Optical Thermal Ratchet

Abstract

We present an optical realization of a thermal ratchet. Directed motion of Brownian particles in water is induced by modulating in time a spatially periodic but asymmetric optical potential. The net drift shows a maximum as a function of the modulation period. The experimental results agree with a simple theoretical model based on diffusion.PACS numbers: 05.40.+j Let us consider a Brownian particle diffusing in a one-dimensional periodic well-shaped potential.If the potential height is much larger than the thermal noise, the particle is localized in a minimum. Suppose that this potential is asymmetric and characterized by two length scales Af and Ab (forward and backward) and assume that Ab is larger than Af (time r = 0 in Fig. 1). In an equilibrium situation, not net motion of particles can be induced by a periodic potential, since there is no large scale gradients. However, a time modulation of such a potential, when asymmetric, can induce motion in the following way: Turn the potential off; the particle diffuses freely (time r~r, « in Fig. 1). We call Pf the probability that the particle diffuses forward by more than Af during the time r"«(and similarly Pb for the backward probability).Switching the potential on again after a time~, ff forces the particle to the forward well with a probability Pf and to the backward one with a probability Pq (time r = r,ff in Fig. 1). We define as J = Pf -Pb, the probability current for a particle to advance one step in the periodic potential. Because Ab is larger than Af, Pb is smaller than Pf and the drift is nonzero. As proposed earlier, the time modulation of a periodic asymmetric potential creates directed motion of thermally fluctuating particles [1]. Similar models of engines that extract work from random noise have been recently proposed under the denomination of "thermal ratchets" [2 -6]. These models may have some connection with biological motor proteins [7 -14].How does one experimentally realize such a spatially periodic but asymmetric forcing of Brownian particles?One way is to deposit two metallic films on a glass substrate in a periodic but asymmetric fashion, so that applying an ac electric field through these electrodes creates the desired potential for colloidal particles in an aqueous solution.Recent experiments using such a setup confirmed the induced drift [15,16]. However, hydrodynamic interactions and the complicated electrical response of charges in water limited these experiments to only qualitative agreement with theory. In this Letter, to avoid hydrodynamic interactions we study only one particle (a 1.5 p, m diameter polystyrene 7='Toff Pb (1-Pb-Pf) Pf FIG. 1. The asymmetric potential is drawn as the thickline. The forward and backward length scales defining the asymmetry are Af and Ab. The particle probability densities are drawn as thin lines. At time 7-= 0, the particle is localized and the probability density is sharply peaked. For times 7.~~, «, the potential is off and the particle diffuses freely. At time T 7 ff the potential is back on and t...

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