Xu Xue-Xiang(徐学翔)a)b),Hu Li-Yun(胡利云) a)b)†, and Fan Hong-Yi(范洪义)a)
a Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China; b College of Physics & Communication Electronics, Jiangxi Normal University, Nanchang 330022, China
Abstract It is known that $\exp[{\rm i}\lambda(Q_1P_1-{\rm 2}/2)]$ 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 $S_{n}\equiv \exp\bigg[{\rm i} \lambda \sum_{i=1}^{n}(Q_{i} P_{i+1}+Q_{i+1} P_{i}))\bigg]$, $(Q_{n+1}=Q_{1}, P_{n+1}=P_{1})$, is an n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive Sn'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.
Received: 22 May 2009
Revised: 08 June 2009
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 10775097 and
10874174), and the Research Foundation of the Education Department of Jiangxi Province of China.
Cite this article:
Xu Xue-Xiang(徐学翔),Hu Li-Yun(胡利云), and Fan Hong-Yi(范洪义) The N-mode squeezed state with enhanced squeezing 2009 Chin. Phys. B 18 5139
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