epl draft Influence of the lattice topography on a three-dimensional, con- trollable Brownian motor

We study the influence of the lattice topography and the coupling between motion in different directions, for a three-dimensional Brownian motor based on cold atoms in a double optical lattice. Due to controllable relative spatial phases between the lattices, our Brownian motor can induce drifts in arbitrary directions. Since the lattices couple the different directions, the relation between the phase shifts and the directionality of the induced drift is non trivial. Here is therefore this relation investigated experimentally by systematically varying the relative spatial phase in two dimensions, while monitoring the vertically induced drift and the temperature. A relative spatial phase range of 2π × 2π is covered. We show that a drift, controllable both in speed and direction, can be achieved, by varying the phase both parallel and perpendicular to the direction of the measured induced drift. The experimental results are qualitatively reproduced by numerical simulations of a simplified, classical model of the system. Introduction. – A Brownian motor (BM) converts random fluctuations into deterministic work [1–3]. Brownian motors exits naturally as, e.g., protein motors and intra-cell motion [4], and a general understanding of their mechanism is of fundamental interest. The rectification mechanism requires that the system is both brought out of thermal equilibrium [1] and spatially or temporally asymmetric [1, 5]. Although it has not been proven, fulfilling these two requirements are generally sufficient to realise a BM. These requirements can be met using ultra cold atoms trapped in optical lattices [6,7]. Generally, the symmetry is broken by using a spatially asymmetric or flashing potential. In this type of noise rectifier, the direction of the induced drift is often fixed for a given potential or controllable in just 1D [1–3,8–12]. Our BM [13, 14] is based on two symmetric potentials, with an asymmetry that originates from a combination of a relative spatial phase shift between the potentials and an unequal transfer rate between them. Our system possesses an inherent ability to induce drifts in an arbitrary direction in three dimensions for the ultra cold atoms interacting with the potentials. The direction is mainly controlled by the relative spatial phase between the two potentials. In [13,14] we demonstrated that our BM does work in more (a)E-mail: [email protected] than one dimension, but how this works was not investigated. This question is especially complicated since the four-beam configuration induces a coupling between the different spatial dimensions. This coupling affects the 3D behaviour of our BM profoundly and is the key to any understanding and control of the three-dimensional aspects of our BM. In this paper, we present a study of the dimensional coupling between the relative spatial phases and its influence on the induced drift, in two dimensions. This is done both experimentally and with numerical simulations. This study results in a better understanding of the multidimensionality of our BM, and in a good control to set the induced drift to a chosen speed and direction. This also renders a controlled dynamical BM possible, where a time-dependent phase can induce realtime drifts along any pre-chosen trajectory. It even allows to control the induced drift in the vertical direction by purely controlling the phase shift horizontally, and vice versa. By studying the phase dependence, we can also study the coupling between the dimensions of the two potentials. Information about what potentials the atoms really experience and the adiabaticy [7] of the interaction can therefore be investigated. The numerical simulations are done with a simplified, classical model, which mimics the main features of p-1 ar X iv :0 70 5. 40 41 v2 [ ph ys ic s. at om -p h] 1 9 N ov 2 00 7