Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid

At timescales once deemed immeasurably small by Einstein, the random movement of Brownian particles in a liquid is expected to be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation fast and precise enough to capture this motion. Here we report the observation of the Brownian motion of a single particle in an optical trap with 75 MHz bandwidth and sub-ångström spatial precision and the determination of the particle’s velocity autocorrelation function. Our observation is the first measurement of ballistic Brownian motion of a particle in a liquid. The data are in excellent agreement with theoretical predictions taking into account the inertia of the particle and hydrodynamic memory effects. That Brownian particles in a liquid move diffusively at long times but ballistically at very short times has been understood for more than a century. However, the full details of the transition between these regimes are yet to be explored. Now, the transition from ballistic to diffusive Brownian motion has been measured for the first time.