  Ultracold gases in optical lattices are of great interest, because these
systems bear a great potential for applications in quantum simulations and
quantum information processing, in particular when using particles with a
long-range dipole-dipole interaction, such as polar molecules. Here we show the
preparation of a quantum state with exactly one molecule at each site of an
optical lattice. The molecules are produced from an atomic Mott insulator with
a density profile chosen such that the central region of the gas contains two
atoms per lattice site. A Feshbach resonance is used to associate the atom
pairs to molecules. Remaining atoms can be removed with blast light. The
technique does not rely on the molecule-molecule interaction properties and is
therefore applicable to many systems.
