  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
microparticles, mediated by intermodal scattering and interference inside the
evacuated core of a hollow-core photonic crystal fibre (HC-PCF). Three
polystyrene particles with 1 {\mu}m diameter are stably bound together with an
inter-particle distance of ~40 {\mu}m, or 50 times longer than the wavelength
of the trapping laser. The bound-particle array can be translated to-and-fro
over centimetre distances along the fibre. When evacuated to 6 mbar gas
pressure, the collective mechanical modes of the bound-particle array could be
observed. The measured inter-particle distance at equilibrium and mechanical
eigen-frequencies 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.
