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Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

Parsa Bonderson, Alexei Kitaev, Kirill Shtengel

TL;DR

This work addresses the problem of experimentally validating non-Abelian statistics in the $\nu=5/2$ fractional quantum Hall state. It proposes a two-point-contact interferometer that leverages the Moore–Read ($U(1)\times \mathrm{Ising}$) anyon model to predict braiding-induced interference, yielding a distinct parity-dependent signal: odd numbers of quasiholes yield no interference, while even numbers produce oscillations with period $4\Phi_0$ (modulated by the fusion channel). The key contributions are the explicit interference formulas incorporating braiding via $M_n$ and the parity-dependent outcomes, and the explicit link to the topological qubit scheme of DasSarma et al. The significance lies in providing a concrete, testable experimental path to confirm non-Abelian anyons and to inform the design and operation of topological qubits in MR-based systems.

Abstract

In this letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read state expected to describe the observed FQHE plateau at nu=5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et. al. are also addressed.

Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

TL;DR

This work addresses the problem of experimentally validating non-Abelian statistics in the fractional quantum Hall state. It proposes a two-point-contact interferometer that leverages the Moore–Read () anyon model to predict braiding-induced interference, yielding a distinct parity-dependent signal: odd numbers of quasiholes yield no interference, while even numbers produce oscillations with period (modulated by the fusion channel). The key contributions are the explicit interference formulas incorporating braiding via and the parity-dependent outcomes, and the explicit link to the topological qubit scheme of DasSarma et al. The significance lies in providing a concrete, testable experimental path to confirm non-Abelian anyons and to inform the design and operation of topological qubits in MR-based systems.

Abstract

In this letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read state expected to describe the observed FQHE plateau at nu=5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et. al. are also addressed.

Paper Structure

This paper contains 5 sections, 13 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Proposed experimental setup
  3. The Moore-Read state
  4. Implications for a topological qubit scheme
  5. Conclusion

Figures (2)

  • Figure 1: A two point-contact interferometer for measuring the quasiparticle statistics. The hatched region contains an incompressible FQH liquid. The front gates (grey rectangles) are used to bring the opposite edge currents (indicated by arrows) close to each other to form two tunneling junctions. Applying voltage to the central gate creates an antidot in the middle and controls the number of quasiparticles contained there.
  • Figure 2: The configuration for a topologically protected qubit proposed in DasSarma05. A two-point interferometer is used to measure the combined state of a quasihole pair split onto two separate antidots. A bit flip that switches between the $\mathbb{I}$ and $\psi$ states is performed by tunneling a single quasihole through the switching constriction, whose tunneling amplitude $t_{\text{S}}$ can be turned on and off by controlling the middle set of gates.