Correlations of cascaded photons: An analytical study in the two-photon Mollow regime

Mollow physics in the two-photon regime shows interesting features such as path-controlled time-reordering of photon pairs without the need to delay them. Here, we calculate analytically the two-photon correlations $g^{(2)}(\tau)$, essential to discuss and study such phenomena in the resonant-driven dressed-state regime. It is shown that there exists upper and lower bounds of the $g^{(2)}(\tau)-$ function for certain spectrally-selected photon pairs. Recent reported experiments agree with the presented theory and thereby it is shown that the resonant-driven four-level system is an interesting source for steerable quantum light in quantum cascade setups. We furthermore discuss the unlikeliness to observe antibunching for the delay time $\tau=0$ in the exciton-biexciton correlation functions in such experiments, since antibunching stems from a coherent and in-phase superposition of different photon emission events. Due to the occuring laser photon scattering, this coherent superposition state is easily disturbed and leads to correlation functions of $g^{(2)}(0)=1$.