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| Cover of the May 1994 issue of Science, illustrating optical tweezer techniques as applied to penmanship. |
The optical tweezer technique was first developed around 1986 and has since found many applications in soft condensed matter physics and biology. The image to the left illustrates a strand of fluorescent DNA being manipulated through a semi-dilute solution of non-fluorescent, but otherwise similar, DNA with optical tweezer techniques in order to study reptation, i.e. a polymer's snake-like motion.
This module brings together the principles of electromagnetism, ray optics, statistical mechanics, and the fluctuation-dissipation theorem.
Our goals are as follows:
- To become familiar with the use and alignment of standard optics, including lenses, microscope objectives, mirrors, polarizers, etc. and understand how diffraction determines the size of a focus.
- To understand how a light beam can trap and manipulate a material particle. This depends crucially on the fact that light photons carry momentum, and is a vivid illustration of this phenomenon.
- To provide an introduction to data acquisition via a CCD camera interfaced to a computer, image processing, and computer-based data analysis.
- To provide an introduction to random processes and their power spectra.
- To determine the strength of the optical trap, using the Brownian motion of a micro-sized polystyrene sphere together with the Boltzmann factor of statistical mechanics.
- To introduce the fluctuation-dissipation theorem.
Specifically, you will carry out three different measurements after assembling the apparatus. First, you will determine the distribution of bead positions, which are sampled as a result of the Brownian motion of the bead within a trap. This can be related to the trap depth and shape via the Boltzmann factor. Specifically, we have that  , permitting a determination of the spring constant,  , that characterizes the potential energy of the trap near its minimum. Second, you will measure the power spectrial density [ ] versus frequency ( ) of bead displacements in the trap - i.e. the spectrum of the bead's positional fluctuations within the trap - using a quadrant photodiode. You will compare this to theory and determine the characteristic relaxation rate ( ) of such fluctuations. Finally, you will determine the diffusion coefficient ( ) of a free bead. These seemingly unrelated quantities are actually linked by, in effect, the fluctuation-dissipation theorem, so that we expect
 (1)
Albert Einstein wrote three great papers in 1905. One concerned special relativity, another the photoelectric effect. The third paper had to do with Brownian motion and its main conclusion was the Einstein relation, which is equivalent to Eq. 1.
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