Suppression of Zeeman splitting and polarization steps in localized exciton-polariton condensates

We show that the condensation of exciton-polaritons in semiconductor microcavities in an applied magnetic field manifests itself in the quenching of the Zeeman splitting of an elliptically polarized condensate. The circular polarization degree of a localized condensate with a finite number of particles increases as a function of the magnetic field with a step-like behavior. The width of each polarization step is fixed by the polariton-polariton interaction constants and the number of steps is fixed by the number of polaritons in the condensate. The magnetic susceptibility of the condensate depends qualitatively on the parity of the number of polaritons.