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

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...

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Bibliographic Details
Published inChinese physics B Vol. 23; no. 6; pp. 18 - 22
Main Author 范洪义 展德会
Format Journal Article
LanguageEnglish
Published 01.06.2014
Subjects
Construction
Functions (mathematics)
Hermite polynomials
Hermite多项式
Mathematical analysis
Operators
Polynomials
Quantum optics
埃尔米特多项式
奇数
对偶数
应用
环境
生成函数
量子光学
Online AccessGet full text
ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/23/6/060301

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Summary: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.
Bibliography:generating function, even- and odd-Hermite polynomials, Hermite polynomial method, techniqueof integral within an ordered product of operators
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.
Fan Hong-Yi Zhan De-Hui（ Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China）
11-5639/O4
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/23/6/060301