An optical lattice consists of cold atoms trapped and organized in crystal-like fashion in a periodic structure of potential wells induced by the interference of several laser beams. Optical lattices are of great interest to the scientific community because, as opposed to solid-state crystals, the experimenter has the freedom to create "designer crystals" - for example, the lattice parameters, such as the depth and shape of the potential wells, can be adjusted at will by varying laser intensity, polarization, and frequency.

We are interested in studying the unusual transport properties of cold atoms confined in an optical lattice by measuring correlations in the scattered light. Specifically, our goal is to observe non-Brownian random walks (i.e., Levy walks) by cold atoms, which have been predicted to exist under certain conditions. Levy walks are a fascinating topic, touching many fields of science, because they describe a random walk process that results in motion fundamentally different from Brownian motion. Levy walks are expected to be as prevalent in complex systems (turbulent fluid flow, micelle dynamics, air / water pollution, etc.) as Brownian motion is in simple systems. Our experiments will shed light on the anomalous diffusion properties of cold atoms in optical lattices, an area that remains relatively unexplored. Further, our experiments may enable full exploitation of new technologies like nanolithography, which depends upon a thorough understanding of the transport of slow atoms in cold environments.

We are also interested in the possibility of making the first observation of a Quantum Random Walk. In a quantum random walk, if the random walker encounters more than one indistinguishable paths leading to the same position, interference between the probability amplitudes for the different paths may occur. Optical lattices are a promising candidate for such a demonstration. Understanding the quantum random walk is essential for developing algorithms for quantum computing.