlated phases of the fractional quantum Hall effect (FQH) have been predicted to host anyons carrying a fractional charge and obeying fractional statistics. The fractional charge has been observed twenty years ago by partitioning a beam of anyons and by measuring the resulting current noise, which is proportional to the fractional charge. However, despite numerous attempts, no direct signature of fractional statistics had been observed until two distinct experiments provided the first observations of fractional statistics this year. The first one performed by our consortium extended previous noise measurements in collider geometries to the FQH case in an anyon collider. Current noise measurements revealed the tendency of anyons to form larger charge packets in the collision process which is a signature of their intermediate exclusion statistics. The second experiment, performed by the Purdue group, observed braiding signatures in an anyon interferometer.
Building upon this success, the project ANY-HALL aims at studying, experimentally and theoretically, the quantum statistics of anyons using the anyon collider as a test bench for fractional statistics. More precisely, the project will focus on the realization of three different objectives:
The first objective of the project is to quantitatively study the fractional statistics of anyons for different topological orders. We will study anyon collisions for different filling factors (controlled by the magnetic field) corresponding to different FQH states with different statistics (and different values of the exchange phase f).
The second objective of the project is to understand the role of decoherence and relaxation on the experimental signatures of fractional statistics in the collider geometry. We will investigate the role of temperature and relaxation which are known to be important in the context of electron collisions. These effects, governed by the distance between the anyon emission and the central beam-splitter will be studied both experimentally and theoretically.
The third objective of the project is the quantitative study of the dynamical regime. Anyon emission will be triggered by time-dependent drives in order to control the synchronization of the arrival times of anyons on the beam-splitter. We will also investigate how the number of anyons colliding on beam-splitter can be controlled by varying the amplitude of the current pulses.

Our consortium is constructed such as to gather all the expertise necessary to tackle these questions. Experimentalists have the know-how to implement anyon collisions with state-of-the-art resolution. Specialists of sample growth and sample fabrication will fabricate high quality samples with good stability necessary for accurate noise measurements. Finally, theoreticians will provide the description of anyon collisions for complex edge channel structures, capturing the effects of relaxation and time-dependent drives.