Probing anyon statistics on a single-edge loop in the fractional quantum Hall regime

We propose a setup to directly measure the anyonic statistical angle on a single edge of a fractional quantum Hall system, without requiring independent knowledge of non-universal parameters. We consider a Laughlin edge state bent into a closed loop geometry, where tunneling processes are controllably induced between the endpoints of the loop. To illustrate the underlying physical mechanism, we compute the time-dependent current generated by the injection of multiple anyons, and show that its behavior exhibits distinctive features governed by the anyonic statistical angle. The measured current reflects quantum interference effects due to the time-resolved braiding of anyons at the junction. To establish experimental relevance, we introduce a protocol where anyons are probabilistically injected upstream of the loop via a quantum point contact (QPC) source. Unlike in Fabry-Perot interferometers, where phase jumps occur spontaneously due to stochastic quasi-particle motion, here the phase jumps are deliberately induced by source injections. These events imprint measurable signatures in the cross-correlation noise, enabling a controlled statistical analysis of the braiding phase. We further show that, by varying the magnetic field while remaining within the same fractional quantum Hall plateau, the statistical angle can be extracted without relying on the knowledge of other non-universal system parameters. Our results provide a minimal and accessible platform for probing anyonic statistics using a single chiral edge.