Fig. 1

Complete control over the phase-locked state is demonstrated experimentally with colloidal rotors. a Schematic of optical tweezers “rotors” experiment: two rotors are made by driving colloidal particles along predefined closed circular trajectories of radius R, using a feedback-controlled optical trap to exert a force-clamp. The force magnitude depends on the angular position [F _i  = F(ϕ _i )] by maintaining the optical trap a distance ε(ϕ) ahead of the particle. In addition to the optical trap, the particles experience viscous friction, hydrodynamic interaction with each other, and thermal fluctuations. The confinement to the circular trajectory is soft, and the radius can deviate from R. This arrangement results in a pair of rotating particles for which the phase difference is not controlled externally; we show that control over the strength of coupling and the properties of the dynamical steady state can be achieved by tuning a set of parameters. b An example of temporal evolution of the phase difference Δ = Φ₁ − Φ₂ between rotors when varying the amplitude A of the modulation force over time as indicated (δ = 3π/4, R = 4.63 ± 0.03 μm, d = 15.60 ± 0.03 μm and h = 10 ± 1 μm). In these experiments, the imposed optical force F(ϕ) = 6πηav(ϕ) has an angular dependence; c shows for one condition the imposed (line) and actual (points) force over an experimental run