Theory of quantum light emission from a strongly-coupled single quantum dot photonic-crystal cavity system.

We present a rigorous medium-dependent theory for describing the quantum field emitted and detected from a single quantum dot exciton, strongly coupled to a planar photonic crystal nanocavity, from which the exact spectrum is derived. By using simple mode decomposition techniques, this exact spectrum is subsequently reduced to two separate user-friendly forms, in terms of the leaky cavity mode emission and the radiation mode emission. On application to study exciton-cavity coupling in the strong coupling regime, besides a pronounced modification of the usual vacuum Rabi spectral doublet, we predict several new effects associated with the leaky cavity mode emission, including the appearance of an off-resonance cavity mode and a loss-induced on-resonance spectral triplet. The cavity mode emission is shown to completely dominate the emitted spectrum, even for large cavity-exciton detunings, whereby the usual cavity-QED formulas developed for radiation-mode emission drastically fail. These predictions are in qualitative agreement with several "mystery observations" reported in recent experiments, and apply to a wide range of semiconductor cavities.