New effects of polarization multistability and polarization hysteresis in a coherently driven polariton condensate in a semiconductor microcavity are predicted and theoretically analyzed. The multistability arises due to polarization-dependent polariton-polariton interactions and can be revealed in polarization resolved photoluminescence experiments. The pumping power required to observe this effect is of 4 orders of magnitude lower than the characteristic pumping power in conventional bistable optical systems.
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