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

preprint2010arXivOpen access

In a 3-wave mixing process occurring in some nonlinear optical medium when } $a_{1}^{\dagger}$ {\small mode interacts with both } $a_{2}^{\dagger}%$ {\small mode and } $a_{3}^{\dagger}$ {\small mode, we theoretically study the squeezing effect generated by the operator } $S_{3}\equiv \exp[μ(a_{1}% a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+ν(a_{1}a_{3}-a_{1}^{\dagger}% a_{3}^{\dagger})]$ {\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.

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

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