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arXiv:2312.04475 · Physical Review Letters

Effect of the Soliton Width on Nonequilibrium Exchange Phases of Anyons

Matthias Thamm, Bernd Rosenow

Published Apr 10, 2024• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.132.156501

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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.
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.
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θ. θ = 0, π correspond to bosons and fermions, respectively; at intermediate values, we say that we have fractional statistics. In two dimensions, θ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve nonabelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of nonabelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern–Simons terms. The crossings of one-dimensional anyons on a ring are unidirectional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently, the anyon behavior predicted for quasiparticles in the ν = 1/3 fractional quantum Hall state has been observed in both scattering and interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θθθ. θ=0,πθ= 0, πθ=0,π correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, θθθ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of non-abelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern--Simons terms. The crossings of one-dimensional anyons on a ring are uni-directional, such that a fractional phase θθθ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently the anyon behavior predicted for quasiparticles in the ν=1/3ν= 1/3ν=1/3 fractional quantum Hall state has been observed both in scattering and in interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.
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.
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.
Anyons are low-dimensional quasiparticles that obey fractional statistics, hence interpolating between bosons and fermions. In two dimensions, they exist as elementary excitations of fractional quantum Hall states and they are believed to enable topological quantum computing. One-dimensional (1D) anyons have been theoretically proposed, but their experimental realization has proven to be difficult. Here, we observe anyonic correlations, which emerge through the phenomenon of spin-charge separation, in a 1D strongly-interacting quantum gas. The required spin degree of freedom is provided by a mobile impurity, whose effective anyonic correlations are associated with an experimentally tunable statistical angle. These anyonic correlations are measured by monitoring the impurity momentum distribution, whose asymmetric feature demonstrates the transmutation of bosons via anyons to fermions. Going beyond equilibrium conditions, we study the dynamical properties of the anyonic correlations via dynamical fermionization of the anyons. Our work opens up the door to the exploration of non-equilibrium anyonic phenomena in a highly controllable setting.