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Entanglement protection of two qubits moving in an environment with parity-deformed fields

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Abstract

In this paper, we discuss a scheme for protecting entanglement between two qubits by employing the technique of reservoir engineering through the utilization of a leaky cavity with parity deformed fields. The qubits are moving inside the cavity reservoir, interacting with each other via the dipole-dipole coupling, and asymmetrically coupled to the parity deformed cavity modes. The parity deformed cavity modes introduce an intensity-dependent coupling between the qubits and cavity which acts as a control factor. We obtain the time-dependent as well as steady-state forms of the system’s density matrix when the total excitation number is one. Then, we discuss in detail the effects of different parameters on the entanglement protection in both the Markovian and non-Markovian regimes. It is deduced from the numerical results that the initial entanglement in the moving two-qubit system can be strongly protected by suitably choosing the parity deformation parameter. We find a region of qubit–environment couplings with values slightly deviated from the vicinity of the symmetric couplings configurations that may lead to much better protection. This region can be extended to include all the allowed qubit–environment coupling values by tailoring the parity deformation parameter. We show that a stronger entanglement protection can be also obtained by regularly increasing the velocity of the qubits, although, without the parity deformation, higher velocities do not necessarily guarantee entanglement protection. These results are helpful for the practical control of entanglement dynamics in the future.

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Data availability

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. Here we focus on the non-relativistic quantum description of the atom–cavity interaction. The relativistic effects of the light–matter interaction can be understood by means of the Unruh–DeWitt (UDW) model [51, 52]. The relativistic effect of particle detectors moving along the central axis of a cavity can be found in Ref. [53].

  2. In the optical regime, the atomic transition frequencies and atom–cavity couplings are of the order of \(10^{15}\) Hz and \(10^{7}\) Hz, respectively.

References

  1. E. Schrodinger, Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555 (1935)

    Article  ADS  MATH  Google Scholar 

  2. C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  3. M. Murao, D. Jonathan, M.B. Plenio, V. Vedral, Phys. Rev. A 59, 156 (1999)

    Article  ADS  Google Scholar 

  4. C.H. Bennett, S.J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  5. A.K. Ekert, Phys. Rev. Lett. 67, 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  6. R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  7. C. Simon, J. Kempe, Phys. Rev. A 65, 052327 (2002)

    Article  ADS  Google Scholar 

  8. T. Yu, J.H. Eberly, Phys. Rev. B 66, 193306 (2002)

    Article  ADS  Google Scholar 

  9. W. Dur, H.J. Briegel, Phys. Rev. Lett. 92, 180403 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. J.I. Cirac, T. Pellizzari, Science 273, 1207 (1996)

    Article  ADS  Google Scholar 

  12. M. Rafiee, A. Nourmandipour, S. Mancini, Phys. Rev. A 94, 012310 (2016)

    Article  ADS  Google Scholar 

  13. A.R.R. Carvalho, A.J.S. Reid, J.J. Hope, Phys. Rev. A 78, 012334 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  15. N. Ba An, J. Kim, K. Kim, Phys. Rev. A 82, 032316 (2010)

    Article  ADS  Google Scholar 

  16. X. Xiao, Y. Li, K. Zeng, C. Wu, J. Phys. B: At. Mol. Opt. Phys. 42, 235502 (2009)

    Article  ADS  Google Scholar 

  17. H. Li-Yuan, F. Mao-Fa, Chin. Phys. B 19, 090318 (2010)

    Article  Google Scholar 

  18. B. Raffah, S. Abdel-Khalek, K. Berrada et al., Eur. Phys. J. Plus 135, 467 (2020)

    Article  Google Scholar 

  19. M. Forozesh, A. Mortezapour, A. Nourmandipour, Eur. Phys. J. Plus 136, 778 (2021)

    Article  Google Scholar 

  20. S. Damodarakurup, M. Lucamarini, G. Di Giuseppe, D. Vitali, P. Tombesi, Phys. Rev. Lett. 103, 040502 (2009)

    Article  ADS  Google Scholar 

  21. D. Vitali, P. Tombesi, Phys. Rev. A 59, 4178 (1999)

    Article  ADS  Google Scholar 

  22. M.A. Fasihi, B. Mojaveri, Quantum Inf. Process. 18, 75 (2019)

    Article  ADS  Google Scholar 

  23. Z.X. Man, Y.J. Xia, R. Lo Franco, Sci. Rep. 5, 13843 (2015)

    Article  ADS  Google Scholar 

  24. N. Behzadi, B. Ahansaz, E. Feizi, Eur. Phys. J. D 71, 280 (2017)

    Article  ADS  Google Scholar 

  25. B. Mojaveri, A. Dehghani, Z. Ahmadi, Eur. Phys. J. Plus 136, 1 (2021)

    Article  Google Scholar 

  26. A. Dehghani, B. Mojaveri, M. Vaez, Quantum Inf. Process. 19, 1 (2020)

    Article  Google Scholar 

  27. Y. Jia, J. Hu, Phys. E. Low-Dimens. Syst. Nanostruct 114, 113583 (2019)

    Article  Google Scholar 

  28. Y. Akbari-Kourbolagh, S. Razavian, Eur. Phys. J. Plus 135, 284 (2020)

    Article  Google Scholar 

  29. A. Nourmandipour, A. Vafafard, A. Mortezapour, R. Franzosi, Sci. Rep. 11, 16259 (2021)

    Article  ADS  Google Scholar 

  30. J. Taghipour, B. Mojaveri, A. Dehghani, Eur. Phys. J. Plus 137, 772 (2022)

    Article  Google Scholar 

  31. A. Mortezapour, M.A. Borji, R.L. Franco, Laser Phys. Lett. 14, 055201 (2017)

    Article  ADS  Google Scholar 

  32. W. Chao, F. Mao-Fa, Chin. Phys. B 19, 020309 (2010)

    Article  Google Scholar 

  33. D. Park, arXiv preprint arXiv:1703.09341 (2017)

  34. S. Golkar, M.K. Tavassoly, A. Nourmandipour, J. Opt. Soc. Am. B 37, 400 (2020)

    Article  ADS  Google Scholar 

  35. S. Golkar, M.K. Tavassoly, Mod. Phys. Lett. A 34, 1950077 (2019)

    Article  ADS  Google Scholar 

  36. J. Taghipour, B. Mojaveri, A. Dehghani, Int. J. Theor. Phys. 61, 213 (2022)

    Article  Google Scholar 

  37. B. Mojaveri, A. Dehghani, J. Taghipour, Eur. Phys. J. Plus 137, 1065 (2022)

    Article  Google Scholar 

  38. J. Taghipour, B. Mojaveri, A. Dehghani, Mod. Phys. Lett. A 37, 2250141 (2022)

    Article  ADS  Google Scholar 

  39. C.H. Alderete, L. Villanueva Vergara, B.M. Rodriguez-Lara, Phys. Rev. A 95, 043835 (2017)

    Article  ADS  Google Scholar 

  40. C.H. Alderete, B.M. Rodriguez-Lara, Phys. Rev. A 95, 013820 (2017)

    Article  ADS  Google Scholar 

  41. B. Mojaveri, A. Dehghani, Eur. Phys. J. D 67, 179 (2013)

    Article  ADS  Google Scholar 

  42. A. Dehghani, B. Mojaveri, S. Shirin, M. Saedi, Ann. Phys. 362, 659 (2015)

    Article  ADS  Google Scholar 

  43. B. Mojaveri, A. Dehghani, S.A. Faseghandis, Eur. Phys. J. Plus 132, 128 (2017)

    Article  Google Scholar 

  44. B. Mojaveri, A. Dehghani, Z. Ahmadi, S. AmiriFaseghandis, Eur. Phys. J. Plus 1, 25 (2020)

    Google Scholar 

  45. B. Mojaveri, A. Dehghani, Z. Ahmadi, Phys. Scr. 96, 115102 (2021)

    Article  Google Scholar 

  46. A. Dehghani, B. Mojaveri, S. Shirin, S. Amiri Feseghandis, Sci. Rep. 6, 38069 (2016)

    Article  ADS  Google Scholar 

  47. A. Dehghani, B. Mojaveri, R. Jafarzadeh Bahrbeig, F. Nosrati, R.L. Franco, J. Opt. Soc. Am. B 33, 1858 (2019)

    Article  ADS  Google Scholar 

  48. H. Fakhri, S. Mirzaei, M. Sayyah-Fard, Quantum Inf. Process. 20, 1 (2021)

    Article  Google Scholar 

  49. H. Fakhri, M. Sayyah-Fard, Sci. Rep. 11, 1 (2021)

    Article  Google Scholar 

  50. R. Lang, M.O. Scully, W.E. Lamb Jr., Phys. Rev. A 7, 1778 (1973)

    Article  ADS  Google Scholar 

  51. W.G. Unruh, Phys. Rev. D 14, 870 (1976)

    Article  ADS  Google Scholar 

  52. B. DeWitt, in General Relativity: An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, 1979)

  53. R. Lopp, E. Martin-Martinez, D.N. Page, Class. Quantum Grav. 35, 224001 (2018)

    Article  ADS  Google Scholar 

  54. B.G. Englert, J. Schwinger, A.O. Barut, M.O. ScuUy, Europhys. Lett. 14(25), 25 (1991)

    Article  ADS  Google Scholar 

  55. S. Haroche, M. Brune, J.M. Raimond, Europhys. Lett. 14, 19 (1991)

    Article  ADS  Google Scholar 

  56. C. Leonardi, A. Vagliea, Opt. Commun. 97, 130 (1993)

    Article  ADS  Google Scholar 

  57. R.J. Cook, Phys. Rev. A 20, 224 (1979)

    Article  ADS  Google Scholar 

  58. M. Wilkens, Z. Bialynicka-Birula, P. Meystre, Phys. Rev. A 45, 477 (1992)

    Article  ADS  Google Scholar 

  59. C.J. Hood et al., Science 287, 1447 (2000)

    Article  ADS  Google Scholar 

  60. P.W.H. Pinkse et al., Nature 404, 365 (2000)

    Article  ADS  Google Scholar 

  61. F. Calogero, J. Math. Phys. 10, 2191 (1969)

    Article  ADS  Google Scholar 

  62. H.S. Green, Phys. Rev. 90, 270 (1953)

    Article  ADS  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  65. B. Bellomo, R. Lo Franco, G. Compagno, Phys. Rev. Lett. 99, 160502 (2007)

    Article  ADS  Google Scholar 

  66. D.V. Widder, The Laplace transform (Princeton Univ. Press, Princeton, 1946)

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  68. G. Mouloudakis, P. Lambropoulos, Quantum Inf. Process. 20, 331 (2021)

    Article  ADS  Google Scholar 

  69. A. Nourmandipour, M.K. Tavassoly, Eur. Phys. J. Plus 130, 148 (2015)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Azarbaijan Shahid Madani University, PO Box 51745-406, Tabriz, Iran

    B. Mojaveri & J. Taghipour

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  1. B. Mojaveri
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Correspondence to B. Mojaveri.

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Mojaveri, B., Taghipour, J. Entanglement protection of two qubits moving in an environment with parity-deformed fields. Eur. Phys. J. Plus 138, 263 (2023). https://doi.org/10.1140/epjp/s13360-023-03875-9

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