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Time domain braiding of anyons revealed through a nonequilibrium fluctuation dissipation theorem

Inès Safi A

Published Dec 12, 2025• 0 citations
OpenAlex

Abstract

We derive a novel fluctuation--dissipation theorem (FDT) valid for nonequilibrium initial states that imprint the braiding of anyons in the time domain. The derivation is carried out within the Unifying Nonequilibrium Perturbative Theory (UNEPT), which applies to both standard reservoir geometries and configurations with one or two quantum point contacts (QPCs) injecting dilute anyonic fluxes. Based on this FDT, we propose complementary methods to determine the time-domain braiding phase. The first method relates the DC backscattering noise to the integral of the current with respect to DC drives, while the second connects the AC current phase shift to the DC noise. The latter provides a particularly robust probe of the statistical angle $θ$, offering an intrinsic calibration and cancelling certain nonuniversal renormalization effects. Specializing to a thermalized Tomonaga--Luttinger liquid (TLL), we further show that in the quantum regime the phase shift enables a direct determination of the scaling dimension $δ$ when $δ> 1/2$. These results define experimentally accessible schemes to extract either $θ$ or $δ$ in minimal single-QPC setups, without relying on interferometry or cross-correlation measurements.

Related papers

Robust protocols to reveal anyonic time-exchange phase

Inès Safi A

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 $πδ_m$. In contrast, their sum $δ=\sum_{m=1}^Nδ_m$, 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 $δ>1/2$.

arXiv:2510.10525•Oct 12, 2025•0 citations

Anyonic time exchange in hierarchical Hall states: emergent Luttinger scaling and cross-correlations at finite temperature

A. Latysev, Inès Safi A

We address hierarchical fractional quantum Hall edges coupled by a spatially local quantum point contact within the Unified Nonequilibrium Perturbative (UNEP) framework. Without assuming a Tomonaga-Luttinger liquid (TLL) tunneling correlator, we impose a local anyonic time-exchange (ATE) constraint with phase $\barθ$, yielding a nonequilibrium fluctuation-dissipation integral equation relating DC tunneling current and noise. For thermal initial states, detailed balance closes this equation for the current. Using the Wiener-Hopf method, we find a unique physical solution of local TLL form, with scaling dimension $δ$ determined by $\barθ=πδ\pmodπ$, emerging from the solution rather than being imposed via a TLL correlator. By contrast, ATE and inversion symmetry alone fix the exchange monodromy but not the full transport dynamics. We then study the "anyon collider" beyond Laughlin states at finite temperatures. Detailed balance is broken and noise becomes super-Poissonian, but the relation between nonequilibrium and equilibrium correlators determines current and noise. The output cross-correlation and balanced generalized Fano factor depend on both $δ$ and statistical phase $θ$, identical to $\barθ$ for co-propagating modes with short-range interactions. A temperature-dependent current scale separates the zero-temperature asymptotic regime from the low-current regime, where the balanced Fano factor saturates to a function of $θ$ and $δ$ distinct from its zero-temperature value. This latter regime is particularly relevant to ``anyon collider'' experiments. These complementary regimes constrain the statistical phase and scaling dimension, subject to the symmetry $δ\mapsto1-δ$ at fixed $θ$. For independent statistical phase and scaling dimension, the thermal crossover can reverse the sign of output cross-correlations.

arXiv:2510.20592•Oct 23, 2025•0 citations

Exchange-phase erasure in anyonic Hong-Ou-Mandel interferometry

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.

arXiv:2503.01678•Physical review. B./Physical review. B•May 28, 2025•3 citations

Fluctuation-dissipation relations for strongly correlated out-of-equilibrium circuits

Inès Safi A

We consider strongly correlated quantum circuits where a dc drive is added on top of an initial out-of-equilibrium (OE) stationary state. Within a perturbative approach, we derive unifying OE fluctuation relations for high-frequency current noise, shown to be completely determined by zero-frequency noise and dc current. We apply them to the fractional quantum Hall effect at arbitrary incompressible filling factors, driven by OE sources, without knowledge of the underlying model. We show that such OE relations provide robust methods for an unambiguous determination of the fractional charge or of key interaction parameters entering in the exploration of anyonic statistics within an anyon collider.

arXiv:2004.08130•Physical review. B./Physical review. B•Jul 16, 2020•21 citations

Observation of Time-Domain Braiding of Non-Abelian Anyons at $ν= 5/2$ State

Tomer Alkalay, Jinhong Park, Minseong Oh +7 more

Unlike elementary particles, which obey either bosonic or fermionic exchange statistics, certain quasiparticles, known as anyons, are predicted to exhibit Abelian or non-Abelian braiding statistics. While braiding Abelian anyons modifies the wavefunction by a 'statistical phase', braiding non-Abelian anyons implements a unitary transformation of the state within a degenerate subspace of states. Experimental evidence of non-Abelian braiding has thus far remained elusive. Here, we report a 'time-domain braiding' signature of non-Abelian anyons in the $ν= 5/2$ fractional quantum Hall state, by extending our previously demonstrated approach with Abelian anyons at $ν= 1/3$. Our approach is based on measurements of the current fluctuations arising from weak partitioning of a highly dilute one-dimensional edge mode. We independently probe the partition noise of the downstream charged mode and also that of the upstream neutral mode. These independent measurements agree with our theoretical predictions for 'time-domain braiding' of the downstream Abelian and the upstream non-Abelian anyons, respectively, in the 'particle-hole Pfaffian' topological order. Together, these results provide evidence for the presence of non-Abelian anyons.

arXiv:2608.12897•Aug 13, 2026•0 citations

Robustness of Anyonic Time-Domain Interference Against Dephasing

Hai-Dong Li, Hao-Xiang Long, Gu Zhang +2 more

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.

arXiv:2610.36686•Oct 27, 2026•0 citations
We derive a novel fluctuation--dissipation theorem (FDT) valid for nonequilibrium initial states that imprint the braiding of anyons in the time domain. The derivation is carried out within the Unifying Nonequilibrium Perturbative Theory (UNEPT), which applies to both standard reservoir geometries and configurations with one or two quantum point contacts (QPCs) injecting dilute anyonic fluxes. Based on this FDT, we propose complementary methods to determine the time-domain braiding phase. The first method relates the DC backscattering noise to the integral of the current with respect to DC drives, while the second connects the AC current phase shift to the DC noise. The latter provides a particularly robust probe of the statistical angle θθθ, offering an intrinsic calibration and cancelling certain nonuniversal renormalization effects. Specializing to a thermalized Tomonaga--Luttinger liquid (TLL), we further show that in the quantum regime the phase shift enables a direct determination of the scaling dimension δδδ when δ>1/2δ> 1/2δ>1/2. These results define experimentally accessible schemes to extract either θθθ or δδδ in minimal single-QPC setups, without relying on interferometry or cross-correlation measurements.
We consider hierarchical quantum Hall edge states with NNN 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 θθθ. Short-range inter-edge interactions split the universal anyon charge and phase into NNN fractionalized charges associated with nonuniversal phases πδmπδ_mπδm​. In contrast, their sum δ=∑m=1Nδmδ=\sum_{m=1}^Nδ_mδ=∑m=1N​δm​, which defines the local scaling dimension at the QPC, remains protected and is tied to the statistical angle through πδ=θπδ=θπδ=θ. If the injected anyon is of the same species as the one dominating backscattering at the QPC, time-domain braiding with phase θθθ 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 θθθ 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 θθθ. 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 θθθ whenever δ>1/2δ>1/2δ>1/2.
We address hierarchical fractional quantum Hall edges coupled by a spatially local quantum point contact within the Unified Nonequilibrium Perturbative (UNEP) framework. Without assuming a Tomonaga-Luttinger liquid (TLL) tunneling correlator, we impose a local anyonic time-exchange (ATE) constraint with phase θˉ\barθθˉ, yielding a nonequilibrium fluctuation-dissipation integral equation relating DC tunneling current and noise. For thermal initial states, detailed balance closes this equation for the current. Using the Wiener-Hopf method, we find a unique physical solution of local TLL form, with scaling dimension δδδ determined by θˉ=πδ(modπ)\barθ=πδ\pmodπθˉ=πδ(modπ), emerging from the solution rather than being imposed via a TLL correlator. By contrast, ATE and inversion symmetry alone fix the exchange monodromy but not the full transport dynamics. We then study the "anyon collider" beyond Laughlin states at finite temperatures. Detailed balance is broken and noise becomes super-Poissonian, but the relation between nonequilibrium and equilibrium correlators determines current and noise. The output cross-correlation and balanced generalized Fano factor depend on both δδδ and statistical phase θθθ, identical to θˉ\barθθˉ for co-propagating modes with short-range interactions. A temperature-dependent current scale separates the zero-temperature asymptotic regime from the low-current regime, where the balanced Fano factor saturates to a function of θθθ and δδδ distinct from its zero-temperature value. This latter regime is particularly relevant to ``anyon collider'' experiments. These complementary regimes constrain the statistical phase and scaling dimension, subject to the symmetry δ↦1−δδ\mapsto1-δδ↦1−δ at fixed θθθ. For independent statistical phase and scaling dimension, the thermal crossover can reverse the sign of output cross-correlations.
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 strongly correlated quantum circuits where a dc drive is added on top of an initial out-of-equilibrium (OE) stationary state. Within a perturbative approach, we derive unifying OE fluctuation relations for high-frequency current noise, shown to be completely determined by zero-frequency noise and dc current. We apply them to the fractional quantum Hall effect at arbitrary incompressible filling factors, driven by OE sources, without knowledge of the underlying model. We show that such OE relations provide robust methods for an unambiguous determination of the fractional charge or of key interaction parameters entering in the exploration of anyonic statistics within an anyon collider.
Observation of Time-Domain Braiding of Non-Abelian Anyons at ν=5/2ν= 5/2ν=5/2 State
Unlike elementary particles, which obey either bosonic or fermionic exchange statistics, certain quasiparticles, known as anyons, are predicted to exhibit Abelian or non-Abelian braiding statistics. While braiding Abelian anyons modifies the wavefunction by a 'statistical phase', braiding non-Abelian anyons implements a unitary transformation of the state within a degenerate subspace of states. Experimental evidence of non-Abelian braiding has thus far remained elusive. Here, we report a 'time-domain braiding' signature of non-Abelian anyons in the ν=5/2ν= 5/2ν=5/2 fractional quantum Hall state, by extending our previously demonstrated approach with Abelian anyons at ν=1/3ν= 1/3ν=1/3. Our approach is based on measurements of the current fluctuations arising from weak partitioning of a highly dilute one-dimensional edge mode. We independently probe the partition noise of the downstream charged mode and also that of the upstream neutral mode. These independent measurements agree with our theoretical predictions for 'time-domain braiding' of the downstream Abelian and the upstream non-Abelian anyons, respectively, in the 'particle-hole Pfaffian' topological order. Together, these results provide evidence for the presence of non-Abelian anyons.
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.