(a) A double optical potential well is obtained by focusing two parallel beams through the same objective. The dark line illustrates the path of a particle in an inter-well transition between the equilibrium positions r+ and r− (which are at the level of the rings around the beams and displaced above the focal plane because of scattering forces) through the saddle position at rs. (b) Projection of particle trajectory, acquired by digital video microscopy, along the x-axis perpendicular to the beams, where x+ and x− are the equilibrium positions along the x-axis. The sampling interval is 5 ms and the total duration of the record is approximately 8 s. The particle spends most of its time in the vicinity of the stable equilibrium points, with infrequent transitions between them. (c) Potential obtained from 4 × 106 camera frames containing 94 000 inter-well transitions, represented as two-dimensional contour plots (top) and as one-dimensional graphs (bottom).
Reprinted by permission from Macmillan Publishers Ltd: McCann et al., Nature 402, 785–7, copyright 1999.
Fig. 20.2 — Kramers transitions