The Squeezing Effect of Three-Mode Operator as an Extension from Two-Mode Squeezing Operator |
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Authors: | Xue-xiang Xu |
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Institution: | (1) College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang, 330022, China |
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Abstract: | We theoretically study the squeezing effect in a 3-wave mixing process, generated by the operator S3 o expm(a1a2-a1fa2f)+n(a1a3-a1fa3f)]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})]. The corresponding 3-mode squeezed vacuum state in Fock space and its uncertainty relation are presented. It turns out that S 3 may exhibit enhanced squeezing. By virtue of integration within an ordered product (IWOP) of operators, we also give the S 3’s normally ordered expansion. Finally, we calculate the Wigner function of 3-mode squeezed vacuum state by using the Weyl ordering invariance under similar transformations. |
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