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.
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.
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.
Determination of the anyonic statistical braiding phase has relied on either Aharonov-Bohm inter- ference experiments or cross-correlations measured in collider platforms. Here we consider collider setups, supporting stationary far-from-equilibrium anyonic beams, characterized by an effective chemical potential and an effective temperature, which carry universal information about the ele- mentary charge and the statistical braiding phase. We develop an out-of-equilibrium linear response theory designed to describe charge and thermal quantum transport under deviations from this ef- fective equilibrium (unlike linear response designed to describe transport near genuine equilibrium). Our effective linear-response transport coefficients directly reflect the fractional charge and statistics of the anyons involved, avoiding the need to measure higher-order current correlations. Moreover, the emergence of finite thermoelectric (Peltier and Seebeck) coefficients signifies the presence of real anyon collisions (as opposed to virtual braiding in the time domain), intimately associated with the breaking of a characteristic particle-hole symmetry specific to anyonic gases.
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.
In a Laughlin fractional quantum Hall state, one- and two-quasihole states can be obtained by diagonalizing the many-body Hamiltonian with a trapping potential or, for larger systems, from the linear combination of the edge Jack polynomials. The quasihole states live entirely in the subspace of the lowest-energy branch in the energy spectrum with a fixed number of orbits, or a hard-wall confinement. The reduction in the Hilbert space dimension facilitates the study of time evolution of the quasihole states after, say, the removal of the trapping potential. We explore the quench dynamics under a harmonic external potential, which rotates the quasiholes in the droplet, and discuss the effect of long-range interaction and more realistic confinement. Accurate evaluation of the mutual statistics phase of anyons for a wide range of anyon separation can be achieved from the Berry-phase calculation.
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.
Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm that allows to simulate anyonic tight-binding Hamiltonians on two-dimensional lattices. The algorithm is directly derived from the low energy topological quantum field theory and is suited for general Abelian and non-Abelian anyon models. As concrete examples, we apply the algorithm to study the energy level spacing statistics, which reveals level repulsion for free semions, Fibonacci anyons, and Ising anyons. Additionally, we simulate nonequilibrium quench dynamics, where we observe that the density distribution becomes homogeneous for large times---indicating thermalization.