An outstanding goal in quantum optics is the realization of fast optical
non-linearities at the single-photon level. Such non-linearities would allow
for the realization of optical devices with new functionalities such as a
single-photon switch/transistor or a controlled-phase gate, which could form
the basis of future quantum optical technologies. While non-linear optics
effects at the single-emitter level have been demonstrated in different
systems, including atoms coupled to Fabry-Perot or toroidal micro-cavities,
super-conducting qubits in strip-line resonators or quantum dots (QDs) in
nano-cavities, none of these experiments so far has demonstrated single-photon
switching on ultrafast timescales. Here, we demonstrate that in a strongly
coupled QD-cavity system the presence of a single photon on one of the
fundamental polariton transitions can turn on light scattering on a transition
from the first to the second Jaynes-Cummings manifold with a switching time of
20 ps. As an additional device application, we use this non-linearity to
implement a single-photon pulse-correlator. Our QD-cavity system could form the
building-block of future high-bandwidth photonic networks operating in the
quantum regime