Symmetry and Transport in a Rocking Ratchet for Cold Atoms

Abstract

The ratchet effect [1–3] is the rectification of fluctuations in a periodic potential in the absence of net applied bias forces. In this way directed motion along a macroscopically flat structure is obtained. The archetypal of a ratchet consists of Brownian particles in a periodic potential. In order to obtain directed motion, two main requirements have to be fulfilled. First, the system has to be driven out of equilibrium, so to overcome the limitations imposed by the second principle of thermodynamics. Second, the relevant symmetries of the system, which would otherwise prevent the generation of a current, have to be broken. Among the different possible implementations of the ratchet effect, we mention here the flashing ratchet [1–3], the rocking ratchet [1–3], and the more recently introduced gating ratchet [4–6]. In the rocking ratchet set-up, Brownian particles in a periodic potential experience an additional time-dependent applied force F(t), which is homogeneous and has zero time-average. The oscillating applied force plays a double role. On one hand, it drives the system out of thermodynamic equilibrium, thus avoiding the restrictions imposed by the second principle of thermodynamics. On the other hand, the temporal symmetry properties of the applied force, together with the spatial symmetry properties of the periodic potential, control the directed motion.