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.
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.
We consider hierarchical quantum Hall edge states with
N modes and a spatially local quantum point contact (QPC). In general, the field of an injected anyon does not directly acquire the universal statistical phase
θ. Short-range inter-edge interactions split the universal anyon charge and phase into
N fractionalized charges associated with nonuniversal phases
πδm. In contrast, their sum
δ=∑m=1Nδm, which defines the local scaling dimension at the QPC, remains protected and is tied to the statistical angle through
πδ=θ. If the injected anyon is of the same species as the one dominating backscattering at the QPC, time-domain braiding with phase
θ is recovered either in the absence of inter-edge interactions with equal mode velocities, or by performing a spatially local anyon injection at the QPC. We then exploit a more robust \emph{local} anyonic time-exchange (ATE) link between anyons and quasiholes at the QPC, which is also a necessary ingredient for realizing such braiding. This allows us to propose minimal single-QPC protocols that do not rely on diluted anyon sources and that disentangle the role of
θ as a genuine statistical phase from that as a scaling dimension. From the ATE link we derive two novel nonequilibrium fluctuation--dissipation relations (FDRs) that isolate
θ. They relate the DC backscattering noise either to an integral over the DC current or to the phase shift of the AC current with respect to an applied AC voltage (i.e., the phase of the admittance), accessible down to low frequencies. For thermalized edges, we show that in the quantum regime this admittance phase directly yields
θ whenever
δ>1/2.
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.
We develop a stochastic framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity. Starting from the Stratonovich stochastic Liouville equation, we perform the Stratonovich-Itô conversion to obtain a Lindblad master equation that ties the dissipator directly to the distorted anyon algebra. This construction produces a statistics-dependent dephasing channel, with rates determined by the eigenstructure of the real-symmetric correlation matrix Ξ. The eigenvectors of Ξ select which collective exchange currents-equivalently, which irreducible representations of the system-are protected from stochastic dephasing, providing a natural mechanism for decoherence-free subspaces and noise-induced exceptional points. The key result of our analysis is the universality of the optimal statistical angle: in the minimal two-site model with balanced gain and loss, the protected mode always minimizes its dephasing at θ⋆=π/2, independent of the specific form of Ξ. This robustness highlights a simple design rule for optimizing coherence in noisy anyonic systems, with direct implications for ultracold atomic realizations and other emerging platforms for fractional statistics.
We develop a stochastic framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity. Starting from the Stratonovich stochastic Liouville equation, we perform the Stratonovich--Itô conversion to obtain a Lindblad master equation that ties the dissipator directly to the distorted anyon algebra. This construction produces a statistics--dependent dephasing channel, with rates determined by the eigenstructure of the real symmetric correlation matrix
Dab. The eigenvectors of
D select which collective exchange currents -- equivalently, which irreducible representations of the system -- are protected from stochastic dephasing, providing a natural mechanism for decoherence-free subspaces and noise-induced exceptional points. The key result of our analysis is the universality of the optimal statistical angle: in the minimal two-site model with balanced gain and loss, the protected mode always minimizes its dephasing at
θ⋆=π/2, independent of the specific form of
D. This robustness highlights a simple design rule for optimizing coherence in noisy anyonic systems, with direct implications for ultracold atomic realizations and other emerging platforms for fractional statistics.
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.