The ability to engineer cavity-mediated interactions has emerged as a powerful tool for the generation of non-local correlations and the investigation of non-equilibrium phenomena in many-body systems. Levitated optomechanical systems have recently entered the multiparticle regime, which promises the use of arrays of strongly coupled massive oscillators to explore complex interacting systems and sensing. Here we demonstrate programmable cavity-mediated interactions between nanoparticles in vacuum by combining advances in multiparticle optical levitation and cavity-based quantum control. The interaction is mediated by photons scattered by spatially separated particles in a cavity, resulting in strong coupling that is long-range in nature. We investigate the scaling of the interaction strength with cavity detuning and interparticle separation and demonstrate the tunability of interactions between different mechanical modes. Our work will enable the exploration of many-body effects in nanoparticle arrays with programmable cavity-mediated interactions, generating entanglement of motion, and the use of interacting particle arrays for optomechanical sensing.

设计空腔介导的相互作用的能力已成为生成非局部相关性和研究多体系统中非平衡现象的强大工具。悬浮光机械系统最近已进入多粒子领域，这有望使用强耦合大型振荡器阵列来探索复杂的相互作用系统和传感。在这里，我们通过结合多粒子光学悬浮和基于腔的量子控制的进步，展示了真空中纳米粒子之间的可编程腔介导的相互作用。这种相互作用是由空腔中空间分离的粒子散射的光子介导的，从而导致本质上是长程的强耦合。我们研究了相互作用强度与腔失谐和颗粒间分离的比例，并证明了不同机械模式之间相互作用的可调性。我们的工作将能够通过可编程空腔介导的相互作用来探索纳米粒子阵列中的多体效应，产生运动纠缠，以及使用相互作用的粒子阵列进行光机械传感。