  We investigate the indistinguishability of single photons retrieved from
collective Rydberg excitations in cold atomic ensembles. The Rydberg spin waves
are created either by off resonant two-photon excitation to the Rydberg state
or by Rydberg electromagnetically induced transparency. To assess the
indistinguishability of the generated single photons, we perform Hong-Ou-Mandel
experiments between the single photons and weak coherent states of light. We
analyze the indistinguishability of the single photons as a function of the
detection window and for photons generated by off-resonant excitation we infer
high value of indistinguishability going from 89% for the full waveform to 98%
for small detection windows. In the same way, we also investigate for the first
time the indistinguishability of single photons generated by Rydberg EIT,
showing values lower than those corresponding to single photons generated by
off-resonant excitation. These results are relevant for the use of Rydberg
atoms as quantum network nodes.
