Motion of an optically levitated nanoparticle in high vacuum is sufficiently well isolated from a room temperature environment. Together with recently developed method of cavity cooling by coherent scattering, it has allowed the collaborating group from Vienna to achieve ground state cooling of the nanoparticle motion with an optical cavity, paving the way toward further experiments with nanoparticles in the quantum regime. Within this project we will combine our extensive expertise in the field of optical binding of particles with methods developed in Vienna in order to enhance optical forces between two and more levitated nanoparticles. This will allow us to study their collective degrees of freedom and explore quantum interactions between optically bound particles in high vacuum.