Non-Abelian Electric Field and Zitterbewegung on a Photonic Frequency Chain

Abstract: The synthetic frequency dimension, which realizes fictitious spatial dimensions from the spectral degree of freedom, has emerged as a promising platform for engineering artificial gauge fields in studying quantum simulations and topological physics with photons. A current central task for frequency-domain photons is the creation and manipulation of nontrivial non-Abelian field strength tensors and observing their governing dynamics. Here, we experimentally demonstrate a miniaturized scheme for creating non-Abelian electric fields in a photonic frequency chain using a polarization-multiplexed, time-modulated ring resonator. By engineering spin-orbit coupling via modulation dephasing, polarization rotation, and polarization retardation, we achieve programmable control over synthetic Floquet bands and their quasimomentum spin-resolved textures. Leveraging self-heterodyne coherent detection, we demonstrate Zitterbewegung -- a trembling motion of photons -- induced by non-Abelian electric fields on the frequency chain. We further observe the interference between Zitterbewegung and Bloch oscillations arising from the coexistence of non-Abelian and Abelian electric fields. Our work bridges synthetic dimensions with non-Abelian gauge theory for versatile photonic emulation of relativistic quantum mechanics and spinor dynamics, and can be instrumental in applications like frequency-domain optical computation and multimodal frequency comb control.