  We experimentally probe the non-resonant feeding of photons into the optical
mode of a two dimensional photonic crystal nanocavity from the discrete
emission from a quantum dot. For a strongly coupled system of a single exciton
and the cavity mode, we track the detuning-dependent photoluminescence
intensity of the polariton peaks at different lattice temperatures. At low
temperatures we observe a clear asymmetry in the emission intensity depending
on whether the exciton is at higher or lower energy than the cavity mode. At
high temperatures this asymmetry vanishes when the probabilities to emit or
absorb a phonon become similar. For a different dot-cavity system where the
cavity mode is detuned by \Delta E>5 meV to lower energy than the single
exciton transitions emission from the mode remains correlated with the quantum
dot as demonstrated unambiguously by cross-correlation photon counting
experiments. By monitoring the temporal evolution of the photoluminescence
spectrum, we show that feeding of photons into the mode occurs from
multi-exciton transitions. We observe a clear anti-correlation of the mode and
single exciton emission; the mode emission quenches as the population in the
system reduces towards the single exciton level whilst the intensity of the
mode emission tracks the multi-exciton transitions.
