Braiding of anyonic quasiparticles in charge transfer statistics of a symmetric fractional edge-state Mach-Zehnder interferometer

We have studied the zero-temperature statistics of the charge transfer between the two edges of Quantum Hall liquids of, in general, different filling factors, ν_0,1 =1/ (2 m_0,1 +1), with m₀ ≥ m₁ ≥0, forming Mach-Zehnder interferometer. Expression for the cumulant generating function in the large-time limit is obtained for symmetric interferometer with equal propagation times along the two edges between the contacts and time-independent bias voltage. The low-voltage limit of the generating function can be interpreted in terms of the regular Poisson process of electron tunneling, while its leading large-voltage asymptotics is proven to coincide with the solution of kinetic equation describing quasiparticle transitions between the m states of the interferometer with different effective flux through it, where m≡1+ m₀ + m₁. For m>1, this dynamics reflects both the fractional charge e/m and the fractional statistical angle π/m of the tunneling quasiparticles. Explicit expressions for the second (shot noise) and third cumulants are obtained, and their voltage dependence is analyzed.