The Propagator Formulation Of Parametric Oscillation

Employing the Q-fun ctio ll formalism, we analyze the s(l ueezing spectrumrnand the photon number di strihution for the signal mode as well as the qlladralurnre f1ue t uations, t he photon rHunlwr dis tribution arHI the spectrum of therninten sity-difreren ce flu ctuatio ns for th., sig nal -i(lIer modes generated ill PM"'-rnmetric oscill ators operating below t hreshold . The Q-functio ll is obtained byrnsolving the pertinenl Fokker-PlarH::k equat ion applying the method of evalu -rnating the pro pagator developed by Ff'sspha [IJ. The task of eval uati ng thernpropa.ga.tor by means of this method psst'liti a lly reduces to the pro hlem of solv -rning the p e r ~ illent Euler-Lagrange equa.tio ns.

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