Detecting fractional statistics in anyon interferometry employing thermal excitation

Cheolhee Han, June-Young M. Lee, H.-S. Sim

On the edge of certain fractional quantum Hall states, e.g., at 2/3 and 5/2 filling, a local fractional excitation, occurring by anyon tunneling at a quantum point contact, is further fractionalized into counterpropagating charge and neutral (Abelian or non-Abelian) anyonic excitations. We propose a scheme to detect the braiding statistics of the charge and neutral anyons separately. It is the injection of a dilute beam of a target (charge or neutral) anyon to a Fabry-Perot interferometer. The monodromy of the target anyon is obtained by comparing the amplitude and phase of the interference current with a reference signal of the same setup but without the injection. Our proposal relies on braiding between anyons on the edge, and applies even in the presence of bulk-edge couplings.

Dima E. Feldman

Parsa Bonderson, Kirill Shtengel, Johannes K. Slingerland

Sushanth Varada, Christian Spånslätt, Matteo Acciai

Two-particle interferometry is an important tool for extracting the exchange statistics of quantum particles. We theoretically investigate the prospects of such interferometry to probe the statistics of pointlike anyonic excitations injected in a Hong-Ou-Mandel (HOM) setup based on a quantum point contact device in the fractional quantum Hall regime. We compute the standard HOM ratio, i.e., the ratio of tunneling noises for two- and one-particle injections, and find that for pointlike anyons it only depends on the temperature and the anyon scaling dimension. Importantly, the latter is not necessarily related to the exchange phase. In fact, we establish that the HOM ratio does not reveal the exchange phase of the injected anyons: For injection-time delays that are small compared to the thermal timescale, we find that the exchange phase accumulated due to time-domain braiding between injected and thermally activated anyons is erased due to two mutually canceling subprocesses. In contrast, for time delays large compared to the thermal time, only a single subprocess contributes to the braiding, but the accumulated phase is canceled in the HOM ratio. These findings suggest caution when interpreting HOM interferometry experiments with anyons, and approaches beyond the standard HOM ratio are thus necessary to extract anyonic statistics with two-particle interferometry experiments.

Zezhu Wei, V. F. Mitrović, Dima E. Feldman

Aharonov-Bohm interferometry is the most direct probe of anyonic statistics in the quantum Hall effect. The technique involves oscillations of the electric current as a function of the magnetic field and is not applicable to Kitaev spin liquids and other systems without charged quasiparticles. Here, we establish a novel protocol, involving heat transport, for revealing fractional statistics even in the absence of charged excitations, as is the case in quantum spin liquids. Specifically, we demonstrate that heat transport in Kitaev spin liquids through two distinct interferometer's geometries, Fabry-Perot and Mach-Zehnder, exhibit drastically different behaviors. Therefore, we propose the use of heat transport interferometry as a probe of anyonic statistics in charge insulators.

Chihong Chou