中国物理B ›› 2016, Vol. 25 ›› Issue (12): 120301-120301.doi: 10.1088/1674-1056/25/12/120301

• GENERAL • 上一篇    下一篇

New approach for anti-normally and normally ordering bosonic-operator functions in quantum optics

Shi-Min Xu(徐世民), Yun-Hai Zhang(张运海), Xing-Lei Xu(徐兴磊), Hong-Qi Li(李洪奇), Ji-Suo Wang(王继锁)   

  1. 1. Department of Physics and Electronic Engineering, Heze University, Heze 274015, China;
    2. College of Physics and Engineering, Qufu Normal University, Qufu 273165, China
  • 收稿日期:2016-06-15 修回日期:2016-07-25 出版日期:2016-12-05 发布日期:2016-12-05
  • 通讯作者: Hong-Qi Li E-mail:hzuwlx@126.com
  • 基金资助:

    Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2015AM025) and the Natural Science Foundation of Heze University, China (Grant No. XY14PY02).

New approach for anti-normally and normally ordering bosonic-operator functions in quantum optics

Shi-Min Xu(徐世民)1, Yun-Hai Zhang(张运海)1, Xing-Lei Xu(徐兴磊)1, Hong-Qi Li(李洪奇)1, Ji-Suo Wang(王继锁)2   

  1. 1. Department of Physics and Electronic Engineering, Heze University, Heze 274015, China;
    2. College of Physics and Engineering, Qufu Normal University, Qufu 273165, China
  • Received:2016-06-15 Revised:2016-07-25 Online:2016-12-05 Published:2016-12-05
  • Contact: Hong-Qi Li E-mail:hzuwlx@126.com
  • Supported by:

    Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2015AM025) and the Natural Science Foundation of Heze University, China (Grant No. XY14PY02).

摘要:

In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f(λ+ν) in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations.

关键词: Baker-Hausdorff formula, operator differentiation, mutual transformation

Abstract:

In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f(λ+ν) in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations.

Key words: Baker-Hausdorff formula, operator differentiation, mutual transformation

中图分类号:  (Quantum mechanics)

  • 03.65.-w
03.67.-a (Quantum information) 42.50.Dv (Quantum state engineering and measurements)