Synchronization of colloidal rotors through angular optical binding

Abstract

A mechanism for the synchronization of driven colloidal rotors via optical coupling torques is presented and analyzed. Following our recent experiments [Brzobohat\'y et al., Opt. Express 23, 7273 (2015)], we consider a counterpropagating optical beam trap that carries spin angular momentum, but no net linear momentum, operating in an aqueous solvent. The angular momentum carried by the beams causes the continuous low-Reynolds-number rotation of spheroidal colloids. Due to multiple scattering, the optical torques experienced by these particles depend on their relative orientations, while the effect of hydrodynamic interaction is negligible. This results in frequency pulling, which causes weakly dissimilar spheroids to synchronize their rotation rates and lock their relative phases. The effect is qualitatively captured by a coupled dipole model and quantitatively reproduced by $T$-matrix calculations. For pairs of rotors, the relative torque $\mathrm{\ensuremath{\Delta}}\ensuremath{\tau}$ is shown to vary with relative phase $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}$ according to $\mathrm{\ensuremath{\Delta}}\ensuremath{\tau}\ensuremath{\approx}Asin(2\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}+\ensuremath{\delta})+B$ for constants $A,B,\ensuremath{\delta}$, so the resulting motion is governed by the well-known Adler equation. We show that this behavior can be preserved for larger numbers of particles. The application of these phenomena to the inertial motion of particles in vacuum could provide a route to the sympathetic cooling of mesoscopic particles.