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Quantum statistical properties are derived for stimulated Raman scattering by squeezed phonons including squeezing of vacuum fluctuations in radiation modes and sub-Poisson photon behaviour. Initial radiation can be in squeezed thermalized and/or sub-Poisson states, phonon system can also be squeezed. In particular, effects of initial phase conditions, losses, initial nonclassical behaviour and phonon squeezing are demonstrated in terms of reduced factorial moments up to the fifth order in combined photon-photon and photon-phonon modes. Also photon number distribution, quadrature variances and principał squeeze parameters are shown.
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