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Communications in Theoretical Physics

Squeezing Transformation of Three-Mode Entangled State

Xiao-Qing Qian, Song Tong-Qiang

Published Nov 1, 2005• 1 citation
Publisher

Abstract

We introduce the three-mode entangled state and set up an experiment to generate it. Then we discuss the three-mode squeezing operator squeezed | p , χ 2 , χ 3 ⟩ → μ -3/2 | p /μ, χ 2 /μ, χ 3 /μ ⟩ and the optical implement to realize such a squeezed state. We also reveal that c -number asymmetric shrink transform in the three-mode entangled state, i.e. | p , χ 2 , χ 3 ⟩ → μ -1/2 | p /μ, χ 2 , χ 3 ⟩, maps onto a kind of one-sided three-mode squeezing operator exp {iλ/3 (∑ i =1 3 P i ) (∑ i =1 3 Q i ) − λ/2}. Using the technique of integration within an ordered product (IWOP) of operators, we derive their normally ordered forms and construct the corresponding squeezed states.

DOI
10.1088/6102/44/5/911

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We introduce the three-mode entangled state and set up an experiment to generate it. Then we discuss the three-mode squeezing operator squeezed | p, x2, x3> →μ-3/2|p/μ, x2/μ, x3/μ> and the optical implement to realize such a squeezed state. We also reveal that c-number asymmetric shrink transform in the three-mode entangled state, i.e. |p, x2,x3> →μ-1/2|p/μ,x2,x3>, maps onto a kind of one-sided three-mode squeezing operator exp{iλ/3(∑3i=1 Pi) (∑3i=1 Qi) - λ/2}. Using the technique of integration within an ordered product (IWOP) of operators, we derive their normally ordered forms and construct the corresponding squeezed states.
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We show that c-number dilation transform in the Einstein–Podolsky–Rosen (EPR) entangled state, i.e. |η 1 , η 2 ⟩ → |η 1 , η 2 /μ⟩ (or |η 1 , η 2 ⟩ → |η 1 /μ, η 2 ⟩), maps onto a kind of one-sided two-mode squeezing operator exp {iλ/2( P 1 + P 2 )( Q 1 + Q 2 ) − λ/2}, (or exp{iλ/2( P 1 − P 2 )( Q 1 − Q 2 ) − λ/2}). Using the IWOP technique, we derive their normally ordered form and construct the corresponding squeezed states. In doing so, some new relationship between squeezing and entangled state transformation is revealed. The dynamic Hamiltonian for such a kind of squeezing evolution is derived. The properties and application of the one-sided squeezed state are briefly discussed. These states can also be obtained with the use of a beam splitter.