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A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation |
| Xie Chuan-Mei(谢传梅)a)c)†ger, Fan Hong-Yi(范洪义)b), and Wan Shao-Long(完绍龙) a) |
| a Institute for Theoretical Physics and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China; c College of Physics and Material Science, Anhui University, Hefei 230039, China |
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Abstract Based on the displacement-squeezing related squeezed coherent state representation $|z\rangle _{g}$ and using the technique of integration within an ordered product of operators, this paper finds a generalized Fresnel operator, whose matrix element in the coordinate representation leads to a generalized Collins formula (Huygens--Fresnel integration transformation describing optical diffraction). The generalized Fresnel operator is derived by a quantum mechanical mapping from z to $sz-rz^{\ast }$ in the $|z\rangle _{g}$ representation, while $|z\rangle _{g}$ in phase space is graphically denoted by an ellipse.
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Received: 19 November 2009
Accepted manuscript online:
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PACS:
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42.50.Dv
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(Quantum state engineering and measurements)
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42.50.Ar
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| Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos.~10874174 and
10675108), the President Foundation of the Chinese Academy of
Sciences, and the Specilized Research Fund for the Doctorial Program
of the Higher Education of Ch |
Cite this article:
Xie Chuan-Mei(谢传梅), Fan Hong-Yi(范洪义), and Wan Shao-Long(完绍龙) A generalized Collins formula derived by virtue of the displacement-squeezing related squeezed coherent state representation 2010 Chin. Phys. B 19 064207
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