New 3-mode squeezing operator and squeezed vacuum state in 3-wave mixing

Abstract

In a 3-wave mixing process occurring in some nonlinear optical medium when }$a_1^{†}${\small mode interacts with both }$a_2^{†}${\small mode and }$a_3^{†}${\small mode, we theoretically study the squeezing effect generated by the operator }$S_3\equiv \exp [\mu (a_1${\small . The new 3-mode squeezed vacuum state in Fock space is derived, and the uncertainty relation for it is demonstrated, It turns out that }$S_3${\small may exhibit enhanced squeezing. By virtue of the technique of integration within an ordered product (IWOP) of operators, we also derive }$S_3${\small 's normally ordered expansion. The Wigner function of new 3-mode squeezed vacuum state is calculated by using the Weyl ordering invariance under similar transformations.

10 pages, 2 figures, submitted to EPL