Thermally activated transitions in a bistable three-dimensional optical trap

Activated escape from a metastable state underlies many physical, chemical and biological processes: examples include diffusion in solids, switching in superconducting junctions, chemical reactions and protein folding. Kramers presented the first quantitative calculation of thermally driven transition rates in 1940. Despite widespread acceptance of Kramers' theory, there have been few opportunities to test it quantitatively as a comprehensive knowledge of the system dynamics is required. A trapped brownian particle (relevant to our understanding of the kinetics, transport and mechanics of biological matter) represents an ideal test system. Here we report a detailed experimental analysis of the brownian dynamics of a sub-micrometre sized dielectric particle confined in a double-well optical trap. We show how these dynamics can be used to directly measure the full three-dimensional confining potential-a technique that can also be applied to other optically trapped objects. Excellent agreement is obtained between the predictions of Kramers' theory and the measured transition rates, with no adjustable or free parameters over a substantial range of barrier heights.