Anyon Interferometry and Evidence Standards

Anyon interferometry seeks a phase or fusion-channel response that changes when a controlled quasiparticle enters an interference loop. The same conductance oscillation also depends on magnetic flux, device area, edge velocity, Coulomb charging, tunneling amplitudes, neutral modes, and noise. A strong claim therefore fits all controlled variables and reproduces the inferred charge/statistics across independent regimes.

Required background. Anyon quasiparticles supplies braid and fusion phases; Hall edges supplies the interfering modes and equilibration limits.

Helpful background. Model selection and parameter inference supplies competing-hypothesis tests.

Phase decomposition

For an anyon $a$ of charge $Q_a$ encircling area $A$ and localized quasiparticles $b$, an Abelian interference contribution has phase

$$\varphi=\varphi_{\rm dyn} +2\pi\frac{Q_a}{e}\frac{BA}{\Phi_0} +\sum_bN_b\theta^{\rm mutual}_{ab}, \qquad \Phi_0=\frac{h}{e},$$

up to the declared field and path orientation. Changing $B$ or a plunger gate changes both flux and, through electrostatics, potentially $A$ and $N_b$. In an Aharonov–Bohm-dominated regime, constant-filling trajectories and independently calibrated area can separate these terms. In a Coulomb-dominated regime, area breathing and charge quantization can mimic altered periods Halperin et al. 2011.

For non-Abelian anyons, the interference amplitude can depend on total enclosed fusion charge and may be suppressed after tracing over fusion channels. Such even–odd or channel dependence is stronger than a fractional period, but poisoning, neutral-mode dephasing, and uncontrolled quasiparticle motion must be excluded.

What experiments establish

Fabry–Pérot phase slips at $\nu=1/3$ and collision correlations in a collider geometry provided mutually different evidence for Abelian fractional statistics in 2020 Bartolomei et al. 2020, Nakamura et al. 2020. More recent graphene devices associated telegraph switching with controlled anyon entry and braiding Werkmeister et al. 2025, while a chiral Mach–Zehnder geometry reported filling-dependent anyonic exchange phases Ghosh et al. 2025.

These results constitute convergent device-level evidence for Abelian anyonic behavior in specified fillings and operating regimes. They do not by themselves establish a universal device-independent phase-extraction procedure. At even denominator, coherent Aharonov–Bohm interference and fractional charge constrain candidate states Kim et al. 2026, but fractional charge and coherence do not uniquely identify non-Abelian fusion or braid matrices.

Evidence boundary and decisive controls

The experimental status on this page was checked against primary sources available through 10 August 2026. As of that cutoff, direct material-platform identification of non-Abelian fusion and braiding remains less established than Abelian fractional charge/statistics. Current-source updates belong in Quantum Matter and Emergence Research.

A decisive analysis reports the full two-dimensional gate–field pattern, visibility versus temperature and bias, calibrated area/capacitance, charge-sector stability, phase-slip distribution, repeated cooldowns/devices, and blind comparison with Coulomb, resonant-tunneling, and trap models. Thermal Hall or shot noise constrains complementary data but is not a substitute for fusion-sensitive braiding.

Exercise

A charge-$e/3$ anyon encircles one identical Laughlin $1/3$ quasihole while the magnetic flux is held fixed. What statistical phase change is expected?

Solution

The mutual full-braid phase for identical Laughlin quasiholes is $2\pi/3$. The measured phase shift equals this only if dynamical phase, area, and localized-charge changes are independently held fixed or modeled.

References

• H. Bartolomei, M. Kumar, R. Bisognin, A. Marguerite, J.-M. Berroir, E. Bocquillon, B. Plaçais, A. Cavanna, Q. Dong, U. Gennser, Y. Jin, and G. Fève, “Fractional Statistics in Anyon Collisions,” Science 368 (2020) 173–177, doi:10.1126/science.aaz5601.
• Bikash Ghosh, Maria Labendik, Liliia Musina, Vladimir Umansky, Moty Heiblum, and David F. Mross, “Anyonic Braiding in a Chiral Mach–Zehnder Interferometer,” Nature Physics 21 (2025) 1392–1397, doi:10.1038/s41567-025-02960-3.
• Bertrand I. Halperin, Ady Stern, Izhar Neder, and Bernd Rosenow, “Theory of the Fabry–Pérot Quantum Hall Interferometer,” Physical Review B 83 (2011) 155440, doi:10.1103/PhysRevB.83.155440.
• Jehyun Kim, Himanshu Dev, Amit Shaer, Ravi Kumar, Alexey Ilin, André Haug, Shelly Iskoz, Kenji Watanabe, Takashi Taniguchi, David F. Mross, Ady Stern, and Yuval Ronen, “Aharonov–Bohm Interference in Even-Denominator Fractional Quantum Hall States,” Nature 649 (2026) 323–329, doi:10.1038/s41586-025-09891-2.
• James Nakamura, Shuang Liang, Geoffrey C. Gardner, and Michael J. Manfra, “Direct Observation of Anyonic Braiding Statistics,” Nature Physics 16 (2020) 931–936, doi:10.1038/s41567-020-1019-1.
• Thomas Werkmeister, James R. Ehrets, Marie E. Wesson, Danial H. Najafabadi, Kenji Watanabe, Takashi Taniguchi, Bertrand I. Halperin, Amir Yacoby, and Philip Kim, “Anyon Braiding and Telegraph Noise in a Graphene Interferometer,” Science 388 (2025) 730–735, doi:10.1126/science.adp5015.