  Strong interaction between two single photons is a long standing and
important goal in quantum photonics. This would enable a new regime of
nonlinear optics and unlock several applications in quantum information
science, including photonic quantum gates and deterministic Bell-state
measurements. In the context of quantum networks, it would be important to
achieve interactions between single photons from independent photon pairs
storable in quantum memories. So far, most experiments showing nonlinearities
at the single-photon level have used weak classical input light. Here, we
demonstrate the storage and retrieval of a paired single photon emitted by an
ensemble quantum memory in a strongly nonlinear medium based on highly excited
Rydberg atoms. We show that nonclassical correlations between the two photons
persist after retrieval from the Rydberg ensemble. Our result is an important
step towards deterministic photon-photon interactions, and may enable
deterministic Bell-state measurements with multimode quantum memories.
