  Highly excited Rydberg atoms are a powerful platform for quantum simulation
and information processing. Here, we propose atomic ring networks to study
chiral currents of Rydberg excitations. The currents are controlled by a phase
pattern imprinted via a Raman scheme and can persist even in the presence of
dephasing. Depending on the interplay between the Rabi coupling of Rydberg
states and the dipole-dipole atom interaction, the current shows markedly
different features. The excitations propagate with a velocity displaying a
characteristic peak in time, reflecting the chiral nature of the current. We
find that the time-averaged current in a quench behaves similarly to the
ground-state current. This analysis paves the way for the development of new
methods to transport information in atomic networks.
