Skip to main content
SpringerLink
Log in

Dynamics and Protection of Quantum Discord of a Two-qubit System Moving in a (non)-Markovian Reservoir Under a Classical Driving: Two-photon Relaxation

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We study quantum discord dynamic of two atomic qubits moving inside a leaky cavity, where the two-qubit system is driven by a classical field. We suppose that the qubits are coupled to each other through dipole-dipole interaction and interacting asymmetrically with the cavity field via a two-photon relaxation. Using the time-dependent Schrödinger equation, we obtain the quantum state of the two-qubit system and study the dynamical behavior of the corresponding quantum discord. We discuss in detail the effects of the dipole-dipole interaction, atomic motion, atom-cavity coupling strength, classical driving and detuning between the qubit and the classical field (laser detuning) on the protection of initial qubit-qubit correlation in both the Markovian and non-Markovian regimes. We show that the dipole-dipole interaction and laser detuning destroy the initial correlation between the qubits in the stationary limit, however, the classical driving can effectively eliminate their destructive effects on the maintaining the initial correlation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. In order to provide a situation where the effects of scattering and trapping are ignored, the values of the system parameters must be chosen in such a way that the qubit momentum is large enough in comparison with the photon momentum [61].

  2. It should be noted that the motion of an atomic qubit can be treated classically if its de Broglie wavelength \(\lambda _B\) is much smaller than the wavelength \(\lambda _0\) of the resonant transition (\(\lambda _B/\lambda _0\ll 1\)) [62, 63].

References

  1. Ollivier, H., Zurek, W.H.: Phys. Rev. Lett. 88, 017901 (2002)

    Article  ADS  Google Scholar 

  2. Rossatto, D.Z., Werlang, T., Duzzioni, E.I., Villas-Boas, C.J.: Phys. Rev. Lett. 107, 153601 (2011)

    Article  ADS  Google Scholar 

  3. Chen, Y.-X., Li, S.-W.: Phys. Rev. A. 81, 032120 (2010)

    Article  ADS  Google Scholar 

  4. Bose, S.: Phys. Rev. Lett. 91, 207901 (2003)

    Article  ADS  Google Scholar 

  5. Ma, X.-S., Cheng, M.-T., Zhao, G.X., Wang, A.M.: Physica A. 391, 2500 (2012)

    Article  ADS  Google Scholar 

  6. Fanchini, F.F., Castelano, L.K., Caldeira, A.O.: New J. Phys. 12, 073009 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Chen, Y.-X., Li, S.-W., Yin, Z.: Phys. Rev. A. 82, 052320 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Datta, A., Shaji, A., Caves, C.M.: Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

  11. Brodutch, A.: Phys. Rev. A. 88, 022307 (2013)

    Article  ADS  Google Scholar 

  12. Su, X.: Chin. Sci. Bull. 59, 1083 (2014)

    Article  Google Scholar 

  13. Dakic, B., et al.: Nature Phys. 8, 666 (2012)

    Article  ADS  Google Scholar 

  14. Pirandola, S.: Sci. Rep. 4, 6956 (2014)

    Article  ADS  Google Scholar 

  15. Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: Phys. Rev. A. 80, 024103 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  22. Nourmandipour, A., Tavassoly, M.K., Bolorizadeh, M.A.: Opt. Soc. Am. B. 33, 1723 (2016)

    Article  ADS  Google Scholar 

  23. Ba An, N., Ba An, J., Kim, K.: Phys. Rev. A. 83, 032316 (2010)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. Huang, L.-Y., Fang, M.-F.: Chin. Phys. B. 19, 090318 (2010)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  32. Nourmandipour, A., Tavassoly, M.K., Rafiee, M.: Phys. Rev. A. 93, 022327 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. Dehghani, A., Mojaveri, B., Vaez, M.: Quantum. Inf. Proc. 19, 1 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. Jia, Y., Hu, J.: Phys. E. Low-dimens. Syst. Nanostruct. 114, 113583 (2019)

    Article  Google Scholar 

  38. Dehghani, A., Mojaveri, B., Vaez, M.: Int. J. Theor. Phys. 59, 3107 (2020)

    Article  Google Scholar 

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

    Article  Google Scholar 

  40. Mojaveri, B., Dehghani, A., Ahmadi, Z., Amiri Faseghandis, S.: Eur. Phys. J. Plus. 1, 25 (2020)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Yune, J., et al.: Opt. Express. 23, 26012 (2015)

    Article  ADS  Google Scholar 

  43. Yu, M., Fang, M.F.: Int. J. Theor. Phys. 56, 1937 (2017)

    Article  Google Scholar 

  44. Behzadi, N., Faizi, E., Heibati, O.: Quantum Inf. Process. 16, 257 (2017)

    Article  ADS  Google Scholar 

  45. Kenfack, L.T., Tchoffo, M., Javed, M., Fai, L.C.: Quantum Inf. Process. 19, 107 (2020)

    Article  ADS  Google Scholar 

  46. Joshi, A., Lawande, S.V.: Phys. Rev. A. 42, 1752 (1990)

    Article  ADS  Google Scholar 

  47. Leach, J., Rice, P.R.: Phys. Rev. Lett. 93, 103601 (2004)

    Article  ADS  Google Scholar 

  48. Breschi, E., et al.: Phys. Rev. A. 82, 063810 (2010)

    Article  ADS  Google Scholar 

  49. Kobayashi, Y., Shiraishi, Y.: Phys. Rev. A. 82, 063401 (2010)

    Article  ADS  Google Scholar 

  50. Hu, Y.-H., Fang, M.-F.: Open Physics. 10, 145 (2012)

    Article  ADS  Google Scholar 

  51. Moustos, D., Anastopoulos, C.: Phys. Rev. D. 95, 025020 (2017)

    Article  ADS  MathSciNet  Google Scholar 

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

  53. Calajo, G., Rabl, P.: Phys. Rev. A. 95, 043824 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  56. Wang, Q., Liu, R., Zou, H.-M., Long, D., Wang, J.: Phys. Scr. 97, 055101 (2022)

    Article  ADS  Google Scholar 

  57. Mojaveri, B., Dehghani, A., Taghipour, J.: Control of entanglement, single excited-state population and memory-assisted entropic uncertainty of two qubits moving in a cavity by using a classical driving field. Submitted to Eur. Phys. J, Plus (2022)

    Google Scholar 

  58. Mojaveri, B., Dehghani, A., Taghipour, J.: Witnessing entanglement between two two-level atoms coupled to a leaky cavity via two-photon relaxation Submitted to Eur. Phys. J. Plus. 137, 772 (2022)

  59. Englert, B.G., Schwinger, J., Barut, A.O., Sculy, M.O.: Europhys. Lett. 14, 25 (1991)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  65. Man, Z.-X., Su, F., Xia, Y.-J.: Chin. Sci. Bull. 58, 2423 (2013)

    Article  Google Scholar 

  66. Faraji, E., Baghshahi, H.R., Tavassoly, M.K.: Mod. Phys. Lett. B. 31, 1750038 (2017)

    Article  ADS  Google Scholar 

  67. Fei, S.-M., Jing, N.: Phys. Lett. A. 342, 77 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  68. Katsuki, H., et al.: Nat. Commun. 4, 2801 (2013)

    Article  ADS  Google Scholar 

  69. Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  73. Datta, A., Shaji, A., Caves, C.M.: Phys. Rev. Lett. 100, 050502 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    J. Taghipour & B. Mojaveri

  2. Department of Physics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

    A. Dehghani

Authors
  1. J. Taghipour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Mojaveri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Dehghani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Mojaveri.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Taghipour, J., Mojaveri, B. & Dehghani, A. Dynamics and Protection of Quantum Discord of a Two-qubit System Moving in a (non)-Markovian Reservoir Under a Classical Driving: Two-photon Relaxation. Int J Theor Phys 61, 213 (2022). https://doi.org/10.1007/s10773-022-05192-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-022-05192-w

Keywords

Search

Navigation