  We employ a master equation approach to study the second-order quantum
autocorrelation functions for up to two independent quantum dot excitons,
coupled to an off-resonant cavity in a photonic crystal - single quantum dot
system. For a single coupled off-resonant exciton, we observe novel oscillatory
behaviour in the early-time dynamics of the cavity autocorrelation function,
which leads to decreased antibunching relative to the exciton mode. With a
second coupled exciton in the system, we find that the magnitude and the
lifetime of these oscillations greatly increases, since the cavity is then able
to exchange photons with multiple excitonic resonances. We unambiguously show
that this spoils the antibunching characteristics of the cavity quasi-mode,
while the autocorrelation of the first exciton is unaffected. We also examine
the effects of detector time resolution and make a direct connection to a
series of recent experiments.
