Multidimensional coupling in a controllable three-dimensional Brownian motor in optical lattices

We study the dimensional coupling in 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. Here, the multidimensional coupling of the relative spatial phases and its effect on the induced drift is investigated. This is done both experimentally and with numerical simulations of a Brownian particle, by systematically varying the relative spatial phase in two dimensions while monitoring the vertical induced drift and the temperature. A relative spatial phase range of 2π × 2π in the a vertical plane is covered. We show that a drift, controllable both in speed and direction, can be achieved. 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. This dependence is straightforward if the phase is varied along one of the coordinate axes [13, 14]. However, if the phase is given a non-zero value in two or more (a)E-mail: [email protected] dimensions, the induced drift will not be a sum of the onedimensional cases, since the three-dimensional potentials are constructed out of just four laser beams. Knowledge of this non-trivial phase dependence of the induced drift velocity is crucial for a full three-dimensional control of our BM. In this paper, we present a study of the multidimensional coupling between the induced drift and the relative spatial phase in two dimensions. This is done both experimentally and with numerical simulations. This study results in a better understanding of our BM, and 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. 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. System. – The potentials used are realised from a double optical lattice (DOL) [15, 16], interacting with Cs. An optical lattice is a periodic potential where atoms can be cooled and trapped due to dissipation and light shifts [6], and is created from the interference between two or more light fields. A DOL consists of two spatially overlapped state-dependent optical lattices [15,16]. p-1 ar X iv :0 70 5. 40 41 v1 [ ph ys ic s. at om -p h] 2 8 M ay 2 00 7