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 extende
d 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.
