Quantum versus classical descriptions of sub-Poissonian light generation in three-wave mixing

Sub-Poissonian light generation in the non-degenerate three-wave mixing is studied numerically and analytically within quantum and classical approaches. Husimi Q-functions and their classical trajectory simulations are analysed to reveal a special regime corresponding to the time-stable sub-Poissonian photocount statistics of the sum-frequency mode. Conditions for observation of this regime are discussed. Theoretical predictions of the Fano factor and explanation of the extraordinary stabilization of the sub-Poissonian photocount behavior are obtained analytically by applying the classical trajectories. Scaling laws for the maximum sub-Poissonian behavior are found. Noise suppression levels in the non-degenerate vs degenerate three-wave mixing are discussed on different time scales compared to the revival times. It is shown that the non-degenerate conversion offers much better stabilization of the suppressed noise in comparison to that of degenerate process.