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Coping with attenuation of quantum correlations of two qubit systems in dissipative environments: multi-photon transitions

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Abstract

In this paper we investigate the dynamics of entanglement and quantum discord, as two measures of quantum correlation resources, between two effective two-level atoms interacting with a dissipative environment at zero temperature in the presence of Kerr medium and Stark shift where m-photon transitions are allowed. Also, dipole–dipole interaction between the two atoms is taken into account. The results show that, the entanglement and quantum discord between the two atoms, which have similar behaviour qualitatively, both can be protected by means of the adjustment of Stark shift, Kerr parameter and dipole–dipole interaction. In other words, the Stark shift besides Kerr medium effect always ensure a noticeable maintenance of entanglement for m-photon processes in the Markovian and non-Markovian regimes. In particular, we find that in the non-Markovian regime, as the strengths of Stark shift, the Kerr medium and dipole–dipole interaction are increased, the amount of entanglement, as well as quantum discord approach to their maximum value, i.e., quantum correlations are well-protected.

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References

  1. M.A. Nielsen, I.L. Chuang,Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

  2. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  Google Scholar 

  3. H. Ollivier, W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  Google Scholar 

  4. S. Luo, Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

  5. F. Ciccarello, T. Tufarelli, V. Giovannetti, New J. Phys. 16, 013038 (2014)

    Article  ADS  Google Scholar 

  6. S. Luo, S. Fu, Phys. Rev. Lett. 106, 120401 (2011)

    Article  ADS  Google Scholar 

  7. A.B.A. Mohamed, H. Eleuch, J. Opt. Soc. Am. B 35, 47 (2018)

    Article  ADS  Google Scholar 

  8. A.B.A. Mohamed, Quant. Inf. Proc. 17, 96 (2018)

    Article  Google Scholar 

  9. A.B.A. Mohamed, H. Eleuch, Eur. Phys. J. D 69, 191 (2015)

    Article  ADS  Google Scholar 

  10. B. Dakic et al., Nat. Phys. 8, 666 (2012)

    Article  Google Scholar 

  11. A. Streltsov, W.H. Zurek, Phys. Rev. Lett. 111, 040401 (2013)

    Article  ADS  Google Scholar 

  12. M. Gu et al., Nat. Phys. 8, 671 (2012)

    Article  Google Scholar 

  13. H.S. Zeng, Y.P. Zheng, N. Tang, G.Y. Wang, Quant. Inf. Proc. 12, 1637 (2013)

    Article  Google Scholar 

  14. Z. Xu, W. Yang, X. Xiao, M. Feng, J. Phys. A: Math. Theor. 44, 395304 (2011)

    Google Scholar 

  15. Q.H. Chen, Y. Yang, T. Liu, K.L. Wang, Phys. Rev. A 82, 052306 (2010)

    Article  ADS  Google Scholar 

  16. J. Ma, Z. Sun, X.G. Wang, F. Nori, Phys. Rev. A 85, 062323 (2012)

    Article  ADS  Google Scholar 

  17. S. Golkar, M.K. Tavassoly, Chin. Phys. B 27, 040303 (2018)

    Article  ADS  Google Scholar 

  18. T. Yu, J. Eberly, Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  19. C.W. Gardiner, P. Zoller,Quantum Noise (Springer, Berlin, 1999)

  20. B. Bellomo, R.Lo. Franco, S. Maniscalco, G. Compagno, Phys. Rev. A 78, 060302(R) (2008)

    Article  ADS  Google Scholar 

  21. Y. Zhang, Z. Man, Y. Xia, Eur. Phys. J. D. 55, 173 (2009)

    Article  ADS  Google Scholar 

  22. Z. Man, Y. Zhang, F. Su, Y. Xia, Eur. Phys. J. D 58, 147 (2010)

    Article  ADS  Google Scholar 

  23. S. Maniscalco, F. Francica, R.L. Zaffino, N.L. Gullo, F. Plastina, Phys. Rev. Lett. 100, 090503 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  24. A. Nourmandipour, M.K. Tavassoly, M. Rafiee, Phys. Rev. A 93, 02232 (2016)

    Article  Google Scholar 

  25. C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  26. J.W. Pan, S. Gasparoni, R. Ursin, G. Weihs, A. Zeilinger, Nature (London) 423, 417 (2003)

    Article  ADS  Google Scholar 

  27. R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, U.L. Andersen, Nat. Phys. 4, 919 (2008)

    Article  Google Scholar 

  28. P.W. Shor, Phys. Rev. A 52, 2493(R) (1995)

    Article  ADS  Google Scholar 

  29. A.M. Steane, Phys. Rev. Lett. 77, 793 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  30. I. Sainz, G. Bjork, Phys. Rev. A 77, 052307 (2008)

    Article  ADS  Google Scholar 

  31. A.N. Korotkov, K. Keane, Phys. Rev. A 81, 040103(R) (2010)

    Article  ADS  Google Scholar 

  32. J.C. Lee, Y.C. Jeong, Y.S. Kim, Y.H. Kim, Opt. Express 19, 16309 (2011)

    Article  ADS  Google Scholar 

  33. Q. Sun, M. Al-Amri, L. Davidovich, M.S. Zubairy, Phys. Rev. A 82, 052323 (2010)

    Article  ADS  Google Scholar 

  34. Y.S. Kim, J.C. Lee, O. Kwon, Y.H. Kim, Nat. Phys. 8, 117 (2012)

    Article  Google Scholar 

  35. Q.J. Tong, J.H. An, H.G. Luo, C.H. Oh, Phys. Rev. A 81, 052330 (2010)

    Article  ADS  Google Scholar 

  36. W.L. Yang, J.H. An, C. Zhang, M. Feng, C.H. Oh, Phys. Rev. A 87, 022312 (2013)

    Article  ADS  Google Scholar 

  37. C. Chen, C.J. Yang, J.H. An, Phys. Rev. A 93, 062122 (2016)

    Article  ADS  Google Scholar 

  38. D. Park, https://doi.org/arXiv:1703.09341

  39. Y.J. Zhang, X.B. Zou, Y.J. Xia, G.C. Guo, J. Phys. B 44, 035503 (2011)

    Article  ADS  Google Scholar 

  40. T.G. Rudolph, H.S. Freedhoff, Z. Ficek, Phys. Rev. A 58, 1296 (1998)

    Article  ADS  Google Scholar 

  41. M. Abdel-Aty, H. Moya-Cessa, Phys. Lett. A 369, 372 (2007)

    Article  ADS  Google Scholar 

  42. H.R. Baghshahi, M.K. Tavassoly, M.J. Faghihi, Laser Phys. 24, 125203 (2014)

    Article  ADS  Google Scholar 

  43. H.R. Baghshahi, M.K. Tavassoly, A. Behjat, Chin. Phys. B 23, 074203 (2014)

    Article  Google Scholar 

  44. T. Nasreen, M.S.K. Razmi, J. Opt. Soc. Am. B 8, 2303 (1991)

    Article  ADS  Google Scholar 

  45. T. Nasreen, M.S.K. Razmi, Phys. Rev. A 46, 4161 (1992)

    Article  ADS  Google Scholar 

  46. Y. Wu, X. Yang, Phys. Rev. Lett. 98, 013601 (2007)

    Article  ADS  Google Scholar 

  47. Y.H. Hu, M.F. Fang, C.L. Jiang, J.W. Cai, J. Mod. Opt. 55, 3549 (2008)

    ADS  Google Scholar 

  48. B. Ghosh, A.S. Majumdar, N. Nayak, J. Phys. B: At, Mol. and Opt. Phys. 41, 065503 (2008)

    Article  Google Scholar 

  49. S. Golkar, M.K. Tavassoly, Laser Phys. Lett. 15, 035205 (2018)

    Article  ADS  Google Scholar 

  50. A.S.F. Obada, M.M.A. Ahmed, E.M. Khalil, S.I. Ali, Opt. Commun. 287, 215 (2013)

    Article  ADS  Google Scholar 

  51. T. Rickes et al., J. Chem. Phys. 113, 534 (2000)

    Article  ADS  Google Scholar 

  52. M. Brune, J.M. Raimond, P. Goy, L. Davidovich, S. Haroche, Phys. Rev. Lett. 59, 1899 (1987)

    Article  ADS  Google Scholar 

  53. A. Biswas, G.S. Agarwal, Phys. Rev. A 69, 062306 (2004)

    Article  ADS  Google Scholar 

  54. S. Dasgupta, A. Biswas, G.S. Agarwal, Phys. Rev. A 71, 012333 (2005)

    Article  ADS  Google Scholar 

  55. X.B. Zou, Y.F. Xiao, S.B. Li, G.C. Guo, Phys. Rev. A 75, 064301 (2007)

    Article  ADS  Google Scholar 

  56. M.J. Fernée, H.R. Dunlop, G.J. Milburn, Phys. Rev. A 75, 043815 (2007)

    Article  ADS  Google Scholar 

  57. F. Soto-Eguibar, V. Arrizon, A. Zuñiga-Segundo, H. Moya-Cessa, Opt. Lett. 39, 6158 (2014)

    Article  ADS  Google Scholar 

  58. M. Hillery, Phys. Rev. A 44, 4578 (1991)

    Article  ADS  Google Scholar 

  59. C.C. Gerry, Phys. Rev. A 59, 4095 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  60. Y.B. Sheng, L. Zhou, S.M. Zhao, B.Y. Zheng, Phys. Rev. A 85, 012307 (2012)

    Article  ADS  Google Scholar 

  61. D. Vitali, M. Fortunato, P. Tombesi, Phys. Rev. Lett. 85, 445 (2000)

    Article  ADS  Google Scholar 

  62. J. Pachos, S. Chountasis, Phys. Rev. A 62, 052318 (2000)

    Article  ADS  Google Scholar 

  63. G. R. Honarasa, M. K. Tavassoly, Phys. Scr. 86, 035401 (2012)

    Article  ADS  Google Scholar 

  64. L.S. Aguiar, P.P. Munhoz, A. Vidiella-Barranco, J.A. Roversi, J. Opt. B 7, S769 (2005)

    Article  ADS  Google Scholar 

  65. X.P. Liao, M.F. Fang, J.W. Cai, X.J. Zheng, Chin. Phys. B 17, 2137 (2008)

    Article  ADS  Google Scholar 

  66. E.K. Bashkirov, M.P. Stupatskaya, Laser Phys. 19, 525 (2009)

    Article  ADS  Google Scholar 

  67. S. Valizadeh, M.K. Tavassoly, N. Yazdanpanah, Indian J. Phys. 92, 955 (2018)

    Article  ADS  Google Scholar 

  68. G.F. Zhang, Z.Y. Chen, Opt. Commun. 275, 274 (2007)

    Article  ADS  Google Scholar 

  69. M. Han, Y.J. Zhang, Y.J. Xia, Int. J. Quant. Inf. 9, 1413 (2011)

    Article  Google Scholar 

  70. R.R. Puri, R.K. Bullough, J. Opt. Soc. Am. B 5, 2021 (1988)

  71. H.P. Breuer, F. Petruccione,The Theory of Open Quantum Systems (Oxford University Press, New York, 2002)

  72. H. Spohn, Rev. Mod. Phys. 52, 569 (1980)

    Article  ADS  Google Scholar 

  73. B.J. Dalton, S.M. Barnett, B.M. Garraway, Phys. Rev. A 64, 053813 (2001)

    Article  ADS  Google Scholar 

  74. B.M. Garraway, Phys. Rev. A 55, 2290 (1997)

    Article  ADS  Google Scholar 

  75. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  76. A.B.A. Mohamed, Quant. Inf. Proc. 12, 1141 (2013)

    Article  Google Scholar 

  77. A.S.F. Obada et al., J. Mod. Opt. 62, 918 (2015)

    Article  ADS  Google Scholar 

  78. L. Henderson, V. Vedral, J. Phys. A: Math. Gen. 34, 6899 (2001)

    Article  ADS  Google Scholar 

  79. V. Vedral, Phys. Rev. Lett. 90, 050401 (2003)

    Article  ADS  Google Scholar 

  80. M. Ali, A.R.P. Rau, G. Alber, Phys. Rev. A 81, 042105 (2010)

    Article  ADS  Google Scholar 

  81. X. Hao, C.L. Ma, J.J. Sha, J. Phys. A 43, 425302 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  82. C.Z. Wang, C.X. Liu, L.Y. Nie, J.F. Li, J. Phys. B 44, 015503 (2011)

    Article  ADS  Google Scholar 

  83. Y. Li, J. Zhou, H. Guo, Phys. Rev. A 79, 012309 (2009)

    Article  ADS  Google Scholar 

  84. G.Y. Wang, Y.N. Guo, Int. J. Theor. Phys. 56, 1585 (2017)

    Article  Google Scholar 

  85. L. Yan, Y.J. Xia, Acta Sin. Quant. Opt. 20, 16 (2014)

    Google Scholar 

  86. X. Xiao, M.F. Fang, Y.L. Li, G.D. Kang, C. Wu, Opt. Commun. 283, 3001 (2010)

    Article  ADS  Google Scholar 

  87. B. Wang, Z.Y. Xu, Z.Q. Chen, M. Feng, Phys. Rev. A 81, 014101 (2010)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Atomic and Molecular Group, Faculty of Physics, Yazd University, Yazd, Iran

    Sare Golkar & Mohammad Kazem Tavassoly

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  1. Sare Golkar
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  2. Mohammad Kazem Tavassoly
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Correspondence to Mohammad Kazem Tavassoly.

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Golkar, S., Tavassoly, M.K. Coping with attenuation of quantum correlations of two qubit systems in dissipative environments: multi-photon transitions. Eur. Phys. J. D 72, 184 (2018). https://doi.org/10.1140/epjd/e2018-90212-x

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