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A three-dimensional Brownian motor is realised using lasercooled caesium atoms trapped in a system of two static, and individually symmetric, optical lattices; a so-called double optical lattice. Isotropic fluctuations, emanating from light scattering, are rectified, and the diffusion of the ensemble of atoms is biased, with a resulting constant velocity that is controllable both in direction and magnitude. The working principle of the Brownian motor can be seen as a pulsation between two different potentials, both symmetric but around different points. The correlation between interferometric spatial offsets, and imbalance in optical pumping rates, leads to a spatio-temporal asymmetry sufficient for generating a controlled, directed motion.

We have developed an alignment tool for optical lattices with arbitrary beam angles, allowing for optical potentials with a range of geometries and topographies. A calibration procedure has been introduced, giving a precision of 10 mrad in the chosen beam angle, and a high degree of flexibility. The tool has been tested in simplified experiments on the confinement and expansion of cold atoms in one-dimensional and two-dimensional optical lattices, and has proved to work well.

Experimental and theoretical studies are made of Brownian particles trapped in a periodic potential, which is very slightly tilted due to gravity. In the presence of fluctuations, these will trigger a measurable average drift along the direction of the tilt. The magnitude of the drift varies with the ratio between the bias force and the trapping potential. This can be closely compared to a theoretical model system, based on a Fokker-Planck equation formalism. We show that the level of control and measurement precision we have in our system, which is based on cold atoms trapped in a three-dimensional dissipative optical lattice, makes the experimental setup suitable as a testbed for fundamental statistical physics. We simulate the system with a very simplified and general classical model, as well as with an elaborate semiclassical Monte Carlo simulation. In both cases, we achieve good qualitative agreement with experimental data.

We have realized real-time steering of the directed transport in a Brownian motor based on cold atoms in optical lattices and demonstrate drifts along predesigned paths. The transport is induced by spatiotemporal asymmetries in the system, where we can control the spatial part, and we show that the response to changes in asymmetry is very fast. In addition to directional steering, a real-time control of the magnitude of the average drift velocity and an on-off switching of the motor are also demonstrated. We use a noninvasive real-time detection of the transport, enabling feedback control of the system.

The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of the performance far from straightforward. In this work, where the Brownian motor consists of atoms interacting with dissipative optical lattices, we adopt existing theory and present experimental measurements for both the efficiency and the transport coherence. We achieve up to 0.3% for the efficiency and 0.01 for the Péclet number.

The directed transport of Brownian particles requires a system with an asymmetry and with non-equilibrium noise. Here we investigate numerically alternative ways of fulfilling these requirements for a two-state Brownian motor, realized with Brownian particles alternating between two phase-shifted, symmetric potentials. We show that, besides the previously known spatio-temporal asymmetry based on unequal transfer rates between the potentials, inequalities in the potential depths, the frictions, or the equilibrium temperatures of the two potentials also generate the required asymmetry. We also show that the effects of the thermal noise and the noise of the transfer's randomness depend on the way the asymmetry is induced.

We investigate the feasibility of carrying out quantum walks with cold atoms in a double optical lattice. Monte Carlo simulations of time-of-flight (TOF) detection and absorption imaging were carried out, focusing on a specific experimental implementation. These indicate that absorption imaging would be best suited for detection of quantum walks. With typical experimental parameters a few hundred quantum walk steps will be needed for an unambiguous detection of the quantum walk signature. We show that in special cases, few-step quantum walks can also be detected in our system if one measures the relative population of the atoms in their internal states rather than their displacement in space, that is, measurements are made in the space of the coin operator rather than in that of the displacement operator.

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.