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We study analytically the dynamics of vortices in strongly coupledexciton--photon fields in the presence of energy detuning. We derive equationsfor the vortex core velocity and mass, where they mainly depend on Rabicoupling and the relative distance between the vortex cores in photon andexciton fields, and as the result core positions oscillate in each field. Weuse Magnus force balanced with a Rabi induced force to show that the core ofthe vortex behaves as an inertial-like particle. Our analysis reveals that thecore is lighter at periphery of the beam and therefore it is faster at thatregion. While detuning induces oscillations in population imbalance ofcomponents through relative phase between coupled fields, in the presence oftopological charges detuning can control the orbital dynamics of the cores.Namely, it brings the vortex core to move on larger or smaller orbits withdifferent velocities, and changes angular momentum and energy content of vortexfield.

Detuning control of Rabi vortex oscillations in light matter coupling