  The strong coupling of quantum emitters to a cavity mode has been of
paramount importance in the development of quantum optics. Recently, also the
strong coupling to more than a single mode of an electromagnetic resonator has
drawn considerable interest. We investigate how this multimode strong coupling
regime can be harnessed to coherently control quantum systems. Specifically, we
demonstrate that a Maxwell-Fish-Eye lens can be used to implement a pulsed
excitation-exchange between two distant quantum emitters. This periodic
exchange is mediated by single-photon pulses and can be extended to a
photon-exchange between two atomic ensembles, for which the coupling strength
is enhanced collectively.
