  We investigate the transport of excitations through a chain of atoms with
non-local dissipation introduced through coupling to additional short-lived
states. The system is described by an effective spin-1/2 model where the ratio
of the exchange interaction strength to the reservoir coupling strength
determines the type of transport, including coherent exciton motion, incoherent
hopping and a regime in which an emergent length scale leads to a preferred
hopping distance far beyond nearest neighbors. For multiple impurities, the
dissipation gives rise to strong nearest-neighbor correlations and
entanglement. These results highlight the importance of non-trivial
dissipation, correlations and many-body effects in recent experiments on the
dipole-mediated transport of Rydberg excitations.
