Abstract
We introduce the three-mode entangled state and set up an experiment togenerate it. Then we discuss the three-mode squeezing operator squeezed| p, χ2, χ3 ⟩ → μ-3/2 | p/μ, χ2/μ, χ3/μ ⟩ and the opticalimplement to realize such a squeezed state. We also reveal that c-numberasymmetric shrink transform in the three-mode entangled state, i.e.| p, χ2, χ3 ⟩ → μ-1/2 | p/μ, χ2, χ3 ⟩,maps onto a kind of one-sided three-mode squeezing operatorexp {iλ/3 (∑i=13 Pi)(∑i=13 Qi) − λ/2}. Usingthe technique of integration within an ordered product (IWOP) of operators,we derive their normally ordered forms and construct the correspondingsqueezed states.
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