Electromagnetically induced transparency of a single-photon in dipole-coupled one-dimensional atomic clouds

We investigate the propagation of a single photon under conditions of electromagnetically induced transparency in two parallel one-dimensional atomic clouds which are coupled via Rydberg dipole-dipole interaction. Initially the system is prepared with a single delocalized Rydberg excitation shared between the two ensembles and the photon enters both of them in an arbitrary path-superposition state. By properly aligning the transition dipoles of the atoms of each cloud we show that the photon can be partially transferred from one cloud to the other via the dipole-dipole interaction. This coupling leads to the formation of dark and bright superpositions of the light which experience different absorption and dispersion. We show that this feature can be exploited to filter the incident photon in such a way that only a desired path-superposition state is transmitted transparently. Finally, we generalize the analysis to the case of N coupled one-dimensional clouds. We show that within some approximations the dynamics of the propagating photon can be mapped on that of a free particle with complex mass.