Anyonic Braiding in a Chiral Mach-Zehnder Interferometer

Fractional quantum statistics are the defining characteristic of anyons. Measuring the phase generated by an exchange of anyons is challenging, as standard interferometry setups -- such as the Fabry-P\'erot interferometer -- suffer from charging effects that obscure the interference signal. Here, we present the observation of anyonic interference and exchange phases in an optical-like Mach-Zehnder interferometer based on co-propagating interface modes. By avoiding backscattering and deleterious charging effects, this setup enables pristine and robust Aharonov-Bohm interference without any phase slips. At various fractional filling factors, the observed flux periodicities agree with the fundamental fractionally charged excitations that correspond to Jain states and depend only on the bulk topological order. To probe anyonic statistics, we use a small, charged top-gate in the interferometer bulk to induce localized quasiparticles without modifying the Aharonov-Bohm phase; however, with introducing periodic phase slips. The magnitude of the observed phase slips and their signs align with the expected value at filling 1/3, but their direction shows systematic deviations at fillings 2/5 and 3/7. Control over added individual quasiparticles in this design is essential for measuring the coveted non-Abelian statistics in the future.