Two-photon correlation in a cascade amplifier: propagation effects via a simple model, nonclassical regimes, and validity of neglecting Langevin noise

We study several aspects of two-photon correlation of an optically driven extended medium (amplifier) with parametric down-conversion (PDC) scheme and three-level cascade scheme. The correlation for the PDC scheme is modeled by coupled parametric equations with constant self-coupling and cross coupling coefficients. This provides simple physical insights to how the correlation profile depends on the sign and magnitude of the coefficients in the presence of propagation group delay between signal and idler photons. The results with constant coefficients are related to the results of the driven three-level cascade scheme obtained from quantum Langevin-Maxwell's equations. The correlation transforms from bunching to antibunching as the pump field increases. Cauchy-Schwartz inequality is violated for all time delay in the case of off-resonant pump, showing nonclassical correlation. We verify that the correlation obtained without noise operators is qualitatively correct regardless of the optical density, especially for large detuning. We also discuss the interesting physics behind antibunching and oscillations found in the reverse correlation