New Normally Ordered Four-Mode Squeezing Operator for Standard Squeezing of Four-Mode Quadratures

By virtue of the technique of integration within an ordered product of operators a new four-modesqueezing operator that squeezes the four-mode quadrature operators of light field in the standard way is found.This operator differs from the direct product of two two-mode squeezing operators. It is the exponential operatorV≡exp [ir(QP+QP+QP+QP)].The Wigner function of the new four-mode squeezed state is calculated,which quite differs from that of the direct-product state of two usual two-mode squeezed states.