n-photon blockade with an n-photon parametric drive

We propose a mechanism to engineer an $n$-photon blockade in a nonlinear cavity with an $n$-photon parametric drive $\ensuremath{\lambda}({\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}n}+{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{n})$. When an $n$-photon-excitation resonance condition is satisfied, the presence of $n$ photons in the cavity suppresses the absorption of the subsequent photons. To confirm the validity of this proposal, we study the $n$-photon blockade in an atom-cavity system, a Kerr-nonlinear resonator, and two-coupled Kerr-nonlinear resonators. Our results demonstrate that $n$-photon bunching and $(n+1)$-photon antibunching can be simultaneously obtained in these systems. This effect is due both to the anharmonic energy ladder and to the nature of the $n$-photon drive. To show the importance of the drive, we compare the results of the $n$-photon drive with a coherent (one-photon) drive, proving the enhancement of antibunching in the parametric-drive case. This proposal is general and can be applied to realize the $n$-photon blockade in other nonlinear systems.