Effective Hamiltonian of the Jaynes-Cummings model beyond rotating-wave approximation

doi:10.1088/1674-1056/abd930

中国物理B ›› 2021, Vol. 30 ›› Issue (6): 64204-064204.doi: 10.1088/1674-1056/abd930

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

收稿日期:2020-11-17 修回日期:2021-01-04 接受日期:2021-01-07 出版日期:2021-05-18 发布日期:2021-05-18
通讯作者: Qing Sun E-mail:sunqing@cnu.edu.cn
基金资助:
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).

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

Received:2020-11-17 Revised:2021-01-04 Accepted:2021-01-07 Online:2021-05-18 Published:2021-05-18
Contact: Qing Sun E-mail:sunqing@cnu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Jaynes-Cummings model, Floquet theory, high-frequency approximation

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.

Key words: Jaynes-Cummings model, Floquet theory, high-frequency approximation

中图分类号: (Cavity quantum electrodynamics; micromasers)

42.50.Pq

42.50.-p (Quantum optics) 37.30.+i (Atoms, molecules, andions incavities)

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[J]. 中国物理B, 2021, 30(6): 64204-064204.

参考文献

[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

Effective Hamiltonian of the Jaynes-Cummings model beyond rotating-wave approximation

Effective Hamiltonian of the Jaynes-Cummings model beyond rotating-wave approximation

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Mengmeng Luo(罗萌萌), Wenxiao Liu(刘文晓), Yuetao Chen(陈悦涛), Shangbin Han(韩尚斌), and Shaoyan Gao(高韶燕). Environmental parameter estimation with the two-level atom probes[J]. 中国物理B, 2022, 31(5): 50304-050304.
[2]	Kang-Ying Du(杜康英), Ya-Jie Ma(马雅洁), Shao-Xiong Wu(武少雄), and Chang-Shui Yu(于长水). Quantum speed limit for the maximum coherent state under the squeezed environment[J]. 中国物理B, 2021, 30(9): 90308-090308.
[3]	Jing-Ying Wei(魏静莹), Qing Wang(王青), and Jian Jing(荆坚). Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces[J]. 中国物理B, 2021, 30(11): 110307-110307.
[4]	Meng-Nan Chen(陈梦南) and Wen-Chao Chen(陈文潮). Photoinduced Weyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator[J]. 中国物理B, 2021, 30(11): 110308-110308.
[5]	王彦懿, 方卯发. Generation of sustained optimal entropy squeezing of a two-level atom via non-Hermitian operation[J]. 中国物理B, 2018, 27(11): 114207-114207.
[6]	M. Mirzaee, M. Batavani. Atom-field entanglement in the Jaynes–Cummings modelwithout rotating wave approximation[J]. , 2015, 24(4): 40306-040306.
[7]	姜海波, 张丽萍, 于建江. Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure[J]. , 2015, 24(2): 20502-020502.
[8]	张永明, 罗纪生. Application of Arnoldi method to boundary layer instability[J]. 中国物理B, 2015, 24(12): 124701-124701.
[9]	Seyed Mahmoud Ashrafi, Mohammad Reza Bazrafkan. New approach to solving master equations of density operator for the Jaynes Cummings model with cavity damping[J]. , 2014, 23(9): 90303-090303.
[10]	马悦, 董锟, 田贵花. Evolution of entanglement between qubits ultra-strongly coupling to a quantum oscillator[J]. , 2014, 23(9): 94204-094204.
[11]	H R Baghshahi, M K Tavassoly, A Behjat. Entropy squeezing and atomic inversion in the k-photon Jaynes-Cummings model in the presence of the Stark shift and a Kerr medium：A full nonlinear approach[J]. , 2014, 23(7): 74203-074203.
[12]	M. Mirzaee, N. Kamani. Analytical approach to dynamics of transformed rotating-wave approximation with dephasing[J]. 中国物理B, 2013, 22(9): 94203-094203.
[13]	胡要花, 王军强. Quantum correlations between two non-interacting atoms under the influence of a thermal environment[J]. 中国物理B, 2012, 21(1): 14203-014203.
[14]	刘王云, 安毓英, 杨志勇. Properties of field quantum entropy evolution in the Jaynes--Cummings model with initial squeezed coherent states field[J]. 中国物理B, 2007, 16(12): 3704-3709.
[15]	高云峰, 冯健, 王继锁. Evolution of field entropy and entanglement in the intensity-dependent two-mode Jaynes-Cummings model　　　　[J]. 中国物理B, 2005, 14(5): 980-984.