  We show that exciton-type transport in certain materials can be dramatically
modified by their inclusion in an optical cavity: the modification of the
electromagnetic vacuum mode structure introduced by the cavity leads to
transport via delocalized polariton modes rather than through tunneling
processes in the material itself. This can help overcome exponential
suppression of transmission properties as a function of the system size in the
case of disorder and other imperfections. We exemplify massive improvement of
transmission for excitonic wave-packets through a cavity, as well as
enhancement of steady-state exciton currents under incoherent pumping. These
results may have implications for experiments of exciton transport in
disordered organic materials. We propose that the basic phenomena can be
observed in quantum simulators made of Rydberg atoms, cold molecules in optical
lattices, as well as in experiments with trapped ions.
