New method for calculating the Berry connection in atom–molecule systems

doi:10.1088/1674-1056/21/11/110303

中国物理B ›› 2012, Vol. 21 ›› Issue (11): 110303-110303.doi: 10.1088/1674-1056/21/11/110303

New method for calculating the Berry connection in atom–molecule systems

崔傅成, 吴宝俊

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2012-04-05 修回日期:2012-05-04 出版日期:2012-10-01 发布日期:2012-10-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10825417).

New method for calculating the Berry connection in atom–molecule systems

Cui Fu-Cheng (崔傅成), Wu Bao-Jun (吴宝俊 )

Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Received:2012-04-05 Revised:2012-05-04 Online:2012-10-01 Published:2012-10-01
Contact: Cui Fu-Cheng E-mail:cfc9qiqi@hotmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10825417).

摘要/Abstract

摘要： In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U(1) symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay's angle suitable for calculating the Berry curvature in the atom-molecule systems. With this Berry curvature, the Berry connection can be naturally computed. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay's angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.

关键词: Berry phase, nonlinearity, Hannay's angle, mean field theory

Abstract: In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U(1) symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay's angle suitable for calculating the Berry curvature in the atom-molecule systems. With this Berry curvature, the Berry connection can be naturally computed. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay's angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.

Key words: Berry phase, nonlinearity, Hannay's angle, mean field theory

中图分类号: (Formalism)

03.65.Ca

03.65.Vf (Phases: geometric; dynamic or topological) 03.75.Mn (Multicomponent condensates; spinor condensates) 32.90.+a (Other topics in atomic properties and interactions of atoms with photons)

崔傅成, 吴宝俊 . New method for calculating the Berry connection in atom–molecule systems[J]. 中国物理B, 2012, 21(11): 110303-110303.

Cui Fu-Cheng (崔傅成), Wu Bao-Jun (吴宝俊 ). New method for calculating the Berry connection in atom–molecule systems[J]. Chin. Phys. B, 2012, 21(11): 110303-110303.

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New method for calculating the Berry connection in atom–molecule systems

New method for calculating the Berry connection in atom–molecule systems

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