  We establish the concept of topological pumping in one-dimensional systems
with long-range interactions and apply it to the transport of a photon in
quantum optical systems. In our theoretical investigation, we introduce an
extended version of the Rice-Mele model with all-to-all exchange interactions.
By analyzing its properties, we identify the general conditions for topological
pumping and demonstrate the topologically protected and dispersionless
transport of a photon on a one-dimensional emitter chain. As concrete examples,
we investigate three different popular quantum optics platforms, namely Rydberg
atom lattices, dense lattices of atoms excited to low-lying electronic states,
and atoms coupled to waveguides, using experimentally relevant parameters. We
observe that despite the long-ranged character of the dipole-dipole
interactions, topological pumping facilitates the transport of a photon with a
fidelity per cycle which can reach 99.9%. Moreover, we find that the photon
pumping process remains topologically protected against local disorder in the
coupling rates.
