We investigate the photon-induced tunneling phenomena in a photonic crystal cavity containing a strongly coupled quantum dot and describe how this tunneling can be used to generate photon states consisting mainly of a particular Fock state. Additionally, we study experimentally the second-order autocorrelation
g2(0) in the photon-induced tunneling regime as a function of the frequency and the power of the probe laser and observe signs of higher manifolds of the Jaynes-Cummings Hamiltonian in the frequency-dependent photon statistics of the transmitted light, as well as the strong power dependence of
g2(0), distinguishing this effect clearly from bunching occurring in a thermal light source.
Nonclassicality cannot be a single-observable property, since the statistics of any quantum observable is compatible with classical physics. We develop a general procedure to reveal nonclassical behavior of light states from the joint statistics arising in the practical measurement of multiple observables. Beside embracing previous approaches, this protocol can disclose nonclassical features for standard examples of classical-like behavior, such as SU(2) and Glauber coherent states. When combined with other criteria, this would imply that every light state is nonclassical.