Generation of motional entangled coherent state in an optomechanical system in the single photon strong coupling regime

The single-photon strong coupling in the deep-resolved sideband of the optomechanical system induces photon blockade (PB) effect. For the PB cavity, an initial mechanical coherent state evolves into superposition of phonon cat states entangled with the cavity Fock states. Measurement of the cavity photon number states produces phonon even and odd cat states. The information leakage effect of two photon states on the fidelity of cat states is calculated, it is shown that for low average phonon number this effect is negligible and decreases by increasing the two photon cavity state. The Lindblad equation is solved numerically to obtain the environmental effects on the fidelity of cat states.