Corralling Interfering Anyons
When you live in theory-land, as I do, anyons in fractional quantum Hall (FQH) systems are an emblem of elegance. They address a fundamental question in quantum mechanics—the classification of indistinguishable particles—by breaking the long-rooted dichotomy between fermions and bosons and replacing it with a continuum of possibilities. Their implications are far reaching. Anyons account for the “hierarchy” of FQH states and they inspire visions of topologically protected quantum computation [1]. In experiment-land, the most direct manifestation of anyons is the phase that the system’s wave function acquires when two anyons are interchanged or when one winds around another. This phase is at the heart of a new experiment performed by Noah Samuelson and Liam Cohen of the University of California, Santa Barbara, and their collaborators [2]. The experiment not only detected the anyonic phase, but it also shed new light on the charge dynamics and thermodynamics of mesoscopic FQH physics.
Measuring an anyonic phase entails taking one anyon (“the interfering anyon”) through an interferometer, such that it encircles a closed loop (“the interference loop”). The interferometer measures an interference phase twice: first when the loop encloses a second anyon (“the localized anyon”) and then when the loop does not. The goal is to determine the difference in phase accumulated in the two cases. It is therefore essential that the interfering anyon goes around the same loop in both cases and that a localized anyon is brought into and out of the loop (Fig. 1). None of this is easy.
Fortunately, current in FQH states flows along the edges of a sample in a loop-like fashion. The interference loop can be defined by adjusting the position of the edges, which can be done by applying voltages to a set of gates. These gates make certain areas of the sample insulating, positioning the edges at the interfaces between the insulating and the FQH regions. The flow of current along the edges is driven by applying another voltage: this time, between the two ends of the bar-shaped sample. As for the localized anyon, it can be placed into the loop by a small variation of the magnetic field or by applying yet another voltage: this time, to a gate that controls the density within the interference loop. Together, the voltages and the magnetic field serve as knobs to control the size of the interference loop, the current that flows around the loop, and the number of anyons in the loop.
Unfortunately, the experimental control of the edges’ position is not perfect. The long-range Coulomb interaction among anyons makes the area of the loop vary with the number of anyons localized within the loop. The phase accumulated by the interfering anyons is a sum of a so-called Aharonov-Bohm phase, which depends on the loop area, and an anyonic phase, which depends not on the area but on the number of localized anyons. However, the area itself changes with the number of localized anyons, which makes it hard to distinguish between the two phases and to extract the coveted anyonic phase. Research conducted in the past few years has largely solved this problem. Interferometers can now be manipulated to operate away from the Coulomb-dominated regime and into the Aharonov-Bohm regime [3].
In their new experiment, Samuelson, Cohen, and their collaborators overcame different difficulties. In theory, the number of localized anyons within the loop is determined by minimizing the system’s free energy, which may be tuned with externally controlled knobs. However, this tactic assumes that the bulk of the loop quickly reaches thermal equilibrium, which is not necessarily true, as the experiment shows. Furthermore, even in thermal equilibrium anyons jump in and out of the loop due to the nonzero temperature, so the number of localized anyons fluctuates in time. Two scales then become relevant for phase measurements: the timescale over which the number of localized anyons varies and the variance in that number, which is a thermodynamic property. Observing anyonic phases requires the variance in the number of localized anyons to be much smaller than a single anyon or the timescale to vastly exceed the time needed for measuring an interference pattern.
Samuelson, Cohen, and their collaborators used their interferometer to measure the phase accumulated by the interfering anyons. In doing so, they turned it into a powerful sensor of the dynamics and thermodynamics of the localized anyons. Their interferometer revealed clear phase jumps whenever anyons went into and out of the interference loops. Using the magnetic field as the main knob to control the number of localized anyons, the researchers found that for a fixed magnetic field, thermal fluctuations in this number happened in minutes—long enough for interference to be measured and short enough for the experiment to be completed. The timescale allowed for exploration and understanding of the underlying dynamics. Furthermore, they found that the variance of the number of localized anyons was of the order of 1. When the magnetic field was varied, the phase jumps showed hysteretic behavior, a general indicator of a system’s struggle to reach equilibrium on the experimental timescale. By examining the value of the phase jumps and the amplitude of the oscillations, the researchers found indications that in some cases anyons entered and exited the loop in pairs.
This beautiful experiment, combined with other interferometric advances of recent years [4–9], shows that anyons are turning from a theoretical concept into an experimental reality. As all good experiments do, they have whetted my and other theorists’ appetite for predicting and witnessing how interferometry could probe many-anyon physics, including the possible tendency of anyons to bunch, the collective states they may form, and the phase transitions anyonic systems may undergo.
The investigation of Samuelson, Cohen, and their collaborators focused on the FQH state of one-third filling of a Landau level ( = 1/3), whose exchange effect is limited to a phase. The more fragile even-denominator FQH states are thought to host non-Abelian anyons, where an exchange may switch the system to an entirely new quantum state. Extending the investigation to these anyons would help to explore their potential as the building blocks of topological quantum computing.
References
- C. Nayak et al., “Non-Abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083 (2008).
- N. L. Samuelson et al., “Slow quasiparticle dynamics and anyonic statistics in a fractional quantum Hall Fabry-Pérot interferometer,” Phys. Rev. X 16, 011062 (2026).
- B. I. Halperin et al., “Theory of the Fabry-Pérot quantum Hall interferometer,” Phys. Rev. B 83, 155440 (2011).
- J. Nakamura et al., “Direct observation of anyonic braiding statistics,” Nat. Phys. 16, 931 (2020).
- J. Nakamura et al., “Fabry-Pérot interferometry at the = 2/5 fractional quantum Hall state,” Phys. Rev. X 13, 041012 (2023).
- J. Kim et al., “Aharonov–Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene,” Nat. Nanotechnol. 19, 1619 (2024).
- T. Werkmeister et al., “Anyon braiding and telegraph noise in a graphene interferometer,” Science 388, 730 (2025).
- B. Ghosh et al., “Coherent bunching of anyons and dissociation in an interference experiment,” Nature 642, 922 (2025).
- B. Ghosh et al., “Anyonic braiding in a chiral Mach–Zehnder interferometer,” Nat. Phys. 21, 1392 (2025).