The N-mode squeezed state with enhanced squeezing

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.