  Vortical flows of rotating particles describe interactions ranging from
molecular machines to atmospheric dynamics. Yet to date, direct observation of
the hydrodynamic coupling between artificial micro-rotors has been restricted
by the details of the chosen drive, either through synchronization (using
external magnetic fields) or confinement (using optical tweezers). Here we
present a new active system that illuminates the interplay of rotation and
translation in free rotors. We developed a non-tweezing circularly polarized
beam that simultaneously rotates hundreds of silica-coated birefringent
colloids. The particles rotate asynchronously in the optical torque field while
freely diffusing in the plane. We observe that neighboring particles orbit each
other with an angular velocity that depends on their spins. We derive an
analytical model in the Stokes limit for pairs of spheres that quantitatively
explains the observed dynamics. We then find that the geometrical nature of the
low Reynolds fluid results in a universal hydrodynamic spin-orbit coupling. Our
findings are of significance for the understanding and development of
far-from-equilibrium materials.
