Anyonic braiding statistics — the fractional phase acquired when one quasiparticle orbits another — is the defining property of topological order. Measuring it is hard because standard interferometry picks up both the anyonic phase and a background Aharonov-Bohm phase, and the two are entangled. Worse, extracting the anyonic phase from the interference pattern has an inherent π-ambiguity: you can't tell θ from θ + π.
Fan, Halperin, and Feldman propose a cross-geometry interferometer that resolves the ambiguity. By combining measurements from two different interferometer geometries — one where the anyons orbit clockwise and one where they orbit counterclockwise — the Aharonov-Bohm background cancels and the anyonic phase doubles. The π-ambiguity is eliminated because the cross-geometry signal depends on 2θ, not θ.
The protocol uses Hanbury Brown-Twiss correlations: coincidence counts between detectors at the two output arms of each interferometer. The correlation function contains a term proportional to cos(2θ_anyon), which oscillates with the double anyonic phase and is independent of the magnetic flux through the interferometer.
The method works for both Abelian anyons (fractional quantum Hall quasiparticles with θ = π/m) and non-Abelian anyons (where the phase depends on the fusion channel). For non-Abelian anyons, the HBT correlations contain additional structure that reveals the fusion multiplicities — information that standard interferometry cannot access.
A clean experimental protocol for the signature property of topological matter. Two geometries, one correlation function, no ambiguity.