Huygens' clocks at the microscale

TL;DR

This study experimentally investigates synchronization phenomena in microscale colloidal oscillators, revealing phase-locking behavior and providing a stochastic model that predicts synchronization rates influenced by natural frequency differences and noise.

Contribution

It introduces a novel experimental system of colloidal clocks and develops a stochastic model to describe their synchronization dynamics at the microscale.

Findings

Oscillators exhibit phase locking before slipping back into sync.

Synchronization rate depends on natural frequency differences and environmental noise.

Model predictions qualitatively match experimental observations.

Abstract

Weakly coupled oscillators adjust their dynamics to work in unison: they synchronize. This ubiquitous phenomenon is observed for oscillating pendulum, electronic devices, as well as clapping crowds or flashing fireflies. In effect, synchronization constitutes an efficient mean to translate microscopic into large scale dynamics. While broadly studied theoretically, experimental investigations of synchronization of systems at the microscale are limited. Here we devise and study a model system of noisy and "measurably imperfect" colloidal oscillators: autonomous clocks made of an active swimmer revolving around a passive sphere. The distribution of natural frequency of the clock is achieved using passive spheres of various sizes, thus without altering the (phoretic) coupling between clocks. We observe that pairs of oscillators lock phases before slipping and returning to sync, and we characterize the synchronicity of the pair. We rationalize our findings with a stochastic model, formalizing synchronization as a classical Kramers escape problem in an adequate potential. This provides an analytical expression for the rate of synchronization of a pair set by the ratio between differences of natural frequency and environmental noise, and agrees qualitatively with the experiment. Our results set a blueprint for synchronization with micrometric autonomous systems.