Generating stationary entanglement and one-way steering in a hybrid cavity electro-optomechanical system via a squeezed vacuum field

We propose a scheme to generate robust bipartite entanglement, genuine tripartite entanglement, and one-way steering in a hybrid cavity electro-optomechanical system with the help of a squeezed vacuum field. The system consists of an optical cavity, a mechanical resonator formed by a thin silicon nitride membrane, and two superconducting microwave circuits. The mechanical resonator is coupled to the optical cavity and two superconducting circuits simultaneously. We find there is steady-state entanglement between different modes and genuine tripartite entanglement among the cavity mode and two microwave modes which are robust against the thermal fluctuations of the mechanical mode. In addition, the robust one-way steering between two microwave modes can be generated by selecting appropriate squeezing parameter. Our scheme may have potential applications in quantum information processing and communication.