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The study of optomechanical systems has attracted much attention, most ofwhich are concentrated in the physics in the small-amplitude regime. While inthis article, we focus on optomechanics in the extremely-large-amplitude regimeand consider both classical and quantum dynamics. Firstly, we study classicaldynamics in a membrane-in-the-middle optomechanical system in which a partiallyreflecting and flexible membrane is suspended inside an optical cavity. We showthat the membrane can present self-sustained oscillations with limit cycles inthe shape of sawtooth-edged ellipses and exhibit dynamical multistability.Then, we study the dynamics of the quantum fluctuations around the classicalorbits. By using the logarithmic negativity, we calculate the evolution of thequantum entanglement between the optical cavity mode and the membrane duringthe mechanical oscillation. We show that there is some synchronism between theclassical dynamical process and the evolution of the quantum entanglement.

Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime