Anyon Statistics in Tiny Electronic Colliders

Introduction

In three-dimensional systems, elementary particles are divided exclusively between fermions (which exclude each other) and bosons (which bunch together) according to the phase acquired by the wavefunction when two particles are exchanged. The situation is different in two-dimensional systems which can host new particles called anyons, for which the exchange phase can take any value, and which obey partial exclusion, between fermions and bosons.

Topological Protection

Interestingly, these quasiparticles keep a memory of the exchanges between them that is protected from local perturbations of their trajectories: one speaks of topological protection. This protection is at the heart of the interest for anyons, as specific types of anyons called non-abelian are the building blocks of topological quantum computing that would be protected from decoherence.

Historical Context

The existence of these quasiparticles was predicted forty years ago in two-dimensional conductors in the fractional quantum Hall regime. However, despite intense experimental and theoretical efforts, direct signatures of their fractional statistics have only been observed recently, offering only now the possibility to characterize fractional statistics and to exploit it for new functionalities.

Project Objectives

The purpose of this project is to quantitatively investigate the statistics of anyons by probing their tendency to bunch together or exclude each other in a nanoscale collider. The different phases of the fractional quantum Hall effect offer a very vast and almost completely unexplored variety of anyons.

1. I will characterize the differences between different statistics, including the most interesting non-abelian case.
2. I will also investigate the robustness of the signatures of fractional statistics and to which extent they can be considered as topologically protected.
3. Finally, I will probe anyon statistics in the time-domain regime, where anyon emission is dynamically controlled, which is a necessary condition for quantum information perspectives.