Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation

doi:10.1088/1674-1056/28/6/060303

中国物理B ›› 2019, Vol. 28 ›› Issue (6): 60303-060303.doi: 10.1088/1674-1056/28/6/060303

Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation

Mei-Jiao Wang(王美姣), Yun-Jie Xia(夏云杰)

1 College of Physics and Engineering, Qufu Normal University, Qufu 273165, China;
2 Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Qufu Normal University, Qufu 273165, China

收稿日期:2019-01-21 修回日期:2019-03-11 出版日期:2019-06-05 发布日期:2019-06-05
通讯作者: Yun-Jie Xia E-mail:yjxia@qfnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61675115 and 11704221).

Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation

Mei-Jiao Wang(王美姣)^1,2, Yun-Jie Xia(夏云杰)^1,2

1 College of Physics and Engineering, Qufu Normal University, Qufu 273165, China;
2 Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Qufu Normal University, Qufu 273165, China

Received:2019-01-21 Revised:2019-03-11 Online:2019-06-05 Published:2019-06-05
Contact: Yun-Jie Xia E-mail:yjxia@qfnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 61675115 and 11704221).

摘要/Abstract

摘要： We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths (IHBs) or two common heat baths (CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steady-state with stronger coupling regime between two qubits than qubit-baths. We do not make the rotating wave approximation (RWA) for the qubit-qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime, the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures. We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong (weak) coupling regime, the heat current increases (decreases) with coupling strength increasing when the temperature of one bath is lower (higher) than the other, and the energy detuning leads to a positive (negative) effect when the temperature is low (high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.

关键词: steady-state entanglement, equilibrium and nonequilibrium baths, heat current, rotating wave approximation

Abstract: We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths (IHBs) or two common heat baths (CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steady-state with stronger coupling regime between two qubits than qubit-baths. We do not make the rotating wave approximation (RWA) for the qubit-qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime, the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures. We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong (weak) coupling regime, the heat current increases (decreases) with coupling strength increasing when the temperature of one bath is lower (higher) than the other, and the energy detuning leads to a positive (negative) effect when the temperature is low (high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.

Key words: steady-state entanglement, equilibrium and nonequilibrium baths, heat current, rotating wave approximation

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

05.30.-d (Quantum statistical mechanics) 05.70.Ln (Nonequilibrium and irreversible thermodynamics)

王美姣, 夏云杰. Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation[J]. 中国物理B, 2019, 28(6): 60303-060303.

Mei-Jiao Wang(王美姣), Yun-Jie Xia(夏云杰). Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation[J]. Chin. Phys. B, 2019, 28(6): 60303-060303.

参考文献 34

[1]	Horodedecki R, Horodedecki P, Horodedecki M and Horodedecki K 2009 Rev. Mod. Phys. 81 865 doi: 10.1103/RevModPhys.81.865
[2]	Zyczkowski K, Horodedecki P, Horodedecki M and Horodedecki R 2001 Phys. Rev. A 65 012101 doi: 10.1103/PhysRevA.65.012101
[3]	Nielsen M and Chuang I 2000 Quantum Information and Computation (Cambridge: Cambridge University Press) pp. 12-15
[4]	Zurek W H 2003 Rev. Mod. Phys. 75 715 doi: 10.1103/RevModPhys.75.715
[5]	Zhang L, Yan Y, Wu C Q, Wang J S and Li B 2009 Phys. Rev. B 80 172301 doi: 10.1103/PhysRevB.80.172301
[6]	Zhang L, Wang J S and Li B 2010 Phys. Rev. B 81 100301(R)
[7]	Werlang T, Marchiori M A, Cornelio M F and Valente D 2014 Phys. Rev. E 89 062109
[8]	Man Z X, An N B and Xia Y J 2016 Phys. Rev. E 94 042135 doi: 10.1103/PhysRevE.94.042135
[9]	Shen H Z, Zhou Y H and Yi X X 2014 Phys. Rev. A 90 023849 doi: 10.1103/PhysRevA.90.023849
[10]	Ordonez-Miranda J, Ezzahri Y and Joulain K 2017 Phys. Rev. E 95 022128
[11]	Li B, Wang L and Casati G 2004 Phys. Rev. Lett. 93 184301 doi: 10.1103/PhysRevLett.93.184301
[12]	Joulain K, Drevillon J, Ezzahri Y and Ordonez-Miranda J 2016 Phys. Rev. Lett. 116 200601 doi: 10.1103/PhysRevLett.116.200601
[13]	Linden N, Popescu S and Skrzypczyk P 2010 Phys. Rev. Lett. 105 130401 doi: 10.1103/PhysRevLett.105.130401
[14]	Brunner N, Linden N, Popescu S and Skrzypczyk P 2012 Phys. Rev. E 85 051117 doi: 10.1103/PhysRevE.85.051117
[15]	Mitchison M T, Woods M P, Prior J and Huber M 2015 New J. Phys. 17 115013 doi: 10.1088/1367-2630/17/11/115013
[16]	Yu C S and Zhu Q Y 2014 Phys. Rev. E 90 052142 doi: 10.1103/PhysRevE.90.052142
[17]	Man Z X and Xia Y J 2017 Phys. Rev. E 96 012122
[18]	Brask J B and Brunner N 2015 Phys. Rev. E 92 062101
[19]	Zagoskin A M, Savel'ev S, Nori F and Kusmartsev F V 2012 Phys. Rev. B 86 014501
[20]	Long R and Liu W 2015 Phys. Rev. E 91 062137 doi: 10.1103/PhysRevE.91.062137
[21]	Zhao L M and Zhang G F 2017 Quantum Inf. Process. 16 216 doi: 10.1007/s11128-017-1665-0
[22]	Louisell W H and Walker L R 1965 Phys. Rev. 137 B204
[23]	Wall D F and Milbum G J 1985 Phys. Rev. A 31 2403 doi: 10.1103/PhysRevA.31.2403
[24]	Liao J Q, Huang J F and Kuang L M 2011 Phys. Rev. A 83 052110 doi: 10.1103/PhysRevA.83.052110
[25]	Huangfu Y and Jing J 2018 Sci. China-Phys. Mech. Astron. 61 010311 doi: 10.1007/s11433-017-9115-2
[26]	Hu L Z, Man Z X and Xia Y J 2018 Quantum Inf. Process. 17 45 doi: 10.1007/s11128-018-1825-x
[27]	Wang C and Chen Q H 2013 New J. Phys. 15 103020 doi: 10.1088/1367-2630/15/10/103020
[28]	Man Z X, Xia Y J and An N B 2011 J. Phys. B: At. Mol. Opt. Phys. 44 9
[29]	Deng W and Deng Y 2018 Phys. A 512 693 doi: 10.1016/j.physa.2018.07.044
[30]	Yang Y, Wang A M, Cao L Z, Zhao J and Lu H X 2018 Chin. Phys. B 27 090302 doi: 10.1088/1674-1056/27/9/090302
[31]	Gao D Y, Gao Q and Xia Y J 2018 Chin. Phys. B 27 060304 doi: 10.1088/1674-1056/27/6/060304
[32]	Decordi G L and Vidiella-Barranco A 2017 Opt. Commun. 387 366 doi: 10.1016/j.optcom.2016.10.017
[33]	Wootters W K 1998 Phys. Rev. Lett. 80 2245 doi: 10.1103/PhysRevLett.80.2245
[34]	Yu T, Eberly J H 2007 Quantum Inf. Comput. 7 459

Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation

Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation

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