Optically levitated micro-and nanoparticles offer an ideal playground for investigating photon-phonon interactions over macroscopic distances.Here we report the observation of long-range optical binding of multiple levitated microparticles,mediated by intermodal scattering and interference inside the evacuated core of a hollow-core photonic crystal fibre (HC-PCF).Three polystyrene particles with a diameter of 1 μm are stably bound together with an inter-particle distance of ~40 μm,or 50 times longer than the wavelength of the trapping laser.The levitated boundparticle array can be translated to-and-fro over centimetre distances along the fibre.When evacuated to a gas pressure of 6 mbar,the collective mechanical modes of the bound-particle array are able to be observed.The measured interparticle distance at equilibrium and mechanical eigenfrequencies are supported by a novel analytical formalism modelling the dynamics of the binding process.The HC-PCF system offers a unique platform for investigating the rich optomechanical dynamics of arrays of levitated particles in a well-isolated and protected environment.
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