Some New Features of Photon Statistics in a Fully Quantized Parametric Amplification Process

Abstract

An exact quantum treatment reveals that signal and idler photon number operators are not well-behaved dynamical operators for studying photon statistics in parametric amplification/down-conversion processes. Contrary to expectations, the mean signal-idler photon number difference varies with time, while the corresponding signal-idler photon number cross-correlation function is complex and experiences an interference phenomenon driven by the interaction parameters. The intensity operators and related polarization operators of the polarized signal-idler photon pair in positive and negative helicity states are identified as the appropriate operators specifying a conservation law and the dynamical symmetry group ( SU (1, 1)) of the parametric amplification process. The conservation of the mean positive and negative helicity photon intensity difference and the purely real positive-negative helicity intensity cross-correlation function correctly account for the simultaneous production of polarized signal and idler photons in positive and negative helicity states.