Influence of the lattice topography on a three-dimensional, controllable Brownian motor

Abstract

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.

Directed transport with real-time steering and drifts along predesigned paths using a Brownian motor

“…Figure 3b (and movie S3 [29]) demonstrates the guiding of the atoms along a triangular path, achieved by rel- ative phase settings of (2π/3, 0, 0) → (−π/3, −π/3, 0) → (−π/3, π/3, 0). Note that the phase settings for off-axis drifts become non-trivial due a coupling between the dimensions of the lattice topography [26].…”

“…1d. Although it contains all the essential ingredients of the Brownian motor, this model is an simplification of the experimental system [13,26]. For cesium atoms, each of the two potentials is a manifold of potentials of different amplitudes [23], of which one dominates the dynamics.…”

Fluctuation-induced drift in a gravitationally tilted optical lattice

“…This can be done by direct imaging of the atoms in situ. However, as a more precise diagnostic, we release the atoms and measure their arrival at a laser probe located at a distance, l = 5 cm, below the sample ('time-of-flight detection' [19]). We do this for a range of different potential depths, V 0 , providing us with data for the mobility as a function of F/V 0 .…”

“…By analyzing the velocity distributions obtained by time-of-flight detection, the fraction of atoms in the running state compared with the total amount of atoms, N run /N tot , can be extracted [19,27,31]. Assuming that the momentum distribution corresponds to a (truncated) Gaussian core of trapped atoms, with wide wings corresponding to untrapped atoms, we can calculate approximate numbers for N run /N tot and by Gaussian fits to the momentum distributions.…”

“…This makes this system a suitable experimental testbed for fundamental studies of fluctuation phenomena. In addition, the setup used here is very close to the double optical lattice arrangement that has been used to create a Brownian motor [17][18][19]. The present work is therefore also of interest for an understanding of the role of gravity in that context.…”