Photon blockade in a system consisting of two optomechanical cavities via photon hopping

Photon blockade is an updated effect having potential application in many scientific fields such as optical communication and quantum information processing. In this paper, we investigate this phenomenon in a system with two coupled optomechanical cavities. Each cavity possesses a movable mirror connected to each other by a coupling constant of ξ (photon hopping occurs). We consider the effect of optical cavity loss on the Hamiltonian system phenomenologically (using a non-Hermitian Hamiltonian). Due to the low intensity of the considered pump laser, the study is limited to Hilbert space states with two-photon excitations. To achieve the purpose of paper, in the study of the photon statistics, we analyze the equal-time second-order correlation function g ( 2 ) ( 0 ) for the cavity radiation field. The obtained results show that by tuning the photon hopping rate between the two cavities, photon blockade can be observed at different frequencies. Also, by reducing the cavity decay rate, the minimum of the second-order correlation function decreases, and the photon blockade is more likely to occur.