  We demonstrate a Brownian motor, based on cold atoms in optical lattices,
where isotropic random fluctuations are rectified in order to induce controlled
atomic motion in arbitrary directions. In contrast to earlier demonstrations of
ratchet effects, our Brownian motor operates in potentials that are spatially
and temporally symmetric, but where spatiotemporal symmetry is broken by a
phase shift between the potentials and asymmetric transfer rates between them.
The Brownian motor is demonstrated in three dimensions and the noise-induced
drift is controllable in our system.
