Probing Non-Abelian Statistics with QuasiParticle Interferometry
arXiv:cond-mat/0601242 · doi:10.1103/PhysRevLett.97.016401
Abstract
We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to FQH interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed nu=12/5 plateau.
5 pages, 1 figure; v2: references added, orientation convention of the modular S-matrix changed, clarification regarding particle-hole transformation added; v3: references updated, clarifying changes made to conform to the version published in PRL
References in corpus (2)
Cited by in corpus (82)
- Non-Abelian Anyons and Topological Quantum Computation
- Symmetry Fractionalization, Defects, and Gauging of Topological Phases
- Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
- Anyons and the quantum Hall effect - a pedagogical review
- Condensate induced transitions between topologically ordered phases
- Theory of the Fabry-Perot Quantum Hall Interferometer
- Fractional Quantum Hall Hierarchy and the Second Landau Level
- Universal entanglement entropy in 2D conformal quantum critical points
- Introduction to topological quantum computation with non-Abelian anyons
- Interferometry of non-Abelian Anyons
- The non-Abelian Interferometer
- Fractional charge and fractional statistics in the quantum Hall effects
- Topological Quantum Compiling
- Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
- Measurement-Only Topological Quantum Computation via Anyonic Interferometry
- Why should anyone care about computing with anyons?
- Realization of Fractional Chern Insulators in the Thin-Torus-Limit with Ultracold Bosons
- Scrambling without chaos in RCFT
- Methods for simulating string-net states and anyons on a digital quantum computer
- Braiding non-Abelian quasiholes in fractional quantum Hall states
- Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state
- Wavefunctions for topological quantum registers
- Robust Electron Pairing in the Integer Quantum Hall Effect Regime
- Quantum transport in electron Fabry-Perot interferometers
- Splitting the Topological Degeneracy of non-Abelian Anyons
- Topological growing of Laughlin states in synthetic gauge fields
- Fibonacci Topological Superconductor
- Coulomb blockade as a probe for non-Abelian statistics in Read-Rezayi states
- Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids
- Competing Topological Orders in the nu=12/5 Quantum Hall State
- Interference, Coulomb blockade, and the identification of non-abelian quantum Hall states
- Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator
- Experimentally Probing Topological Order and Its Breakdown via Modular Matrices
- Experimental signatures of non-Abelian statistics in clustered quantum Hall states
- Towards a universal set of topologically protected gates for quantum computation with Pfaffian qubits
- Quasiparticles and excitons for the Pfaffian quantum Hall state
- Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
- Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
- Fermion Condensation and Gapped Domain Walls in Topological Orders
- The sixteenfold way and the quantum Hall effect at half-integer filling factors
- Coulomb Blockade Doppelgangers in Quantum Hall States
- Multi-channel Kondo Models in non-Abelian Quantum Hall Droplets
- Identifying Non-Abelian Topological Order through Minimal Entangled States
- Validity of the Lowest Landau Level Approximation for Rotating Bose Gases
- Probing the neutral edge modes in transport across a point contact via thermal effects in the Read-Rezayi non-abelian quantum Hall states
- Decoherence of Anyonic Charge in Interferometry Measurements
- Probing Non-Abelian Statistics in nu=12/5 Quantum Hall State
- Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
- Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding
- "Wormhole" geometry for entrapping topologically-protected qubits in non-Abelian quantum Hall states and probing them with voltage and noise measurements
- Clebsch-Gordan and 6j-coefficients for rank two quantum groups
- Majorana-Josephson Interferometer
- Interplay of fractional quantum Hall states and localization in quantum point contacts
- Thermal anyon interferometry in phonon-coupled Kitaev spin liquids
- Quasiparticle tunneling in the Moore-Read fractional quantum Hall State
- Gapped boundaries of (3+1)d topological orders
- Cyclic Depopulation of Edge States in a large Quantum Dot
- Engineering topological states and quantum-inspired information processing using classical circuits
- Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene
- Chirality and Current-Current Correlation in Fractional Quantum Hall Systems
- Braid Matrices and Quantum Gates for Ising Anyons Topological Quantum Computation
- Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots
- Microwave Absorption by a Mesoscopic Quantum Hall Droplet
- Measuring Topological Order
- Double Point Contact in the k=3 Read-Rezayi State
- Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect
- Tunnelling current through fractional quantum Hall interferometers
- Edge-Induced Qubit Polarization in Systems with Ising Anyons
- Correlations, Dynamics, and Interferometry of Anyons in the Lowest Landau Level
- Identification of the Fractional quantum Hall edge modes by density oscillations
- Neutral excitation and bulk gap of the Fractional Quantum Hall liquids in disk geometry
- Parafermions in Moiré Minibands
- Stepped Graphene-based Aharonov-Bohm Interferometers
- Tunneling current and current correlations for anyonic quasiparticles of ν = 1/2 chiral Luttinger liquid in multi-edge geometries
- Field Theoretic Aspects of Condensed Matter Physics: An Overview
- Tunneling between helical Majorana modes and helical Luttinger liquids
- Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
- Twisted Interferometry
- Twisted Interferometry: the topological perspective
- Non-Abelian anyonic interferometry with a multi-photon spin lattice simulator
- Exact modular matrix for the parafermion quantum Hall islands and measurement of non-Abelian anyons
- Extracting the scaling dimension of quantum Hall quasiparticles from current correlations