Originally, the Hubbard model was derived for describing the behavior of strongly correlated
electrons in solids. However, for over a decade now, variations of it have also routinely been …

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with
results from exactly solvable models and computational approaches, the concept of bosonic …

We review recent developments in the physics of ultracold atomic and molecular gases in
optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard …

The physics of quantum degenerate atomic Fermi gases in uniform as well as in
harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is …

Artificial crystals of light, consisting of hundreds of thousands of optical microtraps, are
routinely created by interfering optical laser beams. These so-called optical lattices act as …

Matter waves inside periodic potentials are well known from solid-state physics, where
electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates …

The ability to conduct experiments at length scales and temperatures at which interesting
and potentially useful quantum-mechanical phenomena emerge in condensed-matter or …

We observe a localized phase of ultracold bosonic quantum gases in a 3-dimensional
optical lattice induced by a small contribution of fermionic atoms acting as impurities in a …

A mixture of ultracold bosons and fermions placed in an optical lattice constitutes a novel
kind of quantum gas, and leads to phenomena, which so far has been discussed neither in …

We investigate the effect of interspecies interaction on a degenerate mixture of bosonic Rb
87 and fermionic K 40 atoms in a three-dimensional optical lattice potential. Using a …