In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, an optomechanical system with an asymmetric anharmonic mechanical resonator is studied. The cross-Kerr interaction and the Kerr-like self-interaction of photons and vibration quanta arise in the Hamiltonian. These interactions are induced by both cubic and quartic nonlinearities of oscillations of the mechanical resonator and the cavity-resonator interaction that is linear in mechanical displacements. We demonstrate a bistable behavior of the number of vibration quanta and find that this behavior is controlled by the cross-Kerr interaction. It is shown that, without driving and dissipation, the constructed superposition Yurke–Stoler-like states of the cavity (or the mechanical resonator) disentangle at certain times the entangled modes of the system. The obtained results offer new possibilities for control of optomechanical systems with asymmetric mechanical oscillations.

在基于Bogoliubov平均法的非长期扰动理论的框架下，研究了具有非对称非谐机械谐振器的光机系统。哈密​​顿量中出现了光子和振动量子的交叉克尔相互作用和类似克尔的自相互作用。这些相互作用是由机械谐振器的三次和三次非线性振荡以及机械位移线性的腔谐振器相互作用引起的。我们证明了振动量子数量的双稳态行为，并发现这种行为是由交叉克尔相互作用控制的。结果表明，在没有驱动和耗散的情况下，腔体（或机械谐振器）的构造的类似于Yurke-Stoler的叠加态在某些时候解开了系统的纠缠模式。