Spinning polariton vortices with magnetic field

We study the formation dynamics of spinor polariton condensates trapped in ring-shaped confining potentials created by excitonic reservoirs. We consider in detail the interplay of the effective spin-orbit interaction provided by transverse electric and transverse magnetic photonic modes splitting (TE-TM splitting) and exciton Zeeman splitting provided by an external magnetic field. We demonstrate that tuning of the trap size obtained by shaping of the external nonresonant and depolarized pumping allows formation of pairs of half-vortices of topological charges +/- 1/2 in both spin components. Further, we show that the probabilities of the realizations of four possible vortex configurations strongly depend on the value of the magnetic field. For certain values of the field, the probability of the formation of a vortex with desired topological charge reaches 90%, which opens the possibility of on-demand control of angular momentum of quantum fluids of light with a magnetic field.