The N-mode squeezed state with enhanced squeezing

It is known that exp [iλ (Q1P1 – i/2)] is a unitary single-mode squeezing operator, where Q1, P1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator 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 Sn'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. (general)