  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 2pi x 2pi 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.
