Field-quadrature and photon-number correlations produced by parametric processes

In a previous paper [Opt. Express 13, 4986 (2005)], formulas were derived for the field-quadrature and photon-number variances produced by multiple-mode parametric processes. In this paper, formulas are derived for the quadrature and number correlations. The number formulas are used to analyze the properties of basic devices, such as two-mode amplifiers, attenuators and frequency convertors, and composite systems made from these devices, such as cascaded parametric amplifiers and communication links. Amplifiers generate idlers that are correlated with the amplified signals, or correlate pre-existing pairs of modes, whereas attenuators decorrelate pre-existing modes. Both types of device modify the signal-to-noise ratios (SNRs) of the modes on which they act. Amplifiers decrease or increase the mode SNRs, depending on whether they are operated in phase-insensitive (PI) or phase-sensitive (PS) manners, respectively, whereas attenuators always decrease these SNRs. Two-mode PS links are sequences of transmission fibers (attenuators) followed by two-mode PS amplifiers. Not only do these PS links have noise figures that are 6-dB lower than those of the corresponding PI links, they also produce idlers that are (almost) completely correlated with the signals. By detecting the signals and idlers, one can eliminate the effects of electronic noise in the detectors. (C) 2010 Optical Society of America