Photon blockade in optomechanical systems with a position-modulated Kerr-type nonlinear coupling

We explore the photon blockade in optomechanical systems with a position-modulated Kerr-type
nonlinear coupling, i.e. ##IMG## [http://ej.iop.org/images/1751-8121/51/9/095302/aaaa97dieqn001.gif]
{$H_{\rm int}\sim\hat{a}^{\dagger2}\hat{a}^2(\hat{b}_1^\dagger+\hat{b}_1)$} . We find that the
Kerr-type nonlinear coupling can enhance the photon blockade greatly. We evaluate the equal-time
second-order correlation function of the cavity photons and find that the optimal photon blockade
does not happen at the single photon resonance. By working within the few-photon subspace, we get an
approximate analytical expression for the correlation function and the condition for the optimal
photon blockade. We also find that the photon blockade effect is not always enhanced as the
Kerr-type nonlinear coupling strength g 2 increases. At some values of g 2 , the photon blockade is
even weakened. For the system we considered here, the second-o...