Quantum statistics and blockade of phonon and photon in a dissipative quadratically coupled optomechanical system

There exists a tight relation between single-phonon and -photon source devices with the phonon and photon blockade implementations. These sources possess significant practical applications in quantum information processing and engineering. In this paper, we present a scheme to investigate the quantum statistics, as well as the phonon and photon blockade phenomena in an optomechanical system with quadratic coupling whose cavity has a moving membrane that is placed in the node (or antinode) of the optomechanical cavity. Strong nonlinear interaction between the optical and mechanical modes is induced by a driving field through radiation pressure. Also, the effective coupling strength can be adjusted by controlling the amplitude of an external pump field. Using the obtained effective Hamiltonian, we examine the steady state equal-time second-order correlation function via solving the Lindblad master equation which includes optical and mechanical dissipation sources. Our numerical results show that, with suitable adjustment of the system feasible parameters, we can achieve sub-Poissonian behavior, and as a result, an acceptable degree of phonon blockade. While using the same parameters, for the photon blockade, we arrive at a moderate or even weakly degree of the blockade. It should be emphasized that, as is shown, it is possible to make the scenario vice versa. By this, we mean that one can use a set of parameters by which a high (low) degree of photon (phonon) blockade is occurred. Moreover, we present a set of parameters for an optimal simultaneous occurrence of moderate phonon and photon blockade.