Enhancing cross-Kerr coupling via mechanical parametric amplification.

We present a proposal to enhance the cross-Kerr coupling between the cavity and the mechanical oscillator significantly. Specifically, the periodic modulation of the mechanical spring constant induces strong mechanical parametric amplification, which leads to the cross-Kerr nonlinear enhancement. Also, we discuss its application in photon-phonon blockade and phonon-number measurement. We find that under the strong cross-Kerr coupling condition, not only the photon-phonon blockade effect is dramatically enhanced but also different phonon number is clearly distinguished. Our results offer an alternative approach to perform quantum manipulation between photon and phonon.