  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.
