Generation of entangled Schrödinger cat state of two macroscopic mirrors

We propose a scheme to generate the macroscopic entangled Schrödinger cat state of two mechanical resonators in a hybrid optomechanical system by introducing modulated photon-hopping interaction between two cavities. We show that the obtained entangled cat state possesses large average phonon number and the two base vectors of which are nearly orthogonal, thus causing the high degree of entanglement. To justify the robust of the scheme, the dissipation of the system and the noise from the environment are considered. It shows that the high fidelity between the obtained state and the target state can be achieved in the presence of dissipation and thermal noise within our parameter regions, which suggests that our state-generation proposal is feasible.