Optical binding of two cooled micro-gyroscopes levitated in vacuum

Coupling between mesoscopic particles levitated in vacuum is a prerequisite for the realisation of a large scale array of particles in the quantum ground state as well as potential studies at the classical-quantum interface. Here we demonstrate for the first time optical binding between two rotating microparticles mediated by light scattering in vacuum. We investigate autocorrelations between the two normal modes of oscillation determined by the centre-of-mass and the relative positions of the two-particle system. The inter-particle coupling, as a consequence of optical binding, removes the degeneracy of the normal mode frequencies, which is in good agreement with theory. We further demonstrate that the optically bound array of rotating microparticles retains their optical coupling during gyroscopic cooling, and exhibits cooperative motion whose centre-of-mass is stabilised. This paves the way towards full quantum optical control of nano- and micro-mechanical devices.