Braiding photonic topological zero modes

Abstract

A remarkable property of quantum mechanics in two-dimensional (2D) space is its ability to support "anyons," particles that are neither fermions nor bosons. Theory predicts that these exotic excitations can be realized as bound states confined near topological defects, like Majorana zero modes trapped in vortices in topological superconductors. Intriguingly, in the simplest cases the nontrivial phase that arises when such defects are "braided" around one another is not intrinsically quantum mechanical; rather, it can be viewed as a manifestation of the geometric (Pancharatnam-Berry) phase in wave mechanics, enabling the simulation of such phenomena in classical systems. Here we report the first experimental measurement in any system, quantum or classical, of the geometric phase due to such a braiding process. These measurements are obtained using an interferometer constructed from highly tunable 2D arrays of photonic waveguides. Our results introduce photonic lattices as a versatile playground for the experimental study of topological defects and their braiding, complementing ongoing efforts in solid-state systems and cold atomic gases.

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Photonics
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Electron fractionalization in two-dimensional graphenelike structures
• Fractional statistics in anyon collisions
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Synthesis and Observation of Non-Abelian Gauge Fields in Real Space
• Aharonov-Bohm interference of fractional quantum Hall edge modes
• Photonic Realization of a Transition Between Topological Phases Residing in the Weak and Strong Floquet Driving Regimes
• The Quantum Hall Effect with Wilczek's charged magnetic flux tubes instead of electrons
• Synthetic anyons in noninteracting systems

Cited by in corpus (22)

• Classical higher-order topological insulators
• Non-Abelian braiding on photonic chips
• Observation of degenerate zero-energy topological states at disclinations in an acoustic lattice
• Vortex states in an acoustic Weyl crystal with a topological lattice defect
• On-chip beam rotators, adiabatic mode converters, and waveplates through low-loss waveguides with variable cross-sections
• Dirac-vortex topological photonic crystal fibre
• Nanomechanical topological insulators with an auxiliary orbital degree of freedom
• Room-temperature continuous-wave Dirac-vortex topological lasers on silicon
• Topological photonics: fundamental concepts, recent developments, and future directions
• Non-Abelian effects in dissipative photonic topological lattices
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Topological contextuality and anyonic statistics of photonic-encoded parafermions
• Electric circuit emulation of topological transitions driven by quantum statistics
• Monopole topological resonators
• A topological Dirac-vortex parametric phonon laser
• Properties of 2D anyon gas
• Symmetry-protected non-Abelian geometric phases in optical waveguides with nonorthogonal modes
• Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios
• Experimental measurement of the geometric phase of non-geodesic circles
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Topological photonic crystal fibre
• An exactly solvable model for anyons with non-Abelian flux