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Modern Physics Letters B

BIPARTITE SQUEEZING OPERATOR FROM COHERENT ENTANGLED STATE GENERATED BY ASYMMETRIC BEAMSPLITTER

Qingqiang Kuang, Liyun Hu

Published Feb 14, 2011• 0 citations
Publisher

Abstract

With use of the newly proposed bipartite coherent entangled state (generated by asymmetric beamsplitter) and by projecting both the classical symplectic transform and the classical dilation one in phase space onto quantum mechanical Hilbert space, we construct a six-parameter squeezing operator, which has its own squeezing property, in a natural way. The derivation is implemented on the basis of the technique of integration within an ordered product of operators and the completeness of the bipartite coherent entangled state.

DOI
10.1142/s021798491102578x

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With use of the newly proposed bipartite coherent entangled state (generated by asymmetric beamsplitter) and by projecting both the classical symplectic transform and the classical dilation one in phase space onto quantum mechanical Hilbert space, we construct a six-parameter squeezing operator, which has its own squeezing property, in a natural way. The derivation is implemented on the basis of the technique of integration within an ordered product of operators and the completeness of the bipartite coherent entangled state.
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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 , 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.
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.