  The field of levitodynamics has made significant progress towards controlling
and studying the motion of a levitated nanoparticle. Motional control relies on
either autonomous feedback via a cavity or measurement-based feedback via
external forces. Recent demonstrations of measurement-based ground-state
cooling of a single nanoparticle employ linear velocity feedback, also called
cold damping, and require the use of electrostatic forces on charged particles
via external electrodes. Here we introduce a novel all-optical cold damping
scheme based on spatial modulation of the trap position that is scalable to
multiple particles. The scheme relies on using programmable optical tweezers to
provide full independent control over trap frequency and position of each
tweezer. We show that the technique cools the center-of-mass motion of
particles down to $17\,$mK at a pressure of $2 \times 10^{-6}\,$mbar and
demonstrate its scalability by simultaneously cooling the motion of two
particles. Our work paves the way towards studying quantum interactions between
particles, achieving 3D quantum control of particle motion without cavity-based
cooling, electrodes or charged particles, and probing multipartite entanglement
in levitated optomechanical systems.
