Topologically connected processes by non-Abelian braiding in a fractional quantum Hall interferometer.

We theoretically study a Fabry-Perot interferometer in the fractional quantum Hall regime at filling factor 5/2, into which anyons are dilutely injected via a quantum point contact. We found that in this setup, there appears an interference process where an anyon thermally excited in the Fabry-Perot interferometer effectively braids another anyon injected from the quantum point contact. This process is represented by disconnected Feynman diagram, which are topologically connected by the non-Abelian braiding. In a certain experimentally feasible regime, this process dominantly contributes to the interference current of the setup, resulting in a non-trivial phase shift 3π/2 of the interference pattern. The phase shift is experimentally measurable even in the Coulomb dominated regime with strong bulk-edge coupling. The measurement of the phase shift will provide an evidence of non-Abelian statistics.