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

**Authors:** R.L. Willett (1), K. Shtengel (2), C. Nayak (3, 4), L.N. Pfeiffer, (5), Y.J. Chung (5), M. L. Peabody (1), K.W. Baldwin (5), K. W. West (5)., ((1) Nokia Bell Labs, Murray Hill, New Jersey, USA, (2) Department of, Physics, University of California, Riverside, California, USA, (3) Microsoft, Quantum, Elings Hall, University of California, Santa Barbara, California,, USA,(4) Department of Physics, University of California, Santa Barbara,, California, USA, (5) Department of Electrical Engineering, Princeton, University, Princeton, New Jersey, USA.)

arXiv: 1905.10248 · 2023-03-09

## TL;DR

This study provides experimental evidence for non-Abelian e/4 quasiparticles in quantum Hall states at filling factors 5/2 and 7/2, demonstrating their stability and potential for topological quantum computing through interference measurements.

## Contribution

First experimental observation of non-Abelian e/4 quasiparticles at ν=7/2 using interference in high purity heterostructures, including analysis of fermion parity stability.

## Key findings

- Evidence of non-Abelian e/4 quasiparticles at ν=7/2
- Stable fermion parity over hours near both filling factors
- Observation of Abelian e/2 quasiparticle interference

## Abstract

The quantum Hall states at filling factors $\nu=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ 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 $\nu=7/2$. At both $\nu=5/2$ and $7/2$ 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 $e/4$ 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 $e/4$ 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 $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.

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Source: https://tomesphere.com/paper/1905.10248