Spin-orbit Rabi oscillations in optically synthesized magnetic fields

Rabi oscillation has been proven to be one of the cornerstones of quantum mechanics, triggering substantial investigations in different disciplines and various important applications both in the classical and quantum regimes. So far, two independent classes of wave states in the Rabi oscillations have been revealed as spin waves and orbital waves, while a Rabi wave state simultaneously merging the spin and orbital angular momentum has remained elusive. Here we report on the experimental and theoretical observation and control of spin-orbit-coupled Rabi oscillations in the higher-order regime of light. We constitute a pseudo spin-1/2 formalism and optically synthesize a magnetization vector through light-crystal interaction. We observe simultaneous oscillations of these ingredients in weak and strong coupling regimes, which are effectively controlled by a beam-dependent synthetic magnetic field. We introduce an electrically tunable platform, allowing fine control of transition between different oscillatory modes, resulting in an emission of orbital-angular-momentum beams with tunable topological structures. Our results constitute a general framework to explore spin-orbit couplings in the higher-order regime, offering routes to manipulating the spin and orbital angular momentum in three and four dimensions. The close analogy with the Pauli equation in quantum mechanics, nonlinear optics, etc., implies that the demonstrated concept can be readily generalized to different disciplines.