Skip to main content
Log in

Quantum Coherence in Non-Markovian Quantum Channels

  • Published:
Journal of Russian Laser Research Aims and scope

Abstract

We numerically simulate quantum coherence in a system of two qubits interacting with a reservoir for non-Markovian channels. The explicit form of the master equation is taken in terms of density-operator elements and is solved according to the initial conditions. In particular, we consider the effect of an Ohmic reservoir (OR) with Lorentz–Drude regularization (LDR) on the extent of coherence during dynamics. We describe the dynamical behavior of the coherence for low, intermediate, and high-temperature reservoirs. We explain the effect of the ratio of the cutoff frequency (CF) to the quantum system frequency and the effect of temperature on the quantum coherence. We show that a decreasing ratio enhances coherence, while an increasing temperature decreases it.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W. H. Zurek, Rev. Mod. Phys., 75, 715 (2003).

    Article  ADS  Google Scholar 

  2. W.-L. You, Y. Wang, T.-C. Yi, et al., Phys. Rev. B, 97, 224420 (2018).

    Article  ADS  Google Scholar 

  3. A. Streltsov, G. Adesso, and M. B. Plenio, Rev. Mod. Phys., 89, 041003 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. M. N. Bera, A. Acin, M. Kus, et al., Rep. Prog. Phys., 80, 124001 (2017).

    Article  ADS  Google Scholar 

  6. L. K. Castelano, F. F. Fanchini, and K. Berrada, Phys. Rev. B, 94, 235433 (2016).

    Article  ADS  Google Scholar 

  7. R. Dermez and S. Abdel-Khalek, J. Russ. Laser Res., 32, 287 (2011).

    Article  Google Scholar 

  8. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev., 47, 777 (1935).

    Article  ADS  Google Scholar 

  9. E. Schrödinger, Proc. Cambridge Philos. Soc., 31, 555 (1935).

    Article  ADS  Google Scholar 

  10. J. S. Bell, Physics (Long Island City, N.Y.), 1, 195 (1964).

  11. V. Giovannetti, S. Lloyd, and L. Maccone, Science, 306, 1330 (2004).

    Article  ADS  Google Scholar 

  12. K. Berrada, Phys. Rev. A, 88, 013817 (2013).

    Article  ADS  Google Scholar 

  13. K. Berrada, J. Opt. Soc. Am. B, 34, 1912 (2017).

    Article  ADS  Google Scholar 

  14. K. Berrada, S. Abdel-Khalek, and C. H. R. Ooi, Phys. Rev. A, 86, 033823 (2012).

    Article  ADS  Google Scholar 

  15. M. Algarni, K. Berrada, S. Abdel-Khalek, and H. Eleuch, Symmetry, 13, 2327 (2021).

    Article  ADS  Google Scholar 

  16. M. Lostaglio, D. Jennings, and T. Rudolph, Nat. Commun., 6, 6383 (2015).

    Article  ADS  Google Scholar 

  17. O. Karlström, H. Linke, G. Karlström, and A. Wacker, Phys. Rev. B, 84, 113415 (2011).

    Article  ADS  Google Scholar 

  18. M. B. Plenio and S. F. Huelga, New J. Phys., 10, 113019 (2008).

    Article  ADS  Google Scholar 

  19. S. Lloyd, J. Phys. Conf. Ser., 302, 012037 (2011).

    Article  Google Scholar 

  20. C.-M. Li, N. Lambert, Y.-N. Chen, et al., Sci. Rep., 2, 885 (2012).

    Article  Google Scholar 

  21. T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett., 113, 140401 (2014).

    Article  ADS  Google Scholar 

  22. A. Streltsov, U. Singh, H. S. Dhar, et al., Phys. Rev. Lett., 115, 020403 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  23. X. Yuan, H. Zhou, Z. Cao, and X. Ma, Phys. Rev. A, 92, 022124 (2015).

    Article  ADS  Google Scholar 

  24. A. Winter and D. Yang, Phys. Rev. Lett., 116, 120404 (2016).

    Article  ADS  Google Scholar 

  25. M. O. Scully and M. Suhail Zubairy, Quantum Optics, Cambridge Uni. Press, New York (1997).

    Book  Google Scholar 

  26. M. Tsang, Phys. Rev. A, 88, 021801(R) (2013).

  27. T. Yu and J. H. Eberly, Phys. Rev. Lett., 97, 140403 (2006).

    Article  ADS  Google Scholar 

  28. M. D. Shulman, O. E. Dial, S. P. Harvey, et al., Science, 336, 202 (2012).

    Article  ADS  Google Scholar 

  29. M. J. A. Schuetz, E. M. Kessler, L. M. K. Vandersypen, et al., Phys. Rev. B, 89, 195310 (2014).

    Article  ADS  Google Scholar 

  30. A. Borras and M. Blaauboer, Phy. Rev. B, 84, 033301 (2011).

    Article  ADS  Google Scholar 

  31. T. Hiltunen and A. Harju, Phys. Rev. B, 89, 115322 (2014).

    Article  ADS  Google Scholar 

  32. D. Culcer, L. Cywiński, Q. Li, et al., Phys. Rev. B, 80, 205302 (2009).

    Article  ADS  Google Scholar 

  33. D. M. Kennes, V. Meden, and R. Vasseur, Phys. Rev. B, 90, 115101 (2014).

    Article  ADS  Google Scholar 

  34. R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett., 110, 240601 (2013).

    Article  ADS  Google Scholar 

  35. S. R. White, Phys. Rev. Lett., 69, 2863 (1992).

    Article  ADS  Google Scholar 

  36. G. Vidal, Phys. Rev. Lett., 93, 040502 (2004).

    Article  ADS  Google Scholar 

  37. U. Schollwock, Ann. Phys., 326, 96 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  38. D. Porras and J. I. Cirac, Phys. Rev. Lett., 92, 207901 (2004).

    Article  ADS  Google Scholar 

  39. D. Leibfried, B. DeMarco, V. Meyer, et al., Nature (London), 422, 412 (2003).

    Article  ADS  Google Scholar 

  40. F. Schmidt-Kaler, H. Häffner, M. Riebe, et al., Nature (London), 422, 408 (2003).

    Article  ADS  Google Scholar 

  41. Y.-N. Guo, Q.-L. Tian, K. Zeng, and Z.-D. Li, Quantum Inf. Process., 16, 310 (2017).

    Article  ADS  Google Scholar 

  42. M.-L. Hu and H. Fan, Sci. China-Phys. Mech. Astron., 63, 230322 (2020).

    Article  ADS  Google Scholar 

  43. W. Cui, Z. R. Xi, and Y. Pan, Phys. Rev. A, 77, 032117 (2008).

    Article  ADS  Google Scholar 

  44. S. Maniscalco, S. Olivares, and M. G. A. Paris, Phys Rev. A, 75, 062119 (2007).

    Article  ADS  Google Scholar 

  45. S. Maniscalco, J. Piilo, F. Intravaia, et al., Phys. Rev. A, 70, 032113 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  46. J. Zhang, R. B. Wu, C. W. Li, et al., Phys. Rev. A, 75, 022324 (2007).

    Article  ADS  Google Scholar 

  47. U. Weiss, Quantum Dissipative System, World Scientific Publishing, Singapore (1993).

    Book  MATH  Google Scholar 

  48. A. J. Leggett, S. Chakravarty, A. T. Dorsey, et al., Rev. Mod. Phys., 59, 1 (1987).

    Article  ADS  Google Scholar 

  49. W. Cui, Z. Xi, and Y. Pan, J. Phys. A: Math. Theor., 42, 155303 (2009).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. Berrada.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Algarni, M., Berrada, K. & Abdel-Khalek, S. Quantum Coherence in Non-Markovian Quantum Channels. J Russ Laser Res 43, 397–405 (2022). https://doi.org/10.1007/s10946-022-10064-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10946-022-10064-z

Keywords

Navigation