Rotation of exciton-polariton condensates with TE-TM splitting in a microcavity ring

We investigate exciton-polariton condensates with a rotating potential induced by an electric field in a semiconductor microcavity ring. In the absence of transverse-electric-transverse-magnetic (TE-TM) splitting, we find that there is a critical laser pump rate, above which the quantized phase slips appear with hysteresis, and there exist quantized average angular momenta at fixed angular velocities, regardless of the pump rate. When considering the TE-TM splitting, we find that there are a series of hysteresis loops with the same intervals which are modulated by the magnitude of the splitting for a linear polarization laser. Further, multistability occurs at large pump rate, and there arises a phase slip for only one spin with large absolute value of the polarization degree, owing to the competition of the TE-TM splitting and energy induced by rotation. These results can be verified experimentally with current technology, and are useful for future electro-optic devices.