Two-Photon Blockade with Second-Order Nonlinearity in Cavity Systems

Two-photon and multi-photon blockade have become the research focus recently with the development of single-photon blockade. However, we notice that the study of the two-photon and multi-photon blockades has mainly focused on the systems of an optical cavity strongly coupled to the atoms or the Kerr nonlinearity. In this paper, we study the two-photon blockade in a second-order nonlinear system. We find that a strong two-photon blockade can be obtained in the second-harmonic mode with a coherent light driving to the fundamental mode, while the drive of second-harmonic mode will not give rise to the two-photon blockade, this phenomenon is explained from the effective energy levels enabled by different drivers. Different from the other schemes of photon blockade, the single-photon blockade in the fundamental mode and two-photon blockade in the second-harmonic mode exist simultaneously due to the nature of this system.