Hanbury Brown-Twiss interference of anyons

Landscapes of an Out-of-Equilibrium Anyonic Sea

The low-energy dynamics of two-dimensional topological matter hinges on its one-dimensional edge modes. Tunneling between fractional quantum Hall edge modes facilitates the study of anyonic statistics: it induces time-domain braiding that dominates signals from diluted anyon beams. We develop a framework for characterizing one-dimensional out-of-equilibrium anyonic states and define their effective potential and temperature, both arising from anyonic braiding, as well as the landscape of their excitations. Unlike fermions, the effective anyon potential depends on the type of the tunneling quasiparticles; nonequilibrium anyonic states are underlain by power-law energy distributions. This allows "hot" anyons to tunnel above the chemical potential of the source, which we capture by a measurable universal witness function. Our analysis raises the prospect of generalizing the kinetic approach to compressible anyonic matter in higher dimensions.

Finite Width of Anyons Changes Their Braiding Signature

Anyons are particles intermediate between fermions and bosons, characterized by a nontrivial exchange phase, yielding remarkable braiding statistics. Recent experiments have shown that anyonic braiding has observable consequences on edge transport in the fractional quantum Hall effect (FQHE). Here, we study transport signatures of anyonic braiding when the anyons have a finite width. We show that the width of the anyons, even when extremely small, can have a tremendous impact on transport properties and braiding signatures. In particular, we find that taking the finite width into account allows us to explain recent experimental results on the FQHE at filling factor 2/5 [M. Ruelle et al., Phys. Rev. X 13, 011031 (2023)PRXHAE2160-330810.1103/PhysRevX.13.011031]. Our work shows that the finite width of anyons crucially influences setups involving anyonic braiding, especially when the exchange phase is larger than π/2.

Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer

Despite its ubiquity in quantum computation and quantum information, a universally applicable definition of quantum entanglement remains elusive. The challenge is further accentuated when entanglement is associated with other key themes, e.g., quantum interference and quantum statistics. Here, we introduce two novel motifs that characterize the interplay of entanglement and quantum statistics: an 'entanglement pointer' and a 'statistics-induced entanglement entropy'. The two provide a quantitative description of the statistics-induced entanglement: (i) they are finite only in the presence of quantum entanglement underlined by quantum statistics and (ii) their explicit form depends on the quantum statistics of the particles (e.g., fermions, bosons, and anyons). We have experimentally implemented these ideas by employing an electronic Hong-Ou-Mandel interferometer fed by two highly diluted electron beams in an integer quantum Hall platform. Performing measurements of auto-correlation and cross-correlation of current fluctuations of the scattered beams (following 'collisions'), we quantify the statistics-induced entanglement by experimentally accessing the entanglement pointer and the statistics-induced entanglement entropy. Our theoretical and experimental approaches pave the way to study entanglement in various correlated platforms, e.g., those involving anyonic Abelian and non-Abelian states.

Effect of the Soliton Width on Nonequilibrium Exchange Phases of Anyons

Unlike bosons and fermions, quasiparticles in two-dimensional quantum systems, known as anyons, exhibit statistical exchange phases that range between 0 and π. In fractional quantum Hall states, these anyons, possessing a fraction of the electron charge, traverse along chiral edge channels. This movement facilitates the creation of anyon colliders, where coupling different edge channels through a quantum point contact enables the observation of two-particle interference effects. Such configurations are instrumental in deducing the anyonic exchange phase via current cross-correlations. Prior theoretical models represented dilute anyon beams as discrete steps in the boson fields. However, our study reveals that incorporating the finite width of the soliton shape is crucial for accurately interpreting recent experiments, especially for collider experiments involving anyons with exchange phases θ>π/2, where prior theories fall short.

Signatures of Fractional Statistics in Nonlinear Pump-Probe Spectroscopy

We show that the presence of anyons in the excitation spectrum of a two-dimensional system can be inferred from nonlinear spectroscopic quantities. In particular, we consider pump-probe spectroscopy, where a sample is irradiated by two light pulses with an adjustable time delay between them. The relevant response coefficient exhibits a universal form that originates from the statistical phase acquired when anyons created by the first pulse braid around those created by the second. This behavior is shown to be qualitatively unchanged by nonuniversal physics including nonstatistical interactions and small nonzero temperatures. In magnetic systems, the signal of interest can be measured using currently available terahertz-domain probes, highlighting the potential usefulness of nonlinear spectroscopic techniques in the search for quantum spin liquids.

Anyon Statistics through Conductance Measurements of Time-Domain Interferometry

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.

Quasiparticle Andreev scattering in the ν = 1/3 fractional quantum Hall regime

The scattering of exotic quasiparticles may follow different rules than electrons. In the fractional quantum Hall regime, a quantum point contact (QPC) provides a source of quasiparticles with field effect selectable charges and statistics, which can be scattered on an 'analyzer' QPC to investigate these rules. Remarkably, for incident quasiparticles dissimilar to those naturally transmitted across the analyzer, electrical conduction conserves neither the nature nor the number of the quasiparticles. In contrast with standard elastic scattering, theory predicts the emergence of a mechanism akin to the Andreev reflection at a normal-superconductor interface. Here, we observe the predicted Andreev-like reflection of an e/3 quasiparticle into a - 2e/3 hole accompanied by the transmission of an e quasielectron. Combining shot noise and cross-correlation measurements, we independently determine the charge of the different particles and ascertain the coincidence of quasielectron and fractional hole. The present work advances our understanding on the unconventional behavior of fractional quasiparticles, with implications toward the generation of novel quasi-particles/holes and non-local entanglements.

Boltzmann Configurational Entropy Revisited in the Framework of Generalized Statistical Mechanics

As known, a method to introduce non-conventional statistics may be realized by modifying the number of possible combinations to put particles in a collection of single-particle states. In this paper, we assume that the weight factor of the possible configurations of a system of interacting particles can be obtained by generalizing opportunely the combinatorics, according to a certain analytical function f{π}(n) of the actual number of particles present in every energy level. Following this approach, the configurational Boltzmann entropy is revisited in a very general manner starting from a continuous deformation of the multinomial coefficients depending on a set of deformation parameters {π}. It is shown that, when f{π}(n) is related to the solutions of a simple linear difference–differential equation, the emerging entropy is a scaled version, in the occupational number representation, of the entropy of degree (κ,r) known, in the framework of the information theory, as Sharma–Taneja–Mittal entropic form.

Fractional charge and fractional statistics in the quantum Hall effects

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.

Negative Delta-T Noise in the Fractional Quantum Hall Effect

We study the current correlations of fractional quantum Hall edges at the output of a quantum point contact subjected to a temperature gradient. This out-of-equilibrium situation gives rise to a form of temperature-activated shot noise, dubbed delta-T noise. We show that the tunneling of Laughlin quasiparticles leads to a negative delta-T noise, in stark contrast with electron tunneling. Moreover, varying the transmission of the quantum point contact or applying a voltage bias across the Hall bar may flip the sign of this noise contribution, yielding signatures that can be accessed experimentally.

Fusion Channels of Non-Abelian Anyons from Angular-Momentum and Density-Profile Measurements

We present a method to characterize non-Abelian anyons that is based only on static measurements and that does not rely on any form of interference. For geometries where the anyonic statistics can be revealed by rigid rotations of the anyons, we link this property to the angular momentum of the initial state. We test our method on the paradigmatic example of the Moore-Read state that is known to support excitations with non-Abelian statistics of Ising type. As an example, we reveal the presence of different fusion channels for two such excitations, a defining feature of non-Abelian anyons. This is obtained by measuring density-profile properties, like the mean square radius of the system or the depletion generated by the anyons. Our study paves the way to novel methods for characterizing non-Abelian anyons, both in the experimental and theoretical domains.

Classical Model of Quons

By using the kinetic interaction principle, the quons statistics in the framework of kinetic theory is introduced. This is done by properly generalizing the inclusion/exclusion principle of standard boson and fermion statistics within a nonlinear classical model. The related nonlinear Fokker-Planck equation is introduced and the corresponding steady distribution describing quons statistics of type I and type II is derived.

Negative Excess Shot Noise by Anyon Braiding

Anyonic fractional charges e^{*} have been detected by autocorrelation shot noise at a quantum point contact (QPC) between two fractional quantum Hall edges. We find that the autocorrelation noise can also show a fingerprint of Abelian anyonic fractional statistics. We predict the noise of the electrical tunneling current I at the QPC of the fractional-charge detection setup, when anyons are dilutely injected, from an additional edge biased by a voltage, to the setup in equilibrium. At large voltages, the nonequilibrium noise is reduced below the thermal equilibrium noise by the value 2e^{*}I. This negative excess noise is opposite to the positive excess noise 2e^{*}I of the conventional fractional-charge detection and also to the usual positive autocorrelation noises of electrical currents. This is a signature of Abelian fractional statistics, resulting from the effective braiding of an anyon thermally excited at the QPC around another anyon injected from the additional edge.

Melting of Interference in the Fractional Quantum Hall Effect: Appearance of Neutral Modes

We attempted to measure interference of the outer edge mode in the fractional quantum hall regime with an electronic Mach-zehnder interferometer. The visibility of the interferometer wore off as we approached ν_{B}=1 and the transmission of the quantum point contacts (QPCs) of the interferometer simultaneously developed a v=1/3 conductance plateau accompanied by shot noise. The appearance of shot noise on this plateau indicates the appearance of nontopological neutral modes resulting from edge reconstruction. We have confirmed the presence of upstream neutral modes measuring upstream noise emanating from the QPC. The lack of interference throughout the lowest Landau level was correlated with a proliferation of neutral modes.

Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics

We propose a standard time-of-flight experiment as a method for observing the anyonic statistics of quasiholes in a fractional quantum Hall state of ultracold atoms. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. Our proposed method is validated by Monte Carlo calculations for ν=1/2 and 1/3 fractional quantum Hall liquids containing a realistic number of particles. Extensions to quantum Hall liquids of light and to non-Abelian anyons are briefly discussed.

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

Numerical results suggest that the quantum Hall effect at ν=5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau-level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau-level mixing are strong. We show that the recent proposal of a particle-hole (PH)-Pfaffian topological order by Son is consistent with all experiments. The absence of particle-hole symmetry at ν=5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.

Current Correlations from a Mesoscopic Anyon Collider

Fermions and bosons are fundamental realizations of exchange statistics, which governs the probability for two particles being close to each other spatially. Anyons in the fractional quantum Hall effect are an example for exchange statistics intermediate between bosons and fermions. We analyze a mesoscopic setup in which two dilute beams of anyons collide with each other, and relate the correlations of current fluctuations to the probability of particles excluding each other spatially. While current correlations for fermions vanish, negative correlations for anyons are a clear signature of a reduced spatial exclusion as compared to fermions.

Topological vacuum bubbles by anyon braiding

According to a basic rule of fermionic and bosonic many-body physics, known as the linked cluster theorem, physical observables are not affected by vacuum bubbles, which represent virtual particles created from vacuum and self-annihilating without interacting with real particles. Here we show that this conventional knowledge must be revised for anyons, quasiparticles that obey fractional exchange statistics intermediate between fermions and bosons. We find that a certain class of vacuum bubbles of Abelian anyons does affect physical observables. They represent virtually excited anyons that wind around real anyonic excitations. These topological bubbles result in a temperature-dependent phase shift of Fabry-Perot interference patterns in the fractional quantum Hall regime accessible in current experiments, thus providing a tool for direct and unambiguous observation of elusive fractional statistics.

Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene

The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.