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arXiv · 0903.0997

New application of Dirac's representation: N-mode squeezing enhanced operator and squeezed state

Xue-xiang Xu·Li-yun Hu·Hong-yi Fan
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Abstract

It is known that exp[i\lamda(Q_1P_1-i/2)] is a unitary single-mode squeezing operator, where Q_1,P_1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator S_{n}=Exp[i\lamda sum_{i=1}^{n}](Q_{i}P_{i+1}+Q_{i+1}P_{i}))], (Q_{n+1}=Q_1P_{n+1}=P_1), is a n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S_{n}'s normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.

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Xue-xiang Xu, Li-yun Hu, Hong-yi Fan. 2009-03-05. New application of Dirac's representation: N-mode squeezing enhanced operator and squeezed state. https://arxiv.org/abs/0903.0997

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