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We investigate Floquet dynamics of a cavity-spinor Bose-Einstein condensatecoupling system via periodic modulation of the cavity pump laser. Parametricresonances are predicted and we show that due to cavity feedback-inducednonlinearity the spin oscillation can be amplified to all orders of resonance,thus facilitating its detection. Real-time observation on Floquet dynamics viacavity output is also discussed.

Nonlinear Floquet dynamics of spinor condensates in an optical cavity: Cavity-amplified parametric resonance