The Far-from-equilibrium Fluctuation of an Active Brownian Particle in an Optical Trap

Active colloidal particles dissipate energies in a fashion different from Brownian particles, in that active particles undergo directed motions characterized by a persistent length. An outstanding question, debated to date, pertains to how a quantitative and well-defined means can be established to quantify the differences between the statistical behavior of an active particle and a passive Brownian particle. To address this question, we set out to investigate the motions of a single, induced-charge electrophoretic (ICEP) metallic Janus particles in a quadratic potential of an optical trap, by experiments and numerical simulations. The positions of the particle under different driving forces were measured by experiments and simulated numerically using a generalized Langevin equation. The 1-D positional histograms of the active particle, distinctively different from that of a Boltzmann distribution, reveal splitting of the positional distribution of a single peak centered at the bottom of the well into two symmetrical peaks, whose centers move away from the center to a distance increasing with the driven force. Kurtosis of the particle's spatial distribution is used as a way to quantify the deviation from Gaussian distribution and it was found that this deviation is a function of the particle's rotational relaxation, the stiffness of the trap and the driving force. The temporal fluctuations of the active particle in the well are analyzed by their power spectral density (PSD).