Recent technological progress in a precise control of optically trapped objects allows much broader ventures to unexplored territory of thermal motion in non-linear potentials. In this work, we exploit an experimental set-up of holographic optical tweezers to experimentally investigate Brownian motion of a micro-particle near the inflection point of the cubic optical potential. We present two complementary views on the non-linear Brownian motion. On an ensemble of stochastic trajectories, we simultaneously determine (i) the detailed short-time position statistics and (ii) the long-distance first-passage time statistics. We evaluate specific statistical moment ratios demonstrating strongly non-linear stochastic dynamics. This is a crucial step towards a possible massive exploitation of the broad class of complex non-linear stochastic effects with objects of more complex structure and shape including living ones.

Charles University Faculty of Mathematics and Physics Department of Macromolecular Physics 5 Holešovičkách 2 180 00 Praha 8 Czech Republic

Department of Optics Palacký University 17 listopadu 1192 12 771 46 Olomouc Czech Republic

Institute of Scientific Instruments of CAS Královopolská 147 612 64 Brno Czech Republic

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