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arXiv · 1009.2548

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

Xue-xiang Xu·Hong-yi Fan·Li-yun Hu·Hong-chun Yuan
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Abstract

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[\mu(a_{1}% a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(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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Xue-xiang Xu, Hong-yi Fan, Li-yun Hu, Hong-chun Yuan. 2010-09-14. New 3-mode squeezing operator and squeezed vacuum state in 3-wave mixing. https://arxiv.org/abs/1009.2548

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