We propose to manipulate the statistic properties of the photons transport nonreciprocally via quadratic optomechanical coupling. We present a scheme to generate quadratic optomechanical interactions in the normal optical modes of a whispering-gallery-mode (WGM) optomechanical system by eliminating the linear optomechanical couplings via anticrossing of different modes. By optically pumping the WGM optomechanical system in one direction, the effective quadratic optomechanical coupling in that direction will be enhanced significantly, and nonreciprocal photon blockade will be observed consequently. Our proposal has potential applications for the on-chip nonreciprocal single-photon devices.
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