Single-photon blockade in a hybrid optomechanical system involving two qubits in the presence of phononic number and coherent states

Single-photon generation sources have gained a prime importance in quantum information science and technologies. In this regard, serious efforts have been recently performed in the optomechanical systems in order to generate the single-photon states in a macroscopic scale. In this paper, we consider an optomechanical system contains two optical cavities both coupled with a mechanical membrane which is placed between them. Each optical mode interacts with a qubit (two-level atom). Considering the steady-state solution, we analytically obtain the state vector of the entire system wherein the initial mechanical mode has been prepared as phononic number and coherent states. In the continuation, in order to study the single-photon blockade phenomenon, we evaluate the equal-time second-order correlation function (\(g^{2}(0)\)) as well as the probability distribution of single photon (\(P_1\)) to confirm the results obtained from \(g^{2}(0)\). In addition, we investigate the effect of photon tunneling, decay rate of photons and coupling between photons and each qubit on the single-photon blockade within one of the cavities. Our numerical results show that the complete single-photon blockade occurs, i.e., \(g^{(2)}(0)\) tends to very small amounts of the order of \(10^{-8}\) to \(10^{-4}\) via increasing the photon tunneling and the coupling between photons and qubits. Furthermore, increasing the dissipation effects attenuates the single-photon blockade occurrence.