Detuning control of Rabi vortex oscillations in light-matter coupling

We study analytically the dynamics of vortices in strongly coupled exciton-photon fields in the presence of energy detuning. We derive equations for the vortex core velocity and mass, where they mainly depend on Rabi coupling and the relative distance between the vortex cores in photon and exciton fields, and as a result, core positions oscillate in each field. We use Magnus force balanced with a Rabi-induced force to show that the core of the vortex behaves as an inertial-like particle. Our analysis reveals that the core is lighter on the periphery of the beam and therefore it is faster in that region. While detuning induces oscillations in population imbalance of components through the relative phase between coupled fields, in the presence of topological charges detuning can control the orbital dynamics of the cores. Namely, it causes the vortex core to move in larger or smaller orbits with different velocities and changes angular momentum and energy content of the vortex field.