Entanglement dynamics of two coupled mechanical oscillators in modulated optomechanics

We study the entanglement dynamics of two coupled mechanical oscillators, within a modulated optomechanical system. We find that, depending on the strength of the mechanical coupling, one could observe either a stationary or a dynamical behavior of the mechanical entanglement, which is extremely robust against the oscillator temperature. Moreover, we have shown that this entanglement dynamics is strongly related to the stability of the normal modes. Taking mechanical damping effects into account, an analytical expression corresponding to the critical mechanical coupling strength, where the transition from stationary to dynamical entanglement occurs is also reported. The proposed scheme is analysed with experimentally realistic parameters, making it a promising mean to realize macroscopic quantum entanglement within current state-of-the-art experimental setups.