Thermally activated escape from a periodically modulated optical trap

Thermally activated escape is a ubiquitous process that underlies a wide variety of physical, chemical, and biological phenomena, such as diffusion in crystals, chemical reactions, and protein folding. More than 60 years ago, Kramers developed a quantitative theory of thermal activation based on a model of a Brownian particle in a metastable potential well coupled to a thermal reservoir. Fluctuations of the heat bath lead to a finite probability for the particle to escape. Since the escape rate is exponentially sensitive to an external force, modulation of the potential may be used as means to control the escape rate. At large modulation amplitude the rate is enhanced as the barrier is reduced, approaching a bifurcation point where it disappears. Recent theoretical work has predicted a power-law scaling of the mean escape rate W with the amplitude of periodic modulation A, ln( W) ∝ (Ac - A)mu, where Ac is the bifurcation amplitude. The critical exponent mu depends on modulation frequency, and is expected to be mu = 312 for a quasi-stationary system. As frequency increases, the exponent changes to mu = 2 when a nonadiabatic regime is entered. This thesis reports the first observation of a nonadiabatic critical exponent and explores the frequency dependence of the bifurcation amplitude.;The physical system consists of an overdamped Brownian particle in a three dimensional bistable optical potential under periodic modulation. Two visible laser beams are focused through a high-power microscope objective into an aqueous solution containing a 0.6 mum silica sphere. Interaction of the optical fields and sphere creates two stable potential minima, a fraction of a mum apart, with an intervening energy barrier. The surrounding medium causes positional fluctuations of the particle in the vicinity of one of the stable points, until a particularly large fluctuation drives the sphere over the barrier where it is captured by the other stable point. The potential is tilted periodically by modulating the laser power at rates from 0.2 Hz to 2 kHz. A camera records the image of the sphere at 5 ms intervals. Real-time digital image processing is used to obtain the sphere position r&ar;t as a function of time and the time evolution of the particle is analyzed to calculate the full three dimensional potential. Knowledge of the potential enables the components of the relaxation time of the particle in the potential to be calculated. Over-barrier transition rate statistics in the static and modulated potentials are evaluated.;An adiabatic regime is identified at modulation frequencies below 0.5 Hz. The loss of adiabaticity is seen at higher frequencies, consistent with the onset of internal relaxation times that cause the particle to fall out of equilibrium at these driving rates. In the weakly nonadiabatic regime it is found that ln(W) ∝ ( Aslc-A )2.3 +/- 0.3. The critical amplitude Aslc is seen to vary linearly with frequency, as predicted by theoretical considerations. These results are the first experimental observations of nonadiabatic Brownian dynamics as a bifurcation point is approached.