  The dynamical control of tunneling processes of single particles plays a
major role in science ranging from Shapiro steps in Josephson junctions to the
control of chemical reactions via light in molecules. Here we show how such
control can be extended to the regime of strongly interacting particles.
Through a weak modulation of a biased tunnel contact, we have been able to
coherently control single particle and correlated two-particle hopping
processes. We have furthermore been able to extend this control to
superexchange spin interactions in the presence of a magnetic-field gradient.
We show how such photon assisted superexchange processes constitute a novel
approach to realize arbitrary XXZ spin models in ultracold quantum gases, where
transverse and Ising type spin couplings can be fully controlled in magnitude
and sign.
