  Giant optical nonlinearity is observed under both continuous-wave and pulsed
excitation in a deterministically-coupled quantum dot-micropillar system, in a
pronounced strong-coupling regime. Using absolute reflectivity measurements we
determine the critical intracavity photon number as well as the input and
output coupling efficiencies of the device. Thanks to a near-unity
input-coupling efficiency, we demonstrate a record nonlinearity threshold of
only 8 incident photons per pulse. The output-coupling efficiency is found to
strongly influence this nonlinearity threshold. We show how the fundamental
limit of single-photon nonlinearity can be attained in realistic devices, which
would provide an effective interaction between two coincident single photons.
