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Bipartite and tripartite entanglement in the two-qubit quantum Rabi model |
| Lijun Mao(毛丽君)†, Hongmei Wang(王红梅), Yaoyao Zhou(周瑶瑶), and Hui Guo(郭慧) |
| Department of Physics, Taiyuan Normal University, Jinzhong 030619, China |
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Abstract This study investigates the entanglement dynamics of the two-qubit quantum Rabi model (QRM) with both homogeneous and inhomogeneous couplings using the adiabatic approximation. The quantized field is initially prepared in a coherent state, while a separable state and a maximally entangled Bell state are selected as the initial two-qubit states. We characterize distinct types of entanglement generated among the subsystems through qubit-field interactions, with a focus on the bipartite entanglement between a single qubit and the field. Building on this, we examine tripartite correlations through the I-residual tangle, a measure that conclusively verifies the presence of genuine tripartite entanglement among the two qubits and the field. This work provides insights into the generation of tunable multipartite entanglement and the detection of quantum phase transitions in light-matter systems, such as circuit quantum electrodynamics (QED).
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Received: 24 February 2026
Revised: 16 May 2026
Accepted manuscript online: 03 July 2026
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PACS:
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03.65.Ud
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(Entanglement and quantum nonlocality)
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42.50.Pq
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(Cavity quantum electrodynamics; micromasers)
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42.50.Md
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(Optical transient phenomena: quantum beats, photon echo, free-induction decay, dephasings and revivals, optical nutation, and self-induced transparency)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11847111 and 11804246), the Scientific and Technological Innovation Program of Higher Education Institutions in Shanxi, China (Grant Nos. 2019L0822 and 2022L409), and the Natural Science Foundation of Shanxi Province, China (Grant No. 202203021221214). |
Corresponding Authors:
Lijun Mao
E-mail: maolijun516@163.com
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Cite this article:
Lijun Mao(毛丽君), Hongmei Wang(王红梅), Yaoyao Zhou(周瑶瑶), and Hui Guo(郭慧) Bipartite and tripartite entanglement in the two-qubit quantum Rabi model 2026 Chin. Phys. B 35 080303
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[1] Rabi I I 1936 Phys. Rev. 49 324
[2] Rabi I I 1937 Phys. Rev. 51 652
[3] ScullyMO and ZubairyMS 1997 Quantum Optics (Cambridge: Cambridge University Press)
[4] Makhlin Y, Scön G and Shnirman A 2001 Rev. Mod. Phys. 73 357
[5] Imamoḡlu A, Awschalom D D, Burkard G, DiVincenzo D P, Loss D, Sherwin M and Small A 1999 Phys. Rev. Lett. 83 4204
[6] Jaynes E T and Cummings F W 1963 Proc. IEEE 51 89
[7] 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
[8] Chiorescu I, Bertet P, Semba K, Nakamura Y, Harmans C J P M and Mooij J E 2004 Nature 431 159
[9] Bourassa J, Gambetta J M, Abdumalikov A A, Astafiev O, Nakamura Y and Blais A 2009 Phys. Rev. A 80 032109
[10] Forn-Díaz P, Lamata L, Rico E, Kono J and Solano E 2019 Rev. Mod. Phys. 91 025005
[11] Kockum A F, Miranowicz A, De Liberato S, Savasta S and Nori F 2019 Nat. Rev. Phys. 1 19
[12] Qing Y Q, You W L, Lan Y H and Liu M X 2025 Chin. Phys. Lett. 42 020501
[13] Dicke R H 1954 Phys. Rev. 93 99
[14] Leonau A U, San N Q, Ulyanenkov A P, Skoromnik O D and Feranchuk I D 2022 J. Phys. A: Math. Theor. 55 485301
[15] Chen Q H, Wang C, He S, Liu T and Wang K L 2012 Phys. Rev. A 86 023822
[16] Felicetti S, Pedernales J S, Egusquiza I L, Romero G, Lamata L, Braak D and Solano E 2015 Phys. Rev. A 92 033817
[17] Xie Q T, Cui S, Cao J P, Amico L and Fan H 2014 Phys. Rev. X 4 021046
[18] Dong X F, Xie Y F and Chen Q H 2020 Chin. Phys. B 29 020302
[19] Zhu W T, Ren Q B, Duan L W and Chen Q H 2016 Chin. Phys. Lett. 33 050302
[20] Peng J, Zheng J C, Yu J, Tang P H, Barrios G A, Zhong J X, Solano E, Albarrán-Arriagada F and Lamata L 2021 Phys. Rev. Lett. 127 043604
[21] Zhang Y Y, Hu Z X, Fu L, Luo H G, Pu H and Zhang X F 2021 Phys. Rev. Lett. 127 063602
[22] Grimaudo R, Magalhães de Castro A S, Messina A, Solano E and Valenti D 2023 Phys. Rev. Lett. 130 043602
[23] Sun X M, Cong L, Eckle H P, Ying Z J and Luo H G 2020 Phys. Rev. A 101 063832
[24] Yan Z Y, Qu P H, Xu B B, Zhang S H and Ma J Y 2022 Mod. Phys. Lett. B 35 2150213
[25] Grimaudo R, Falci G, Messina A, Paladino E, Sergi A, Solano E and Valenti D 2024 Phys. Rev. Research 6 043298
[26] Albert V V 2012 Phys. Rev. Lett. 108 180401
[27] Giannelli L, Paladino E, Grajcar M, Paraoanu G S and Falci G 2024 Phys. Rev. Research 6 013008
[28] López-Peña R, Cordero S, Nahmad-Achar E and Castaños O 2023 J. Phys. A: Math. Theor. 56 425303
[29] Shi Y Q, Cong L and Eckle H P 2022 Phys. Rev. A 105 062450
[30] Reyes-Bustos C, Braak D and Wakayama M 2021 J. Phys. A: Math. Theor. 54 285202
[31] Li Z M, Ferri D, Tilbrook D and Batchelor M T 2021 J. Phys. A: Math. Theor. 54 405201
[32] Lu X L, Li Z M, Mangazeev V V and Batchelor M T 2021 Chin. Phys. B 31 014210
[33] Nielsen M A and Chuang I L 2010 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[34] DiCarlo L, Chow J M, Gambetta J M, Bishop L S, Johnson B R, Schuster D I, Majer J, Blais A, Frunzio L, Girvin S M and Schoelkopf R J 2009 Nature 460 240
[35] Young S M, Jacobson N T and Petta J R 2022 Phys. Rev. Applied 18 064082
[36] HeWH, ZhangWH, Yuan X, Shen Y C and Zhang X M 2024 J. Phys. A: Math. Theor. 57 375306
[37] Bhattacharjee A, Jain P, Deshmukh J, Das S, Chand M, Patankar M P and Vijay R 2025 Sci. Rep. 15 4426
[38] Dey A 2025 Phys. Rev. A 111 043705
[39] Huan T T, Zhou R G and Ian H 2020 Sci. Rep. 10 12975
[40] Zhou Y, Xie S Y, Zhu C J and Yang Y P 2022 Phys. Rev. B 106 224404
[41] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[42] Coffman V, Kundu J and Wootters W K 2000 Phys. Rev. A 61 052306
[43] Osborne T J 2005 Phys. Rev. A 72 022309
[44] Mao L J, Huai S N and Zhang Y B 2015 J. Phys. A: Math. Theor. 48 345302
[45] Agarwal S, Hashemi Rafsanjani S M and Eberly J H 2012 Phys. Rev. A 85 043815
[46] Rungta P, Bužek V, Caves C M, Hillery M and Milburn G J 2001 Phys. Rev. A 64 042315
[47] Tessier T E, Deutsch I H, Delgado A and Fuentes-Guridi I 2003 Phys. Rev. A 68 062316
[48] DiCarlo L, Reed M D, Sun L, Johnson B R, Chow J M, Gambetta J M, Frunzio L, Girvin S M, Devoret M H and Schoelkopf R J 2010 Nature 467 574
[49] Devoret M H and Schoelkopf R J 2013 Science 339 1169
[50] Mo X T and Xue Z Y 2019 Front. Phys. 14 31602
[51] Blais A, Grimsmo A L, Girvin S M and Wallraff A 2021 Rev. Mod. Phys. 93 025005
[52] Qi S and Jing J 2023 Phys. Rev. A 107 042412
[53] Baksic A and Ciuti C 2014 Phys. Rev. Lett. 112 173601
[54] Soriente M, Donner T, Chitra R and Zilberberg O 2018 Phys. Rev. Lett. 120 183603
[55] CaiM L, Liu Z D, ZhaoWD,Wu Y K, Mei Q X, Jiang Y, He L, Zhang X, Zhou Z C and Duan L M 2021 Nat. Commun. 12 1126
[56] Yang Y T and Luo H G 2024 Chin. Phys. Lett. 41 120501
[57] Xu Y J and Pu H 2019 Phys. Rev. Lett. 122 193201
[58] Gietka K, Chwedeńczuk J,Wasak T and Piazza F 2019 Phys. Rev. B 99 064303
[59] Huang J F and Tian L 2023 Phys. Rev. A 107 063713
[60] Li Y C, Zhou Y H, Zhang Y, Bai Y K and Lin H Q 2024 New J. Phys. 26 023031 |
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