We use the third-and fourth-order autocorrelation functions g (3) (τ1, τ2) and g (4) (τ1, τ2, τ3) 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) (τ1, τ2, τ3) as the first step toward detecting three-photon states.A strongly-coupled quantum dot-cavity system can produce non-classical light by filtering the input stream of photons coming from a classical coherent light source through mechanisms described as 'photon blockade' [1,2] and 'photon-induced tunneling' [2,3]. Recent proposals [4,5] have extended the concept of photon blockade from single photons to two-photon Fock state generation by coupling the probe laser to the second manifold of the Jaynes-Cummings ladder via a two-photon transition [6]. This approach can potentially be further generalized to create third-and higher-order photon states inside the cavity through multi-photon transitions to the corresponding manifold. Following our proposal [4], we report the probing of these multi-photon transitions into the higher manifolds of the Jaynes-Cummings ladder of a strongly coupled quantum dot-photonic crystal nanocavity system [2] by measuring the third-order autocorrelation function (g (3) (τ 1 , τ 2 )) of a probe laser transmitted through such a system. Prior to this work, higherorder photon correlations had been measured for thermal [7][8][9][10] and laser [11] sources, relying on the strong excitation and high count rates available in these systems. Very recently g (3) measurements of the fluorescence from a single quantum dot weakly coupled to a microcavity were reported as well [12]. However, in the low-intensity, strongly-coupled regime of cavity quantum electrodynamics, such correlations have only been measured in an atomic system [13]. Therefore, this work constitutes a significant step towards implementing a solidstate non-classical light source of photon number states.One of the benchmarks used to characterize a source of single photons is the measurement of the the second-order autocorrelation function g (2) (τ ) = a † a † (τ )a(τ )a a † a 2[14] at τ = 0, which quantifies the suppression of multi-photon * armandhr@stanford.edu † mbajcsy@uwaterloo.ca states. In actual experiments, the value of g (2) (0) for a light source is usually estimated from a Hanbury-Brown and Twiss (HBT) setup that measures coincidence counts between two single photon counting modules (SPCMs).A classical coherent light source will produce photons with Poisson statistics (g (2) (0) = 1), while a source whose output contains at most one photon a...