Three-mode squeezed vacuum state in Fock space as an entangled state

We show that the operator $U=\mathrm{exp}[\ensuremath{-}{ir(Q}_{1}{P}_{2}{+Q}_{2}{P}_{3}{+Q}_{3}{P}_{1})]$ is a three-mode squeezing operator for the three-mode quadratures exhibiting the standard squeezing, the corresponding squeezed vacuum state in three-mode Fock space is derived by virtue of the technique of integration within ordered product of operators. The entanglement involved in such a state is explained. The optical network for producing the three-mode squeezed state is proposed.