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

doi:10.1088/1674-1056/23/9/090302

Abstract We consider the quantum mechanical SU(2) transformation e^{2λ J_z}J_±e^{-2λ J_z}=e^±2λJ_± as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU(2) operators (J_±,J_z) from the point of view of squeezing we find that (J_±,J_z) 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 e^{2λ J_z}. 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.

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

Received: 05 February 2014
Revised: 31 March 2014
Accepted manuscript online:

PACS:	03.65.-w	(Quantum mechanics)
	42.50.-p	(Quantum optics)

Fund: 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).

Corresponding Authors: Da Cheng
E-mail: dacheng@ustc.edu

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Da Cheng (笪诚), Chen Qian-Fan (陈千帆), Fan Hong-Yi (范洪义) New 3-mode bosonic operator realization of SU(2) Lie algebra：From the point of view of squeezing 2014 Chin. Phys. B 23 090302

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[5]	Fan H Y 2012 Representation and Transformation Theory in Quantum Mechanics: Progress of Dirac's Symbolic Method (2nd edn.) (Hefei: USTC Press) (in Chinese)
[6]	Schrödinger E 1941 Proc. Roy. Irish Acad. A46 183
[7]	Fan H Y 2009 Mod. Phys. Lett. A 24 615

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

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