We explore entanglement generation between multiple optically levitated nanospheres interacting with a common optical cavity via the coherent scattering optomechanical interaction. We derive the many-particle Hamiltonian governing the unitary evolution of the system and show that it gives rise to quantum correlations among the various partitions of the setup, following a non-Markovian dynamics of entanglement birth, death and revivals. We also consider the effects of coupling the system to external environments and show that under reasonable experimental conditions entanglement between the mechanical modes can survive even at room temperature. Its dependence upon the number of nanoparticles, their initial temperature and coupling strength is studied. A numerical toolbox to simulate the closed and open dynamics of Gaussian optomechanical states and their informational measures is developed.

我们探索了通过相干散射光机械相互作用与公共光学腔相互作用的多个光学悬浮纳米球之间的纠缠生成。我们推导出控制系统幺正演化的多粒子哈密顿量，并表明它在设置的各个部分之间产生量子相关性，遵循纠缠出生、死亡和复兴的非马尔可夫动力学。我们还考虑了将系统耦合到外部环境的影响，并表明在合理的实验条件下，机械模式之间的纠缠即使在室温下也能存在。研究了它对纳米粒子数量、它们的初始温度和耦合强度的依赖性。