Optical Thermal Ratchets

Whilst searching for pictures for my talk on Saturday I discovered a paper which discusses a quasi-one-dimensional `thermal' ratchet using holographic optical tweezers. Lee and Grier develop a simple "two-state" ratchet in 1D and demonstrate a "three-state" ratchet in 2D.
The ratchet is based around a simple idea: some spatial or temporal symmetry must be broken in order for Brownian motion (which is isotropic and time invariant in a thermal system) to be rectified. This is the same idea that we were exposed to last year. In this case the potential energy landscape in which the ratchet operates is not due to some mechanical constraint (e.g. the teeth on a cog for a Feynman ratchet, etc.) but is an externally-imposed optical potential. For more details on optical trapping see some of my earlier posts, or ask.
Holographic optical tweezers use devices known as spatial light modulators (SLM) to dynamically alter the phasefront of the laser used to trap particles. In the focal plane this phase patterning results in interference between different parts of the beam, with the net result being a change in the irradiance pattern. This can be used to split a single laser trap into an array of sub-traps.
Lee uses this ability to create arrays of lines of Gaussian trapping potentials, where the distance between traps within a strip is much less than the distance between strips. The positions of these lines may also be dynamically altered.
Brownian motion was rectified simply by turning the traps on in one arrangement and leaving them for a short time before translating the entire array one-third of the strip separation rightwards. How does this work? Particles first become localised in the traps, where they still undergo Brownian motion. As the traps are displaced this region goes from low-potential to being essentially force-free, so the Brownian motion takes over and the particle diffuses. It is essentially equally likely to head in either direction, but on average it takes much less time to reach the traps to the right than the left (especially seeing as the traps will be shifted back to their original positions). By tuning the time the traps spend in each configuration it is therefore possible to control the net flux through the system (within statistical limits, of course).
Lee and Grier also looked into a radial version of the same experiment: this allowed size-dependent sorting of particles (the optical forces are sensitive to particle size).
The paper is reasonably straightforward and contains some interesting maths, which I would recommend. It really highlights the similarities between the formalisms of quantum mechanics, diffusion and electromagnetism (Green's functions, for those who have heard of them)!