Non-classical effect of quantum non-demolition measurement in presence of parametric amplification

A full quantum treatment of the problem of quantum non-demolition measurements in non-linear optical media is considered. The system consists of four different coupling parameters in addition to different phase parameters. The solution of the Heisenberg equations of motion for the dynamical operators is obtained. The phenomenon of squeezing is examined for both normal and principal squeezing and it has been shown that it is more pronounced for the compound mode case. The intensity correlation function is also calculated and discussed where the observation of the antibunching can be reported. In addition to the higher-order moments we examined the quantum correlation functions, joint quasidistribution functions, as well as photon-number distribution and its factorial moments. It has shown that the non-classical properties is apparent of this system and more pronounced for the compound mode (1,3).