中国物理B ›› 2014, Vol. 23 ›› Issue (9): 90302-090302.doi: 10.1088/1674-1056/23/9/090302

• GENERAL • 上一篇    下一篇

New 3-mode bosonic operator realization of SU(2) Lie algebra：From the point of view of squeezing

笪诚, 陈千帆, 范洪义   

  1. Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2014-02-05 修回日期:2014-03-31 出版日期:2014-09-15 发布日期:2014-09-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11275123) and the Key Project of Natural Science Fund of Anhui Province, China (Grant No. KJ2013A261).

New 3-mode bosonic operator realization of SU(2) Lie algebra：From the point of view of squeezing

Da Cheng (笪诚), Chen Qian-Fan (陈千帆), Fan Hong-Yi (范洪义)   

  1. Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2014-02-05 Revised:2014-03-31 Online:2014-09-15 Published:2014-09-15
  • Contact: Da Cheng E-mail:dacheng@ustc.edu
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113 and 11275123) and the Key Project of Natural Science Fund of Anhui Province, China (Grant No. KJ2013A261).

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摘要： We consider the quantum mechanical SU(2) transformation e2λ JzJ±e-2λ Jz=e±2λJ± as if the meaning of squeezing with e±2λ being squeezing parameter. By studying SU(2) operators (J±,Jz) from the point of view of squeezing we find that (J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation (the eigenvectors of J+ or J-) of the 3-mode squeezing operator e2λ Jz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.

关键词: quantum mechanical SU(2) transformation, 3-mode squeezing operator, new 3-mode bosonic operator realization of SU(2) Lie algebra

Abstract: We consider the quantum mechanical SU(2) transformation e2λ JzJ±e-2λ Jz=e±2λJ± as if the meaning of squeezing with e±2λ being squeezing parameter. By studying SU(2) operators (J±,Jz) from the point of view of squeezing we find that (J±,Jz) can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation (the eigenvectors of J+ or J-) of the 3-mode squeezing operator e2λ Jz. The idea of considering quantum SU(2) transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU(2) and new squeezing operators.

Key words: quantum mechanical SU(2) transformation, 3-mode squeezing operator, new 3-mode bosonic operator realization of SU(2) Lie algebra

中图分类号:  (Quantum mechanics)

  • 03.65.-w
42.50.-p (Quantum optics)