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 wellbehaved dynamical operators for studying photon statistics in parametric amplification/downconversion processes. Contrary to expectations, the mean signal-idler photon number difference nt nt 1 2 ( ) − ( ) varies with time, while the corresponding signal-idler photon number cross-correlation function n tn t 1 2 ( ) ( ) 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.