Cavity-Mediated Strong Matter Wave Bistability in a Spin-1 Condensate

We study matter-wave bistability in a spin-1 Bose-Einstein condensate dispersively coupled to a unidirectional ring cavity. A unique feature is that the population exchange among different modes of matter fields is accomplished via spin-exchange collisions. We show that the interplay between the atomic spin mixing and the cavity light field can lead to a strong matter-wave nonlinearity, making matter-wave bistability in a cavity at the single-photon level achievable.