Optical control of mechanical motion of solid-state objects weakly interacting with the environment, referred to as optomechanics, continues to enable new, ground-breaking methods and applications in the area of ultra- weak force sensing and quantum technologies. The platform based on optically levitated nanoparticles in vacuum (referred to as levitated optomechanics) constitutes an entirely new type of light-matter interface, which provides a broad and an easy tunability of all the system parameters. However, the majority of the previously reported experimental achievements in this area have only dealt with a single levitated object. Here, we demonstrate for the first time scalability of the levitated optomechanics to systems containing up to tens of nanoparticles and provide a unique methodology for characterizing the system parameters and non-linear inter-particle interactions. This work represents the first and crucial step in accessing many-body dynamical effects in the classical and quantum regimes. In particular, it opens the door to the experimental studies of many-body stochastic thermodynamics and to the preparation of mesoscopic entangled states between relatively massive objects.
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