New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states

doi:10.1088/1674-1056/23/8/080301

›› 2014, Vol. 23 ›› Issue (8): 80301-080301.doi: 10.1088/1674-1056/23/8/080301

New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states

范洪义^a, 王震^b

a Department of Physics, Ningbo University, Ningbo 315211, China;
b College of Science, Changzhou Institute of Technology, Changzhou 213002, China

收稿日期:2013-09-15 修回日期:2014-01-28 出版日期:2014-08-15 发布日期:2014-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11175113).

New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states

Fan Hong-Yi (范洪义)^a, Wang Zhen (王震)^b

a Department of Physics, Ningbo University, Ningbo 315211, China;
b College of Science, Changzhou Institute of Technology, Changzhou 213002, China

Received:2013-09-15 Revised:2014-01-28 Online:2014-08-15 Published:2014-08-15
Contact: Fan Hong-Yi E-mail:fhym@ustc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11175113).

摘要/Abstract

摘要： For directly normalizing the photon non-Gaussian states (e.g., photon added and subtracted squeezed states), we use the method of integration within an ordered product (IWOP) of operators to derive some new bosonic operator-ordering identities. We also derive some new integration transformation formulas about one- and two-variable Hermite polynomials in complex function space. These operator identities and associative integration formulas provide much convenience for constructing non-Gaussian states in quantum engineering.

关键词: IWOP method, squeezed states, Hermite polynomials

Abstract: For directly normalizing the photon non-Gaussian states (e.g., photon added and subtracted squeezed states), we use the method of integration within an ordered product (IWOP) of operators to derive some new bosonic operator-ordering identities. We also derive some new integration transformation formulas about one- and two-variable Hermite polynomials in complex function space. These operator identities and associative integration formulas provide much convenience for constructing non-Gaussian states in quantum engineering.

Key words: IWOP method, squeezed states, Hermite polynomials

中图分类号: (Quantum mechanics)

03.65.-w

42.50.-p (Quantum optics) 03.67.-a (Quantum information)

范洪义, 王震. New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states[J]. , 2014, 23(8): 80301-080301.

Fan Hong-Yi (范洪义), Wang Zhen (王震). New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states[J]. Chin. Phys. B, 2014, 23(8): 80301-080301.

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New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states

New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states

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