| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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Effective Hamiltonian of the Jaynes-Cummings model beyond rotating-wave approximation |
| Yi-Fan Wang(王伊凡), Hong-Hao Yin(尹洪浩), Ming-Yue Yang(杨明月), An-Chun Ji(纪安春), and Qing Sun(孙青)† |
| Department of Physics, Capital Normal University, Beijing 100048, China |
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Abstract The Jaynes-Cummings model with or without rotating-wave approximation plays a major role to study the interaction between atom and light. We investigate the Jaynes-Cummings model beyond the rotating-wave approximation. Treating the counter-rotating terms as periodic drivings, we solve the model in the extended Floquet space. It is found that the full energy spectrum folded in the quasi-energy bands can be described by an effective Hamiltonian derived in the high-frequency regime. In contrast to the Z2 symmetry of the original model, the effective Hamiltonian bears an enlarged U(1) symmetry with a unique photon-dependent atom-light detuning and coupling strength. We further analyze the energy spectrum, eigenstate fidelity and mean photon number of the resultant polaritons, which are shown to be in accordance with the numerical simulations in the extended Floquet space up to an ultra-strong coupling regime and are not altered significantly for a finite atom-light detuning. Our results suggest that the effective model provides a good starting point to investigate the rich physics brought by counter-rotating terms in the frame of Floquet theory.
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Received: 17 November 2020
Revised: 04 January 2021
Accepted manuscript online: 07 January 2021
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PACS:
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42.50.Pq
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(Cavity quantum electrodynamics; micromasers)
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42.50.-p
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(Quantum optics)
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37.30.+i
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(Atoms, molecules, andions incavities)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11875195) and the Foundation of Beijing Education Committees, China (Grant Nos. CIT&TCD201804074 and KZ201810028043). |
Corresponding Authors:
Qing Sun
E-mail: sunqing@cnu.edu.cn
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Cite this article:
Yi-Fan Wang(王伊凡), Hong-Hao Yin(尹洪浩), Ming-Yue Yang(杨明月), An-Chun Ji(纪安春), and Qing Sun(孙青) Effective Hamiltonian of the Jaynes-Cummings model beyond rotating-wave approximation 2021 Chin. Phys. B 30 064204
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[1] Jaynes E T and Cummings F W 1963 Proc. IEEE 51 89
[2] Shore B W and Knight P L 1993 J. Mod. Opt. 40 1195
[3] Cummings F W 1965 Phys. Rev. 140 A1051
[4] Eberly J H, Narozhny N B and Sanchez-Mondragon J J 1980 Phys. Rev. Lett. 44 1323
[5] Narozhny N B, Sanchez-Mondragon J J and Eberly J H 1981 Phys. Rev. A 23 236
[6] Knight P L and Radmore P M 1982 Phys. Rev. A 26 676
[7] Rempe G, Walther H and Klein N 1987 Phys. Rev. Lett. 58 353
[8] Phoenix S J D and Knight P L 1991 Phys. Rev. A 44 6023
[9] Brune M, Haroche S, Raimond J M, Davidovich L and Zagury N 1992 Phys. Rev. A 45 5193
[10] Bužek V, Moya-Cessa H, Knight P L and Phoenix S J D 1992 Phys. Rev. A 45 8190
[11] Brune M, Hagley E, Dreyer J, Maître X, Maali A, Wunderlich C, Raimond J M and Haroche S 1996 Phys. Rev. Lett. 77 4887
[12] Furuya K, Nemes M C and Pellegrino G Q 1998 Phys. Rev. Lett. 80 5524
[13] Sun Q, Hu J, Wen L, Pu H and Ji A C 2018 Phys. Rev. A 98 033801
[14] Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R-S, Majer J, Kumar S, Girvin S M and Schoelkopf R J 2004 Nature 431 162
[15] Hofheinz M, Wang H, Ansmann M, Bialczak R C, Lucero E, Neeley M, O'Connell A D, Sank D, Wenner J, Martinis J M and Cleland A N 2009 Nature 459 546
[16] LaHaye M D, Suh J, Echternach P M, Schwab K C and Roukes M L 2009 Nature 459 960
[17] Niemczyk T, Deppe F, Huebl H, Menzel E P, Hocke F, Schwarz M J, Garcia-Ripoll J J, Zueco D, Hümmer T, Solano E, Marx A and Gross R 2010 Nat. Phys. 6 772
[18] Casanova J, Romero G, Lizuain I, García-Ripoll J J and Solano E 2010 Phys. Rev. Lett. 105 263603
[19] Forn-Díaz P, Lisenfeld J, Marcos D, García-Ripoll J J, Solano E, Harmans C J P M and Mooij J E 2010 Phys. Rev. Lett. 105 237001
[20] Chen Q H, Li L, Liu T and Wang K L 2012 Chin. Phys. Lett. 29 014208
[21] Baust A, Hoffmann E, Haeberlein M, Schwarz M J, Eder P, Goetz J, Wulschner F, Xie E, Zhong L, Quijandría F, Zueco D, García Ripoll J J, García-Álvarez L, Romero G, Solano E, Fedorov K G, Menzel E P, Deppe F, Marx A and Gross R 2016 Phys. Rev. B 93 214501
[22] Forn-Díaz P, Lamata L, Rico E, Kono J and Solano E 2019 Rev. Mod. Phys. 91 025005
[23] Milonni P W, Ackerhalt J R and Galbraith H W 1983 Phys. Rev. Lett. 50 966
[24] Emary C and Brandes T 2003 Phys. Rev. E 67 066203
[25] Chen Q H, Yang Y, Liu T and Wang K L 2010 Phys. Rev. A 82 052306
[26] Liu T, Feng M and Wang K L 2011 Phys. Rev. A 84 062109
[27] Naderi M H 2011 J. Phys. A: Math. Theor. 44 055304
[28] Wang Y M and Du G and Liang J Q 2012 Chin. Phys. B 21 044207
[29] Tang N, Xu T T and Zeng H S 2013 Chin. Phys. B 22 030304
[30] Mirzaee M and Batavani M 2015 Chin. Phys. B 24 040306
[31] Rabi I I 1936 Phys. Rev. 49 324
[32] Rabi I I 1937 Phys. Rev. 51 652
[33] Braak D 2011 Phys. Rev. Lett. 107 100401
[34] Braak D 2019 Symmetry 11 1259
[35] Dong Y H, Zhang W J, Liu J and Xie X T 2019 Chin. Phys. B 28 114202
[36] Feranchuk I D, Komarov L I and Ulyanenkov A P 1996 J. Phys. A: Math. Gen. 29 4035
[37] Tur É A 2000 Opt. Spectrosc. 89 574
[38] Pan F, Guan X, Wang Y and Draayer J P 2010 J. Phys. B: At. Mol. Opt. Phys. 43 175501
[39] Chen Q H, Liu T, Zhang Y Y and Wang K L 2011 Europhys. Lett. 96 14003
[40] He S, Wang C, Chen Q H, Ren X Z, Liu T and Wang K L 2012 Phys. Rev. A 86 033837
[41] Irish E K, Gea-Banacloche J, Martin I and Schwab K C 2005 Phys. Rev. B 72 195410
[42] Irish E K 2007 Phys. Rev. Lett. 99 173601
[43] Zhang Y Y, Chen Q H and Zhao Y 2013 Phys. Rev. A 87 033827
[44] Zhang Y W, Chen G, Yu L X, Liang Q F, Liang J Q and Jia S T 2011 Phys. Rev. A 83 065802
[45] Yu L X, Zhu S Q, Liang Q F, Chen G and Jia S T 2012 Phys. Rev. A 86 015803
[46] Liu M X, Ying Z J, An J H and Luo H G 2015 New J. Phys. 17 043001
[47] Ying Z J, Liu M X, Luo H G, Lin H Q and You J Q 2015 Phys. Rev. A 92 053823
[48] Mao B B, Liu M X, Wu W, Li L S, Ying Z J and Luo H G 2018 Chin. Phys. B 27 054219
[49] Gan C J and Zheng H 2010 Eur. Phys. J. D 59 473
[50] Mirzaee M and Kamani N 2013 Chin. Phys. B 22 094203
[51] Wang Z H and Zhou D L 2013 Chin. Phys. B 22 114205
[52] Wang Y M and Haw J Y 2015 Phys. Lett. A 379 779
[53] Cong L, Sun X M, Liu M X, Ying Z J and Luo H G 2017 Phys. Rev. A 95 063803
[54] Rahav S, Gilary I and Fishman S 2003 Phys. Rev. A 68 013820
[55] Goldman N and Dalibard J 2014 Phys. Rev. X 4 031027
[56] Eckardt A and Anisimovas E 2015 New J. Phys. 17 093039
[57] Bukov M, D'Alessio L and Polkovnikov A 2015 Adv. Phys. 64 139
[58] Eckardt A 2017 Rev. Mod. Phys. 89 011004
[59] Rodriguez-Vega M, Lentz M and Seradjeh B 2018 New J. Phys. 20 093022
[60] Oka T and Aoki H 2009 Phys. Rev. B 79 081406(R)
[61] Hemmerich A 2010 Phys. Rev. A 81 063626
[62] Bermudez A, Schaetz T and Porras D 2012 New J. Phys. 14 053049
[63] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D and Esslinger T 2014 Nature 515 237
[64] Gulácsi B and Dóra B 2015 Phys. Rev. Lett. 115 160402
[65] Meinert F, Mark M J, Lauber K, Daley A J and Nägerl H C 2016 Phys. Rev. Lett. 116 205301
[66] Mikami T, Kitamura S, Yasuda K, Tsuji N, Oka T and Aoki H 2016 Phys. Rev. B 93 144307
[67] Rodriguez-Vega M and Seradjeh B 2018 Phys. Rev. Lett. 121 036402 |
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