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The squeezing effect of three-mode operator as an extension from two-mode squeezing operator. (English) Zbl 1262.81072

Summary: We study theoretically the squeezing effect in a 3-wave mixing process, generated by the operator \(S_{3}\equiv \exp[\mu(a_{1}a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(a_{1}a_{3}-a_{1}^{\dagger}a_{3}^{\dagger})]\). 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 the 3-mode squeezed vacuum state using the Weyl ordering invariance under similar transformations.

MSC:

81R30 Coherent states
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81S05 Commutation relations and statistics as related to quantum mechanics (general)
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