Testing non-Abelian and Abelian statistics by controlled single quasiparticle addition to quantum Hall interferometers

Fractionally charged quasiparticle excitations in two-dimensional electron systems have been proposed to obey anyonic Abelian statistics and in some cases anyonic non-Abelian statistics. Demonstration of these statistics has been difficult but could be made explicit with control of individual quasiparticle number within the interferometer, where these quasiparticles are encircled by the trajectories of interfering quasiparticles. Here we use a Fabry-Perot interferometer equipped with a small interior top gate that allows addition or subtraction of a single encircled quasiparticle/quasihole (e.g. charge e/4). At the 7/2 filling factor fractional quantum Hall state, which is anticipated to have non-Abelian excitations, such controlled addition of quasiparticles results in systematic pi phase changes in the resistance oscillations over the range of magnetic field sweeps. The oscillations themselves are due to change in the number of bulk quasiparticles induced by the changing magnetic field (different from those trapped by the top gate!) . This pi phase shift effect due to change in the number of charge e/4 quasiparticles is a specific signature of non-Abelian statistics at 7/2 (and 5/2), the even-odd effect. The method of central gate charge modulation is substantiated here by its demonstration at filling factor 2+1/3. These results at 7/3 demonstrate controlled phase change consistent with anyonic statistics, and at 7/2 provide further evidence for the non-Abelian nature of charge e/4 excitations at that filling factor.