Two anyons encircling each other acquire a quantized braiding phase that is independent of their spatial separation. We show that detecting this phase in a fractional quantum Hall interference experiment results in a quantum Zeno effect: a localized anyon is trapped by constant observation from a stream of anyons supplied by the measurement current. Interferometers with an embedded antidot are ideal for accessing the Zeno regime, where the bare tunneling rate of localized anyons is much lower than the measurement rate. The Zeno-suppressed tunneling rate of the trapped anyon depends on the braiding phase and the transmission of the quantum point contacts. Our primary prediction is that the autocorrelation time of the conductance through the interferometer increases with the bias current. This effect may be used to experimentally control the anyon dynamics, in particular to increase the lifetime of localized anyons.
Two anyons encircling each other acquire a quantized braiding phase that is independent of their spatial separation. We show that detecting this phase in a fractional quantum Hall interference experiment results in a quantum Zeno effect: a localized anyon is trapped by constant observation from a stream of anyons supplied by the measurement current. Interferometers with an embedded antidot are ideal for accessing the Zeno regime, where the bare tunneling rate of localized anyons is much lower than the measurement rate. The Zeno-suppressed tunneling rate of the trapped anyon depends on the braiding phase and the transmission of the quantum point contacts. Our primary prediction is that the autocorrelation time of the conductance through the interferometer increases with the bias current. This effect may be used to experimentally control the anyon dynamics, in particular to increase the lifetime of localized anyons.
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.
We propose a method to extract the mutual exchange statistics of the anyonic excitations of a general Abelian fractional quantum Hall state, by comparing the tunneling characteristics of a quantum point contact in two different experimental conditions. In the first, the tunneling current between two edges at different chemical potentials is measured. In the second, one of these edges is strongly diluted by an earlier point contact. We describe the case of the dilute beam in terms of a time-domain interferometer between the anyons flowing along the edge and quasiparticle-quasihole excitations created at the tunneling quantum point contact. In both cases, temperature is kept large, such that the measured current is given to linear response. Remarkably, our proposal does not require the measurement of current correlations, and allows us to carefully separate effects of the fractional charge and statistics from effects of intra- and interedge interactions.
The role of anyonic statistics stands as a cornerstone in the landscape of topological quantum techniques. While recent years have brought forth encouraging and persuasive strides in detecting anyons, a significant facet remains unexplored, especially in view of connecting anyonic physics to quantum information platforms-whether and how entanglement can be generated by anyonic braiding. Here, we demonstrate that even when two anyonic subsystems (represented by anyonic beams) are connected only by electron tunneling, entanglement between them, manifesting fractional statistics, is generated. To demonstrate this physics, we rely on a platform where fractional quantum Hall edges are bridged by a quantum point contact that allows only transmission of fermions (so-called Andreev-like tunneling). This invokes the physics of two-beam collisions in an anyonic Hong-Ou-Mandel collider, accompanied by a process that we dub anyon-quasihole braiding. We define an entanglement pointer-a current-noise-based function tailored to quantify entanglement associated with quasiparticle fractional statistics. Our work, which exposes, both in theory and in experiment, entanglement associated with anyonic statistics and braiding, prospectively paves the way to the exploration of entanglement induced by non-Abelian statistics.
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.
Recent anyon-collider experiments have identified time-domain braiding (TDB) as a new route to probing anyonic statistics. However, how such time-domain interference responds to environmental noise remains an open question. Here we show that TDB interference is intrinsically more robust than its spatial counterpart. In conventional spatial interference, environmental noise induces phase fluctuations that accumulate throughout all paths, leading to exponential suppression of the interference as the dephasing rate increases. In TDB, by contrast, the interfering temporal paths experience largely overlapping environmental fluctuations, whose contributions cancel out in the relative phase, so that only a small nonoverlapping temporal window contributes to dephasing. As a result, TDB interference decays only algebraically with the dephasing rate, providing a new experimental hallmark for its identification. We propose a Fabry-Perot fractional quantum Hall setup in which both types of interference coexist and experience the same environmental noise, enabling a direct comparison of their dephasing behaviors. Our results establish robustness against dephasing as a fundamental advantage of TDB and suggest new opportunities for exploiting anyonic interference in noisy mesoscopic systems.
Anyonic interferometry is a direct probe of fractional statistics. We propose an interferometry geometry that parallels an optical Mach-Zehnder interferometer and offers several advantages over existing interferometry schemes. In contrast to the currently studied electronic Mach-Zehnder interferometer, our setup has no drain inside the device so that the trapped topological charge is time-independent. In contrast to electronic Fabry-Pérot interferometry, anyons cannot go around the device more than once. Thus, the interference signal has a straightforward interpretation in terms of anyonic statistical phases. The proposed geometry suppresses the undesirable effects of bulk-edge coupling. Moreover, the setup allows for simple exact solutions for the electric current and noise for an arbitrary quasiparticle tunneling strength in a broad range of conditions. The structure of the solutions is similar to that for non-interacting electrons but reflects fractional charge and statistics. We present results for electric current and noise in Jain states and address thermal interferometry at zero voltage bias.