Abstract: It is known that $\exp[{\rm i}\lambda(Q_1P_1-{\rm 2}/2)]$ is a unitary single-mode squeezing operator, where $Q_1$, $P_1$ are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator $S_{n}\equiv \exp\bigg[{\rm i} \lambda \sum_{i=1}^{n}(Q_{i} P_{i+1}+Q_{i+1} P_{i}))\bigg]$, $(Q_{n+1}=Q_{1}, P_{n+1}=P_{1})$, is an n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S_n's normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

Key words: Dirac's representation, integration within an ordered product technique, squeezing enhanced operator, squeezed sate