Exploring quantum matter with ultracold atoms in optical lattices

Seventy years after Einstein's prediction, the seminal achievement of Bose-Einstein condensation in dilute atomic gases in 1995 has provided us with a new form of quantum matter. Such quantum matter can be described as a single giant matter wave. By loading it into an artificial periodic potential formed by laser light-a so-called optical lattice-it has become possible to probe matter far beyond the wave-like description. In a review of a series of experiments with ultracold quantum gases in optical lattices, we show that the granularity of the matter wave field, caused by the discreteness of atoms, gives rise to effects going beyond the simple single matter wave description. Bose-Einstein condensates in optical lattices have thereby opened novel possibilities for investigating strongly correlated many-particle phenomena of condensed matter physics and have opened new opportunities for quantum information processing with neutral atoms