Anyonic Exchange Phase from Antidot Interferometry

Two-dimensional fractional quantum Hall systems host anyons with fractional charge e* and exchange phase θ, yet most experiments access only the braiding phase 2θ, leaving θ known only modulo π. Building on a recent proposal for a modified interferometer that distinguishes transmission through empty versus occupied anti-dot levels [1], we analyze a Fabry-Perot geometry with a quantum anti-dot embedded in one arm, tuned by a gate under finite inter-edge bias. A perturbative Keldysh treatment of the interference current, benchmarked against an electronic T-matrix calculation at filling fraction ν = 1, isolates contributions from resonant tunneling, non-equilibrium occupation, and the anyonic density-of-states anomaly. For Laughlin states, the transmission phase evolves non-monotonically as the anti-dot level traverses the bias window and approaches a plateau at πν when co-tunneling through the occupied level dominates. This structure is absent for electrons, which show a smooth 0 to π evolution. It yields the exchange phase directly from the plateau value of the transmission phase, without fitting to non-universal parameters. We also show that the signatures persist, with thermal smearing, at experimentally relevant temperatures, and that a coupling asymmetry generates a continuous phase evolution between resonances. Our results provide concrete, flux-dependent criteria for extracting θ = πν in present devices.

[1] S. A. Kivelson and C. Murthy, Physical Review Letters 135, 126605 (2025)