Fig. 3: Temporal AB interference and Wilson loop calculation in a 2D gauge field.
a Schematic of two paths for a particle moving from point A to point B under a gauge field \({{{\bf{{{{\mathcal{A}}}}}}}}\). b, c Evolutions of the state vector of a particle following the two paths under a non-Abelian gauge field in the Bloch sphere. The red (yellow) arrow denotes the initial state (final state). d Plot of the logarithm of S versus parameters of the applied gauge field ϕ and θ, which shows whether the corresponding gauge field is Abelian (blue lines at θ = 0, ±π or ϕ = 0, ±π) or non-Abelian. e Theoretical calculation and g numerical calculation results of the intensity contrast ρ between the two degenerate states after the interference versus initial intensity distribution α and phase difference β under the non-Abelian interference. f, h Theoretical calculation and numerical calculation results of ρ under the Abelian interference. i Theoretical calculation and j numerical simulation results of the Wilson loop ∣WCW∣, where ∣WCW∣ ≠ 2 is a necessary but insufficient condition for a non-Abelian gauge field. Black dash lines indicate the genuine non-Abelian cases.
