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From fractional Fourier transformation to quantum mechanical fractional squeezing transformation |
| Lv Cui-Hong (吕翠红)a, Fan Hong-Yi (范洪义)b, Li Dong-Wei (李东韡)a |
a Faculty of Science, Jiangsu University, Zhenjiang 212013, China;
b Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China |
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Abstract By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function, i.e., tanα→tanhα,sinα→sinhα, we find the quantum mechanical fractional squeezing transformation (FrST) which satisfies additivity. By virtue of the integration technique within the ordered product of operators (IWOP) we derive the unitary operator responsible for the FrST, which is composite and is made of eiπa*a/2 and exp[ia/2(a2+a*2)]. The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.
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Received: 16 June 2014
Revised: 20 September 2014
Accepted manuscript online:
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PACS:
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03.65.-w
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(Quantum mechanics)
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42.50.-p
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(Quantum optics)
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02.90.+p
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(Other topics in mathematical methods in physics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11304126), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20130532), the Natural Science Fund for Colleges and Universities in Jiangsu Province, China (Grant No. 13KJB140003), the Postdoctoral Science Foundation of China (Grant No. 2013M541608), and the Postdoctoral Science Foundation of Jiangsu Province, China (Grant No. 1202012B). |
Corresponding Authors:
Lv Cui-Hong
E-mail: lvch@mail.ujs.edu.cn
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Cite this article:
Lv Cui-Hong (吕翠红), Fan Hong-Yi (范洪义), Li Dong-Wei (李东韡) From fractional Fourier transformation to quantum mechanical fractional squeezing transformation 2015 Chin. Phys. B 24 020301
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