F\"orster interaction induced phase shift in a pair state interferometer

We present experiments measuring an interaction induced phase shift of Rydberg atoms at Stark tuned F\"orster resonances. The phase shift features a dispersive shape around the resonance, showing that the interaction strength and sign can be tuned coherently. We use a pair state interferometer to measure the phase shift. Although the coupling between pair states is coherent on the time scale of the experiment, a loss of visibility occurs as a pair state interferometer involves three simultaneously interfering paths and only one of them is phase shifted by the mutual interaction. Despite additional dephasing mechanisms a pulsed F\"orster coupling sequence allows to observe coherent dynamics around the F\"orster resonance.