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

2010/09/14 by Xue-xiang Xu, Xu, Xue-xiang, Hong-yi Fan +5
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1009.2548

10 pages, 2 figures, submitted to EPL

arxiv created 2010/09/14 · arxiv updated 2010/09/15

Abstract

In a 3-wave mixing process occurring in some nonlinear optical medium when a₁^†\small mode interacts with both a₂^†% \small mode and a₃^†\small mode, we theoretically study the squeezing effect generated by the operator S₃≡ exp[μ(a₁% a₂-a₁^†a₂^†)+ν(a₁a₃-a₁^†% a₃^†)]\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 S₃\small may exhibit enhanced squeezing. By virtue of the technique of integration within an ordered product (IWOP) of operators, we also derive S₃\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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