  We use the third- and fourth-order autocorrelation functions
$g^{(3)}(\tau_1,\tau_2)$ and $g^{(4)}(\tau_1,\tau_2, \tau_3)$ to detect the
non-classical character of the light transmitted through a photonic-crystal
nanocavity containing a strongly-coupled quantum dot probed with a train of
coherent light pulses. We contrast the value of $g^{(3)}(0, 0)$ with the
conventionally used $g^{(2)}(0)$ and demonstrate that in addition to being
necessary for detecting two-photon states emitted by a low-intensity source,
$g^{(3)}$ provides a more clear indication of the non-classical character of a
light source. We also present preliminary data that demonstrates bunching in
the fourth-order autocorrelation function $g^{(4)}(\tau_1,\tau_2, \tau_3)$ as
the first step toward detecting three-photon states.
