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Chinese Physics Letters

New Three—Mode Einstein—Podolsky—Rosen Entangled State Prepresentation and Its Application in Squeezing Theory

范洪义, 姜年权

Published Jan 1, 2002• 0 citations
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Abstract

By extending the Einstein-Podolsky-Rosen bipartite entanglement to the tripartite case,we construct the common eigenvector of the tripartite centre-of -mass coordinate and two mass-weighted relative momenta,which is a new entangled state of continuum variables.The classical dilation transform of varibles in such a state induces new entangled state of continum variables,The classical dilation transform of variables in such a state induces a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.

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By extending the Einstein-Podolsky-Rosen bipartite entanglement to the tripartite case,we construct the common eigenvector of the tripartite centre-of -mass coordinate and two mass-weighted relative momenta,which is a new entangled state of continuum variables.The classical dilation transform of varibles in such a state induces new entangled state of continum variables,The classical dilation transform of variables in such a state induces a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.a new three-mode squeezing operator related to a three-mode bosonic operator realization of SU(1,1) Lie algebra.
Our primary purpose of this work is to explicitly construct the general multipartite Einstein–Podolsky–Rosen (EPR) entangled state in multi-mode Fock space for a system with different masses of particles, which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property. Its entanglement can be seen more clearly by analyzing its standard Schmidt decomposition. In addition, some applications of the multipartite entanglement are proposed including deriving the generalized Wigner operator and squeezing operator.
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.