  Optical lattices have proven to be powerful systems for quantum simulations
of solid state physics effects. Here we report a proof-of-principle experiment
simulating effects predicted by relativistic wave equations with ultracold
atoms in a bichromatic optical lattice that allows for a tailoring of the
dispersion relation. We observe the analog of Klein-tunneling, the penetration
of relativistic particles through a potential barrier without the exponential
damping that is characteristic for nonrelativistic quantum tunneling. Both
linear (relativistic) and quadratic (nonrelativistic) dispersion relations are
investigated, and significant barrier transmission is observed only for the
relativistic case.
