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

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-Pérot 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.

Final version, nearly identical to the one published in Phys. Rev. X sans some questionable superficial changes insisted upon by the PRX editors and with Supplementary Materials included after the main text

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Aharonov-Bohm interference of fractional quantum Hall edge modes
• The non-Abelian Interferometer
• Primary-Filling e/3 Quasiparticle Interferometer
• Melting of interference in the fractional quantum Hall effect: Appearance of neutral modes
• Edge States and Interferometers in the Pfaffian and anti-Pfaffian States
• Bulk-edge coupling in the non-abelian $\nu =5/2$ quantum Hall interferometer
• Confinement of fractional quantum Hall states in narrow conducting channels
• Aharonov-Bohm effect and coherence length of charge e/4 quasiparticles at 5/2 filling factor measured in multiple small Fabry-Perot interferometers

Cited by in corpus (12)

• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Accurately computing electronic properties of a quantum ring
• Simulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer
• Impact of bulk-edge coupling on observation of anyonic braiding statistics in quantum Hall interferometers
• Anyons in Quantum Hall Interferometry
• Edge Probes of Topological Order
• Strongly coupled edge states in a graphene quantum Hall interferometer
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
• Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene
• Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system
• Even-denominator fractional quantum Hall state in conventional triple-gated quantum point contact