Synthesis and Observation of Non-Abelian Gauge Fields in Real Space

Abstract

Gauge fields, real or synthetic, are crucial for understanding and manipulation of physical systems. The associated geometric phases can be measured, for example, from the Aharonov--Bohm interference. So far, real-space realizations of gauge fields have been limited to Abelian (commutative) ones. Here we report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov--Bohm effect with classical waves and classical fluxes. Based on optical mode degeneracy, we break time-reversal symmetry in different manners---via temporal modulation and the Faraday effect---to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely-ordered path integrals, demonstrates the non-commutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.

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• Non-Abelian Braiding of Topological Edge Bands
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• Full spacetime inversion generated by electromagnetic Abelian gauge transformations
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• Synthetic non-Abelian Electric Fields and Spin-Orbit Coupling in Photonic Synthetic Dimensions
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• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Anomalous criticality with bounded fluctuations and long-range frustration induced by broken time-reversal symmetry
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• Enhancing optomechanical force sensing utilizing synthetic magnetism
• Protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a quantum-dot loop
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Three-dimensional non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly trios
• Abelian and non-Abelian topological behavior of a neutral spin-1/2 particle in a background magnetic field
• Modulation instability in the nonlinear Schrödinger equation with a synthetic magnetic field: gauge matters
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• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Experimental observation of energy-band Riemann surface
• Non-Abelian Chern band in rhombohedral graphene multilayers
• On the nature of the new group LB1
• Experimental Realization of Non-Abelian Permutations in a Three-State Non-Hermitian System
• Nonreciprocal Coupling Induced Non-Hermitian Entanglement in Optomechanical Systems
• Topological quantum electrodynamics in synthetic non-Abelian gauge fields
• Building intuition for Quantum Algorithms using the Aharonov-Bohm effect
• An exactly solvable model for anyons with non-Abelian flux
• Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory
• Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion