Probing short time Brownian motion regimes in liquids with bright and dark optical traps

Brownian motion is a foundational physical process characterized by a mean squared displacement that scales linearly with time in thermal equilibrium, known as diffusion. At short times, the mean squared displacement becomes ballistic, scaling as t^2. We show that this ballistic picture, while true for the ensemble average, obscures underlying noisy dynamics. By conditioning on times when the particle starts close to rest, we predict theoretically and confirm by experiment that the mean squared displacement becomes super-ballistic, with a power scaling law of t^(5/2). This result is due to the colored noise of incompressible fluids, distinct from the t^3 super-ballistic scaling characteristic of white noise. To observe the breakdown of incompressible assumptions at even shorter timescales, we propose a new pump-probe experimental setup using a strong pulsed laser transverse kick and two weaker measurement pulses incident on a reflective sphere held in a dark optical trap. Our approach holds promise for the detection of out of equilibrium Brownian dynamics in liquids at unprecedented timescales.