  Optical non-linearities at the single-photon level are key ingredients for
future photonic quantum technologies. Prime candidates for the realization of
strong photon-photon interactions necessary for implementing quantum
information processing tasks as well as for studying strongly correlated
photons in an integrated photonic device setting are quantum dots embedded in
photonic crystal nanocavities. Here, we report strong quantum correlations
between photons on picosecond timescales. We observe (a) photon antibunching
upon resonant excitation of the lowest-energy polariton state, proving that the
first cavity photon blocks the subsequent injection events, and (b) photon
bunching when the laser field is in two-photon resonance with the polariton
eigenstates of the second Jaynes-Cummings manifold, demonstrating that two
photons at this color are more likely to be injected into the cavity jointly,
than they would otherwise. Together,these results demonstrate unprecedented
strong single-photon non-linearities, paving the way for realizing a
single-photon transistor or a quantum optical Josephson interferometer.
