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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.
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Keywords:
- quantum entanglement /
- non-Markovian effect
[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 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 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 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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[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 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 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 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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