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In this paper, we investigate the Berry phase and Hannay's angle of an electromagnetic mode system driven by harmonic field with Born-Oppenheimer approximation and obtain their algebraic expressions by theoretical calculation. The semiclassical relation between Berry phase and Hannay's angle is discussed. We find that besides the usual connection term, the Berry phase of BO hybrid system contains a novel term brought forth by the coupling induced effective gauge potential. This quantum modification can be viewed as an effective Aharonov-Bohm effect. Moreover, a similar phenomenon is founded in the Hannay's angle of classical BO hybrid system, which indicates that the Berry phase and Hannay's angle possess the same relation as the usual one. Besides, our theory can also be used to generate Artificial gauge potentials for neutral atoms.
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Keywords:
- Berry phase /
- Hannay's angle /
- quantum-classical correspondence /
- Born-Oppenheimer approximation
[1] Born M, Oppenheimer J 1927 Ann. Phys. 84 457
[2] Berry M V 1984 Proc. R. Soc. A 392 45
[3] Chruściński D, Jamiolkowski A 2004 Geometric Phases in Classical and Quantum Mechanics (Berlin: Birkhäuser)
[4] Berry M V 1990 edited by Bregda U, Garmo G, Morandi G Anomalies, Phases, Defects (Naples: Bibliopolis)
[5] Robbins J M 1997 arXiv1008.5331.
[6] Bohm A, Mostafazadeh A, Koizumi H, Niu N, Zwanziger J 2003 The Geometric Phase in Quantum Systems (Berlin: Springe-Verlag)
[7] Xiao D, Zhang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
[8] Wang L C, Yan J Y, Yi X X 2010 Chin. Phys. B 19 040512
[9] Jia X Y, Li W D, Liang J Q 2007 Chin. Phys. 16 2855
[10] Wu J W, Guo G C 1995 Chin. Phys. 4 406
[11] Liu H D, Yi X X 2011 Phys. Rev. A 84 022114
[12] Shan C J 2012 Acta Phys. Sin. 61 220302 (in Chinese) [单传家 2012 物理学报 61 220302]
[13] Simon B 1983 Phys. Rev. Lett. 51 2167
[14] Arnold V I 1978 Mathematical Methods of Classical Mechanics (Berlin: Springer-Verlag)
[15] Hannay J H 1985 J. Phys. A 18 221
[16] Berry M V 1985 J. Phys. A 18 15
[17] Giavarini G, Gozzi E, Rohrlich D, Thacker W D 1989 Phys. Rev. D 39 3007
[18] Jarzynski C 1995 Phys. Rev. Lett. 74 1264
[19] Pati A K 1998 Ann. Phys. 270 178
[20] Liu J, Hu B, Li B W 1998 Phys. Rev. Lett. 81 1749
[21] Fu L B, Liu J 2010 Ann. Phys. 325 2425
[22] Mead C A, Truhlar D 1979 J. Chem. Phys. 70 2284
[23] Mead C A 1992 Rev. Mod. Phys. 64 51
[24] Stone M 1986 Phys. Rev. D 33 1191
[25] Berry M V, Robbins J M 1993 Proc. R. Soc. A 442 659
[26] Gozzi E, Thacker W D 1987 Phys. Rev. D 35 2398
[27] Sun C P, Ge M L 1990 Phys. Rev. D 41 1349
[28] Zhang Q, Wu B 2006 Phys. Rev. Lett. 97 190401
[29] Liu H D, Wu S L, Yi X X 2011 Phys. Rev. A 83 062101
[30] Aharonov Y, Bohm D 1959 Phys. Rev. 115 485
[31] Dalibard J, Gerbier F, Juzeliunas G, Öhberg P 2011 Rev. Mod. Phys. 83 1523
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[1] Born M, Oppenheimer J 1927 Ann. Phys. 84 457
[2] Berry M V 1984 Proc. R. Soc. A 392 45
[3] Chruściński D, Jamiolkowski A 2004 Geometric Phases in Classical and Quantum Mechanics (Berlin: Birkhäuser)
[4] Berry M V 1990 edited by Bregda U, Garmo G, Morandi G Anomalies, Phases, Defects (Naples: Bibliopolis)
[5] Robbins J M 1997 arXiv1008.5331.
[6] Bohm A, Mostafazadeh A, Koizumi H, Niu N, Zwanziger J 2003 The Geometric Phase in Quantum Systems (Berlin: Springe-Verlag)
[7] Xiao D, Zhang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
[8] Wang L C, Yan J Y, Yi X X 2010 Chin. Phys. B 19 040512
[9] Jia X Y, Li W D, Liang J Q 2007 Chin. Phys. 16 2855
[10] Wu J W, Guo G C 1995 Chin. Phys. 4 406
[11] Liu H D, Yi X X 2011 Phys. Rev. A 84 022114
[12] Shan C J 2012 Acta Phys. Sin. 61 220302 (in Chinese) [单传家 2012 物理学报 61 220302]
[13] Simon B 1983 Phys. Rev. Lett. 51 2167
[14] Arnold V I 1978 Mathematical Methods of Classical Mechanics (Berlin: Springer-Verlag)
[15] Hannay J H 1985 J. Phys. A 18 221
[16] Berry M V 1985 J. Phys. A 18 15
[17] Giavarini G, Gozzi E, Rohrlich D, Thacker W D 1989 Phys. Rev. D 39 3007
[18] Jarzynski C 1995 Phys. Rev. Lett. 74 1264
[19] Pati A K 1998 Ann. Phys. 270 178
[20] Liu J, Hu B, Li B W 1998 Phys. Rev. Lett. 81 1749
[21] Fu L B, Liu J 2010 Ann. Phys. 325 2425
[22] Mead C A, Truhlar D 1979 J. Chem. Phys. 70 2284
[23] Mead C A 1992 Rev. Mod. Phys. 64 51
[24] Stone M 1986 Phys. Rev. D 33 1191
[25] Berry M V, Robbins J M 1993 Proc. R. Soc. A 442 659
[26] Gozzi E, Thacker W D 1987 Phys. Rev. D 35 2398
[27] Sun C P, Ge M L 1990 Phys. Rev. D 41 1349
[28] Zhang Q, Wu B 2006 Phys. Rev. Lett. 97 190401
[29] Liu H D, Wu S L, Yi X X 2011 Phys. Rev. A 83 062101
[30] Aharonov Y, Bohm D 1959 Phys. Rev. 115 485
[31] Dalibard J, Gerbier F, Juzeliunas G, Öhberg P 2011 Rev. Mod. Phys. 83 1523
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