Optomechanically induced transparency and photon blockade in a graphene coupled nonlinear photonic crystal nanobeam cavity based optomechanical system

In this article we study tunable optically induced transparency and photon blockade in an optomechanical system comprising a suspended single -layer graphene sheet above a one-dimensional photonic crystal nanobeam cavity above which a single layer graphene sheet is suspended where optomechanical coupling exist not only between photonic and mechanical modes of nanobeam, but also between the photonic cavity field and graphene resonator and the photonic cavity exhibits Kerr type nonlinearity. We develop a Hamiltonian for the system and analytically solve for the photon transmission rate in Hamilton-Langevin formulation. It is found that we can manipulate the absorption window by varying both the nanobeam photon-nanobeam phonon coupling and nanobeam photon-graphene phonon coupling. We also theoretically and numerically analyze the photon statistics of the system. We analytically determine the optimal conditions of unconventional photon blockade due to destructive interference between different transition pathways in weak Kerr nonlinear regime. We also numerically evaluate the second order photon correlation function and plot it against different system parameters to find that the numerical results are in agreement with analytical optimal conditions.