Non-equilibrium quantum transport to detect the anyonic statistics

Abstract

Anyon is an exotic quasiparticle that is neither fermion nor boson, which can emerge in low-dimensional systems. Upon exchange of the identitcal particles, the wavefunction of Abelian anyons gets an aribtrary phase factor, and that of non-Abelian anyons can be transformed to the others. While the anyons are expected to be used as a fault-tolerant quantum computing, their existence had not yet been confirmed.

In this dissertation, we study the non-equilibrium quantum transport phenomena of the anyons to detect their braiding statistics, mainly based on the quantum Hall edges. We show that diluted anyons injected to a beam splitter behave fundamentally different from the fermion or boson. Rather than being partitioned into one of the output channels of the beam splitter, a particle-hole pair of the anyons is excited at the beam splitter instead, and experiences time-domain braiding with the anyons in the diluted beams. We consider various mesoscopic devicess that can observe the time-domain braiding process. Firstly, we propose a Mach-Zehnder interferometer and collider on integer quantum Hall edges that can detect the fractional mutual statistics among fractional charges and electrons. Secondly, we study anyon collider, which can discriminate various Abelian and non-Abelian anyons. Thirdly, we attribute the experimental results of the anomalously large partition noise of the diluted anyon beam on the fractional quantum Hall edge at filling factor $\nu=1/3$, and confirm the fractional exchange statistics of the Abelian anyons.