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Laser Tweezers Test Kramers’ Theory

Photonics Spectra
Jun 2000
Daniel S. Burgess

Nearly 60 years after Hendrik A. Kramers described the thermally driven transitions of Brownian particles, researchers at Michigan State University have experimentally verified his theory. One of the most-cited articles in 20th-century physics, Kramers' 1940 piece in Physica has influenced reaction-rate theories across disciplines from materials science and electronics to photonics and biochemistry.

Kramers contemplated the behavior of a randomly moving particle subject to thermal fluctuations in a potential well. His theory relates the particle's rate of transition from a metastable state to the shape of the well and to 19th-century chemist Svante A. Arrhenius' recognition of an exponential dependence on temperature. Transitions from one metastable state to another are at the heart of phenomena such as mode hopping in lasers, radioactive decay, protein folding and doping crystals in the manufacture of computer chips.

Since the theory was built on the work of Arrhenius, who boasted that he had never performed an exact experiment in his life, it perhaps is no surprise that it took so long to confirm it in the lab. "Being exact isn't always the most important thing. Often, being insightful is," said Lowell I. McCann, now a professor of physics at the University of Wisconsin in River Falls. He and his fellow researchers published the results of their study in the Dec. 16, 1999, issue of Nature.

The team created its potential wells with an adjacent pair of laser tweezers, formed by focusing two 17-mW HeNe lasers, which were stabilized with Pockels cell electro-optic modulators, through a single objective lens. They placed a dielectric silica sphere 0.6 µm in diameter in the system and imaged it with a CCD camera from Dalsa Inc. of Waterloo, Ontario, Canada, at 200 fps through a 100 x 1.4-NA objective. A pattern-matching algorithm monitored the movements of the particle in three dimensions, with image analysis of its apparent size providing its coordinates in the propagation direction of the beams. The thousands of measured transitions confirmed the accuracy of Kramers' theory.

While McCann acknowledged that sophisticated technology was required to build their setup, the researchers were surprised to find that no one else had ever tested the theory. "After making the measurements, we searched the literature and asked colleagues for any reference to a previous experimental test," he said. "Most people felt the same way that we did: 'Someone must have done this before, but I don't know of anyone.' "

Kramers' theory, McCann said, has been so widely accepted (by the team's estimate, it was cited more than 2600 times from 1987 to 1998) that its verification by exact science is all the more important. "It is easy to have a theory that makes sense," he said, "but a theory that accurately predicts the behavior of real, physical systems is truly useful."

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