Abstract

We consider the control problem of moving a harmonic trap containing a Brownian particle (as a load) over a given distance in a given time, with the goal of spending as little work as possible. For viscous media, it is well established that the optimal protocol involves a sudden jump at the beginning and end, and is linear in time in between [1]. However, in various real-world scenarios, such as subcellular transport processes, the assumption of a purely memoryless medium is not justified. We show that memory effects in the environment lead to significantly different optimal strategies where the trap velocity needs to be continuously modulated [2]. Surprisingly, we find that in all linear media optimal solutions nevertheless possess a universal symmetry, independent of the memory properties of the environment. We present experimental evidence for our findings using a colloidal particle dragged by an optimal trap through viscous and viscoelastic fluids. [1] T Schmiedl and U Seifert, PRL 98 , 108301, (2007). [2] S AM Loos, S Monter, F Ginot, C Bechinger, in preparation.