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Chin. Phys. B, 2014, Vol. 23(6): 060301    DOI: 10.1088/1674-1056/23/6/060301
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New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

Fan Hong-Yi, Zhan De-Hui
Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
Abstract  By combining the operator Hermite polynomial method and the technique of integration within an ordered product of operators, for the first time we derive the generating function of even- and odd-Hermite polynomials which will be useful in constructing new optical field states. We then show that the squeezed state and photon-added squeezed state can be expressed by even- and odd-Hermite polynomials.
Keywords:  generating function      even- and odd-Hermite polynomials      Hermite polynomial method      technique of integral within an ordered product of operators     
Received:  04 November 2013      Published:  15 June 2014
PACS:  03.65.-a  
  02.30.Gp (Special functions)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11175113) and the Fundamental Research Funds for the Central Universities of China (Grant No. WK2060140013).
Corresponding Authors:  Zhan De-Hui     E-mail:  dhzhan@mail.ustc.edu.cn

Cite this article: 

Fan Hong-Yi, Zhan De-Hui New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics 2014 Chin. Phys. B 23 060301

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