  In recent years it has become clear that the transport of excitons and charge
carriers in molecular systems can be enhanced by coherent coupling with
photons, giving rise to the formation of hybrid excitations known as
polaritons. Such enhancement has far-reaching technological implications,
however, the enhancement mechanism and the transport nature of these composite
light-matter excitations in such systems still remain elusive. Here we map the
ultrafast spatiotemporal dynamics of surface-bound optical waves strongly
coupled to a self-assembled molecular layer and fully resolve them in
energy/momentum space. Our studies reveal intricate behavior which stems from
the hybrid nature of polaritons. We find that the balance between the molecular
disorder and long-range correlations induced by the coherent mixing between
light and matter leads to a mobility transition between diffusive and ballistic
transport, which can be controlled by varying the light-matter composition of
the polaritons. Furthermore, we directly demonstrate that the coupling with
light can enhance the diffusion coefficient of molecular excitons by six orders
of magnitude and even lead to ballistic flow at two-thirds the speed of light.
