New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

doi:10.1088/1674-1056/23/6/060301

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
Revised: 05 December 2013
Accepted manuscript online:

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 (范洪义), Zhan De-Hui (展德会) 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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[5]	Fan H Y, He R, Da C and Liang Z F 2013 Chin. Phys. B 22 080301
[6]	Yang Y and Fan H Y 2013 Chin. Phys. B 22 020303
[7]	Zhou J, Fan H Y and Song J 2012 Chin. Phys. B 21 070301

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New generating function formulae of even- and odd-Hermite polynomials obtained and applied in the context of quantum optics

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