  Simple, paradigmatic systems are important tools in understanding strongly
correlated systems. One such system is the Bose-Hubbard model, which can be
realized using atoms in optical lattices with delta-function interactions. We
report the first experimental observation of two features of the Bose-Hubbard
model: superexchange via virtual molecules in excited bands and off-site
contact interactions. Adiabatic sweeps confirm the creation of such molecules,
exemplifying a new kind of Feshbach resonance.
