The Propagator Formulation Of Parametric Oscillation

Employing the Q-function formalism, we analyze the squeezing spectrumrnand the photon number distribution for the signal mode as weU as the quadraturernfluctuations, the photon number distribution and the spectrum of thernintensity-difference fluctuations for the signal-idler modes generated in parametricrnoscillators operating below threshold. The Q-function is obtained byrnsolving the pertinent Fokker-Planck equation applying the method of evaluatingrnthe propagator developed by Fesseha [1 J. The task of evaluating thernpropagator by means of this method essentially reduces to the problem of solvingrnthe pertinent Euler-Lagrange equations

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