Optimal design strategy for non-Abelian geometric phases using Abelian gauge fields based on quantum metric

Abstract

Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized, non-Abelian geometric phases can be realized using electromagnetic waves travelling through coupled photonic waveguide structures. The waveguides implement an effective Hamiltonian possessing a degenerate dark subspace, in which an adiabatic evolution can occur. The associated quantum metric induces the notion of a geodesic that defines the optimal adiabatic evolution. We exemplify the non-Abelian evolution of an Abelian gauge field by a Wilson loop.

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• Highly-Degenerate Photonic Waveguide Structures for Holonomic Computation
• Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing
• Protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a quantum-dot loop
• Symmetry-protected non-Abelian geometric phases in optical waveguides with nonorthogonal modes
• Deterministic photonic entanglement arising from non-Abelian quantum holonomy
• Optical lattice with spin-dependent sub-wavelength barriers
• An exactly solvable model for anyons with non-Abelian flux
• Particle-Number Threshold for Non-Abelian Geometric Phases
• Generation of Half-Integer Harmonics and Efficient THz-to-Visible Frequency Conversion in Strained Graphene