Optical lattices,ultracold atoms and quantum information processing

We review novel methods for the investigation, control and manipulation of neutral atoms in optical lattices. These setups allow unprecedented quantum control over large numbers of atoms and thus are very promising for applications in quantum information processing. After introducing optical lattices we discuss the superfluid (SF) and Mott insulating (MI) states of neutral atoms trapped in such lattices and investigate the SF-MI transition as observed experimentally recently. In the second part of the paper we give an overview of proposals for quantum information processing and show different ways to entangle the trapped atoms, in particular the usage of cold collisions and Rydberg atoms. Finally, we discuss briefly the implementation of quantum simulators, entanglement enhanced atom interferometers, and ideas for robust quantum memory in optical lattices.