Extended Data Fig. 8: Band structure measurements with different strengths of non-Abelian scalar potentials.
From: Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions
(a) Theoretical band energies along the sampling line ky = 3kx (mod 2π), calculated by diagonalizing the lattice Hamiltonian. (b), (c) Simulated and measured results of time-dependent transmission spectra of the system. In (b) and (c), we plot the quantity \(\mathop{\xi }\limits^{\approx }(\delta \omega ,t)=\frac{1}{3}[\widetilde{\xi }(\delta \omega ,t)+\widetilde{\xi }(\delta \omega +{\varOmega }_{{\rm{R}}}/3,t)+\widetilde{\xi }(\delta \omega +2{\varOmega }_{{\rm{R}}}/3,t)]\). In the simulation, we use the interleaving modulation scheme, take the modulation strength g = 0.14 ΩR and round trip power loss in the resonator as 0.87 dB. In both the simulation and experiment, the input state is fixed to be left circularly polarized, and the color scale is normalized to [0, 1] for each individual subplot. The time origin in (c) is chosen such that the comparison with (a) and (b) is transparent.
