Exactly solvable anyonic interferometer on a single edge of a topological liquid

Experimental signatures of anyonic statistics are a key focus in physics. A major milestone in this pursuit has been the direct confirmation of anyonic statistics through interferometry. Within this realm, two configurations of interferometers, namely Fabry-P{'e}rot and Mach-Zehnder setups, have been successfully implemented. However, since the theoretical considerations resort to perturbative treatment, simple theoretical expressions for the electric currents and noises are unavailable at higher visibility of Aharonov-Bohm osculations.

In this talk, we introduce an alternative version of the Mach-Zehnder interferometer [1] in which the quasiparticles tunnel between co-propagating chiral channels on the edges of quantum Hall liquid at the bulk filling factors $ u= n/(2n + 1)$. Unlike the conventional Mach-Zehnder interferometers, this configuration does not require the placement of an Ohmic contact inside the device and directly parallels the optical Mach-Zehnder geometry. Remarkably, this setup admits an easy exact solution for any visibility, including the experimentally optimal regime. The simple expressions found for electric current and noise contain information about fractional charge and fractional statistics.

[1] N. Batra, Z. Wei, S. Vishveshwara, and D. E. Feldman, ArXiv:2308.05236