Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding

The quantum Hall states at filling factors $\nu =5\mathrm{/}2$ and $7\mathrm{/}2$ are expected to have Abelian charge $e\mathrm{/}2$ quasiparticles and non-Abelian charge $e\mathrm{/}4$ quasiparticles. The non-Abelian statistics of the latter has been predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of magnetic field in Fabry-P'erot interferometers using new high purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations at $\nu =7\mathrm{/}2$. At both $\nu =5\mathrm{/}2$ and $7\mathrm{/}2$ we also examine, for the first time, the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles. The phase of observed $e\mathrm{/}4$ oscillations is reproducible and stable over long times (hours) near both filling factors, indicating stability of the fermion parity. At both fractions, when phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with either fermion parity change or change in the number of the enclosed $e\mathrm{/}4$ quasiparticles. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e\mathrm{/}4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.