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.
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