  Motivated by entanglement protection, our work utilizes a resonance effect to
enhance optomechanical entanglement in the coherent-state representation. We
propose a filtering model to filter out the significant detuning components
between a thermal-mechanical mode and its surrounding heat baths in the weak
coupling limit. We reveal that protecting continuous-variable entanglement
involves the elimination of degrees of freedom associated with significant
detuning components, thereby resisting decoherence. We construct a nonlinear
Langevin equation of the filtering model and numerically show that the
filtering model doubles the robustness of the stationary maximum optomechanical
entanglement to the thermal fluctuation noise and mechanical damping.
Furthermore, we generalize these results to an optical cavity array with one
oscillating end-mirror to investigate the long-distance optimal optomechanical
entanglement transfer. Our study breaks new ground for applying the resonance
effect to protect quantum systems from decoherence and advancing the
possibilities of large-scale quantum information processing and quantum network
construction.
