Correlated photon emission from multi--atom Rydberg dark states

We consider three level atoms driven by two resonant light fields in a ladder scheme where the upper level is a highly excited Rydberg state. We show that the dipole--dipole interactions between Rydberg excited atoms prevents the formation of single particle dark states and leads to strongly correlated photon emission from atoms separated by distances large compared to the emission wavelength. For two atoms, correlated photon pairs are emitted with an angular distribution given by a coherent sum of the independent dipolar fields.