与热库耦合的光学腔内三原子间的纠缠动力学

邢贵超; 夏云杰

doi:10.7498/aps.67.20172546

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摘要

研究了与热库耦合的光学腔中三个相互作用的二能级原子间的纠缠动力学.采用拉普拉斯变换和下限共生等方法，通过数值计算，分析了原子间三体纠缠的演化以及腔场与热库间的两体纠缠演化，讨论了各耦合参数对系统纠缠演化的影响.研究结果表明：原子间纠缠在短时间内随着原子间耦合强度的增加而增加，随原子与腔场耦合强度的增加而减小，在长时极限下趋于一稳定值；体系的非马尔科夫性由原子与腔场的耦合强度以及热库的谱宽度共同决定，当热库与腔场为强耦合时，原子与腔场组成的系统遵循非马尔科夫动力学，此时随着热库谱宽的增加，原子系统由非马尔科夫性变为马尔科夫性，随着谱宽的继续增加，原子与腔场组成的系统遵循马尔科夫动力学，原子系统又表现出非马尔科夫性；调整腔场与热库的失谐可以有效抑制热库耗散对纠缠衰减的影响.

关键词:

量子纠缠 /
非马尔科夫效应

作者及机构信息

1.
曲阜师范大学物理工程学院, 山东省激光偏光与信息技术重点实验室, 曲阜 273165

通信作者: 夏云杰, yjxia_sd@126.com

基金项目: 国家自然科学基金（批准号：61675115，11704221，11647172）和山东省自然科学基金（批准号：ZR2016AP09）资助的课题.

参考文献

[1]	Horodedecki R, Horodedeck P, Horodedecki M, Horodedecki K 2009 Rev. Mod. Phys. 81 865
[2]	Zyczkowski K, Horodedecki P, Horodedecki M, Horodedecki R 2001 Phys. Rev. A 65 012101
[3]	Zhang Y D 2012 Principles of Quantum Information Physics (Beijing: Science Press) pp258-307 (in Chinese) [张永德 2012 量子信息物理原理(第一版) (北京: 科学出版社) 第258307页]
[4]	Bennett C H, Brassard G, Crpeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[5]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1892
[6]	Ekert A K 1991 Phys. Rev. Lett. 67 661
[7]	Yan L H, Gao Y F, Zhao J G 2009 Int. J. Theor. Phys. 48 2445
[8]	Murao M, Vedral V 2001 Phys. Rev. Lett. 86 352
[9]	Deng F G, Ren B C, Li X H 2017 Sci. Bull. 62 44
[10]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025
[11]	Yu T, Eberly J H 2006 Phys. Rev. Lett. 97 140403
[12]	Almeida M P, de Melo F, Hor-Meyll M, Salles A, Walborn S P, Souto Ribeiro P H, Davidovich L 2007 Science 316 579
[13]	Zong X L, Yang M 2016 Acta Phys. Sin. 65 080303 (in Chinese) [宗晓岚, 杨名 2016 物理学报 65 080303]
[14]	Breuer H P, Petruccione F 2002 Theory of Oopen Qquantum Systems (Oxford: Oxford University Press) pp568-617
[15]	Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[16]	Wu Q, Zhang Z M 2014 Chin. Phys. B 23 034203
[17]	Bai Y K, Ye M Y, Wang Z D 2009 Phys. Rev. A 80 044301
[18]	Bai Y K, Xu Y F, Wang Z D 2014 Phys. Rev. Lett. 113 100503
[19]	Maniscalco S, Francica F, Zaffino R L, Gullo N L, Plastina F 2008 Phys. Rev. Lett. 100 090503
[20]	Bellomo B, Lo Franco R, Compagno G 2008 Phys. Rev. A 77 032342
[21]	He Z, Li L W 2013 Acta Phys. Sin. 62 180301 (in Chinese) [贺志, 李龙武 2013 物理学报 62 180301]
[22]	Ma X S, Wang A M, Yang X D, You H 2005 J. Phys. A 38 2761
[23]	Ma X S, Wang A M, Cao Y 2007 Phys. Rev. B 76 155327
[24]	Ma X S, Liu G S, Wang A M 2011 Int. J. Quant. Inf. 9 791
[25]	Feng L J, Xia Y J 2015 Acta Phys. Sin. 64 010302 (in Chinese) [封玲娟, 夏云杰 2015 物理学报 64 010302]
[26]	Yang L Q, Feng L J, Song X X, Xue L J, Man Z X 2016 Acta Sin. Quantum Opt. 22 6 (in Chinese) [杨丽青, 封玲娟, 宋晓晓, 薛利娟, 满忠晓 2016 量子光学学报 22 6]
[27]	Ma T T, Chen Y S, Chen T, Hedemann S R, Yu T 2014 Phys. Rev. A 90 042108
[28]	Wootters W K 1998 Phys. Rev. Lett. 80 2245
[29]	Li M, Fei S M, Song H S 2009 J. Phys. A: Math. Theor. 42 145303
[30]	Sabn C, Garcia-Alcaine G 2008 Eur. Phys. J. D 48 435
[31]	An B N, Kim J, Kim K 2010 Phys. Rev. A 82 032316

施引文献

[1]	Horodedecki R, Horodedeck P, Horodedecki M, Horodedecki K 2009 Rev. Mod. Phys. 81 865
[2]	Zyczkowski K, Horodedecki P, Horodedecki M, Horodedecki R 2001 Phys. Rev. A 65 012101
[3]	Zhang Y D 2012 Principles of Quantum Information Physics (Beijing: Science Press) pp258-307 (in Chinese) [张永德 2012 量子信息物理原理(第一版) (北京: 科学出版社) 第258307页]
[4]	Bennett C H, Brassard G, Crpeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[5]	Hillery M, Bužek V, Berthiaume A 1999 Phys. Rev. A 59 1892
[6]	Ekert A K 1991 Phys. Rev. Lett. 67 661
[7]	Yan L H, Gao Y F, Zhao J G 2009 Int. J. Theor. Phys. 48 2445
[8]	Murao M, Vedral V 2001 Phys. Rev. Lett. 86 352
[9]	Deng F G, Ren B C, Li X H 2017 Sci. Bull. 62 44
[10]	Sheng Y B, Zhou L 2017 Sci. Bull. 62 1025
[11]	Yu T, Eberly J H 2006 Phys. Rev. Lett. 97 140403
[12]	Almeida M P, de Melo F, Hor-Meyll M, Salles A, Walborn S P, Souto Ribeiro P H, Davidovich L 2007 Science 316 579
[13]	Zong X L, Yang M 2016 Acta Phys. Sin. 65 080303 (in Chinese) [宗晓岚, 杨名 2016 物理学报 65 080303]
[14]	Breuer H P, Petruccione F 2002 Theory of Oopen Qquantum Systems (Oxford: Oxford University Press) pp568-617
[15]	Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[16]	Wu Q, Zhang Z M 2014 Chin. Phys. B 23 034203
[17]	Bai Y K, Ye M Y, Wang Z D 2009 Phys. Rev. A 80 044301
[18]	Bai Y K, Xu Y F, Wang Z D 2014 Phys. Rev. Lett. 113 100503
[19]	Maniscalco S, Francica F, Zaffino R L, Gullo N L, Plastina F 2008 Phys. Rev. Lett. 100 090503
[20]	Bellomo B, Lo Franco R, Compagno G 2008 Phys. Rev. A 77 032342
[21]	He Z, Li L W 2013 Acta Phys. Sin. 62 180301 (in Chinese) [贺志, 李龙武 2013 物理学报 62 180301]
[22]	Ma X S, Wang A M, Yang X D, You H 2005 J. Phys. A 38 2761
[23]	Ma X S, Wang A M, Cao Y 2007 Phys. Rev. B 76 155327
[24]	Ma X S, Liu G S, Wang A M 2011 Int. J. Quant. Inf. 9 791
[25]	Feng L J, Xia Y J 2015 Acta Phys. Sin. 64 010302 (in Chinese) [封玲娟, 夏云杰 2015 物理学报 64 010302]
[26]	Yang L Q, Feng L J, Song X X, Xue L J, Man Z X 2016 Acta Sin. Quantum Opt. 22 6 (in Chinese) [杨丽青, 封玲娟, 宋晓晓, 薛利娟, 满忠晓 2016 量子光学学报 22 6]
[27]	Ma T T, Chen Y S, Chen T, Hedemann S R, Yu T 2014 Phys. Rev. A 90 042108
[28]	Wootters W K 1998 Phys. Rev. Lett. 80 2245
[29]	Li M, Fei S M, Song H S 2009 J. Phys. A: Math. Theor. 42 145303
[30]	Sabn C, Garcia-Alcaine G 2008 Eur. Phys. J. D 48 435
[31]	An B N, Kim J, Kim K 2010 Phys. Rev. A 82 032316

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与热库耦合的光学腔内三原子间的纠缠动力学

1. 曲阜师范大学物理工程学院, 山东省激光偏光与信息技术重点实验室, 曲阜 273165

通信作者: 夏云杰, yjxia_sd@126.com

基金项目:

国家自然科学基金（批准号：61675115，11704221，11647172）和山东省自然科学基金（批准号：ZR2016AP09）资助的课题.

收稿日期: 2017-11-28

修回日期: 2018-01-18

刊出日期: 2018-04-05

摘要: 研究了与热库耦合的光学腔中三个相互作用的二能级原子间的纠缠动力学.采用拉普拉斯变换和下限共生等方法，通过数值计算，分析了原子间三体纠缠的演化以及腔场与热库间的两体纠缠演化，讨论了各耦合参数对系统纠缠演化的影响.研究结果表明：原子间纠缠在短时间内随着原子间耦合强度的增加而增加，随原子与腔场耦合强度的增加而减小，在长时极限下趋于一稳定值；体系的非马尔科夫性由原子与腔场的耦合强度以及热库的谱宽度共同决定，当热库与腔场为强耦合时，原子与腔场组成的系统遵循非马尔科夫动力学，此时随着热库谱宽的增加，原子系统由非马尔科夫性变为马尔科夫性，随着谱宽的继续增加，原子与腔场组成的系统遵循马尔科夫动力学，原子系统又表现出非马尔科夫性；调整腔场与热库的失谐可以有效抑制热库耗散对纠缠衰减的影响.

关键词:

量子纠缠 /
非马尔科夫效应

Entanglement dynamics of three atoms in optical cavity coupled to reservior

1.
Shandong Provincial Key Laboratory of Laser Polarization and Information Technology, Colleg of Physics and Engineering, Qufu Normal University, Qufu 273165, China

Fund Project:

Project supported by the National Natural Science Foundation of China (Grant Nos. 61675115, 11704221, 11647172) and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2016AP09).

Received Date: 28 November 2017

Accepted Date: 18 January 2018

Published Online: 05 April 2018

Abstract: Quantum entanglement is one of most remarkable features of quantum mechanics,and in recent years it has played a more and more important role in quantum information.However,real quantum system inevitably interacts with the environment,resulting in the entanglement decay or even entanglement sudden death,so it is necessary to study the entanglement dynamical properties of an open system under different environments.In this paper,we investigate the entanglement dynamic behaviors of three interacting two-level atoms in an optical cavity which is coupled to a structured zero-temperature bosonic reservoir.Laplace transform,LBC and other methods are utilized,through numerical method we analyze the entanglement dynamic behavios of tripartite of three atoms and bipartite of cavity and reservoir.We also discuss how the coupling parameters affect the entanglement dynamics.Results show that in a short time,the entanglement of tripartite increases with coupling strength of three atoms increasing,and a periodic oscillation appears, but entanglement of bipartite decreases.The entanglement of tripartite decreases with the coupling strength between atoms and cavity increasing and damping oscillation appears,but the entanglement of bipartite increases.In a long-time limit,the entanglement approaches to a steady value.The non-Markovian dynamics of the qubits is determined by both the coupling strength and the spectral width.The strong system-reservoir coupling regime results in the non-Markovian dynamics of system.As the spectral width increases,the system of three atoms transforms from non-Markovian regime to Markovian regime.The increasing of spectral width results in the Markovian dynamic behavior of system,but the system of the atoms falls into the non-Markovian regime once more.When the coupling between the cavity and reservoir is weak,the entanglement of three atoms increases as the detuning of the cavity and reservoir increases,but it is not obvious.When the coupling between the cavity and reservoir is strong,the entanglement of three atoms increases and a periodic oscillation appears with increasing the detuning between the cavity and reservoir,so we can effectively restrain the effects of dissipation of reservoir on entanglement decay by adjusting the detuning between the cavity and reservoir.

Keywords:

quantum entanglement /
non-Markovian effect

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