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Robustness of Wigner function negativity under the exciton-exciton interaction effects inside two coupled semiconductor quantum dots

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Abstract

We analyze theoretically the Wigner function negativity for thermal density matrix of analogous and equidistant two coupled semiconductor quantum dots at different temperatures. In this respect, we explore the quantum influences of the temperature, the external electric field, the Förster interaction and the exciton-exciton dipole interaction energy on its behavior. In particular, we show that the negativity of wigner function still survives for large values of temperature ensuring that the non-classicality of the two coupled semiconductor quantum dots system does not get lost under thermal effect. Moreover, we show that this negativity is hypersensitive to the external electric field effect, nevertheless, its sensitivity to this effect is extensively perturbed for higher values of Förster interaction, temperature and exciton-exciton dipole interaction energy. Further, we show that increasing this latter enhances the quantumness of system as the negativity of wigner function also increases.

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References

  1. Wigner, E.P.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749 (1932)

    Article  ADS  MATH  Google Scholar 

  2. Kenfack, A., Zyczkowski, K.: Negativity of the Wigner function as an indicator of non-classicality. J. Opt. B: Quant. Semiclass. Opt. 6, 396 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  3. Lee, K.F., Reil, F., Bali, S., Wax, A., Thomas, J.E.: Heterodyne measurement of Wigner distributions for classical optical fields. Opt. Lett. 24, 1370 (1999)

    Article  ADS  Google Scholar 

  4. Mukamel, E., Banaszek, K., Walmsley, I.A., Dorrer, C.: Direct measurement of the spatial Wigner function with area-integrated detection. Opt. Lett. 28, 1317 (2003)

    Article  ADS  Google Scholar 

  5. Smith, B.J., Killett, B., Raymer, M.G., Walmsley, I.A., Banaszek, K.: Measurement of the transverse spatial quantum state of light at the single-photon level. Opt. Lett. 30, 3365 (2005)

    Article  ADS  Google Scholar 

  6. Szydłowski, D., Wołoszyn, M., Spisak, B.J.: Phase-space description of wave packet approach to electronic transport in nanoscale systems. Semicond. Sci. Technol. 28, 105022 (2013)

    Article  ADS  Google Scholar 

  7. Benedict, G.M., Czirjk, A.: Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms. Phys. Rev. A 60, 4034 (1999)

    Article  ADS  Google Scholar 

  8. Sadeghi, P., Khademi, S., Nasiri, S.: Nonclassicality indicator for the real phase-space distribution functions. Phys. Rev. A 82, 012102 (2010)

    Article  ADS  Google Scholar 

  9. Siyouri, F.Z.: Comparative study of entanglement and wigner function for multi-qubit GHZ-Squeezed state. Commun. Theor. Phys. 68, 729 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  10. Siyouri, F., El Baz, M., Hassouni, Y.: The negativity of Wigner function as a measure of quantum correlations. Quantum Inf. Proc. 15, 4237–4252 (2016)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Siyouri, F., El Baz, M., Hassouni, Y.: Role of Wigner function in studying quantum correlations. Int. J. Mod. Phys. B 30, 1650187 (2016)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Siyouri, F.Z.: Markovian and non-Markovian dynamics of non-classical correlations and Wigner function for GHZ-type coherent states. Int. J. Theor. Phys. 58(1), 103–113 (2019)

    Article  MATH  Google Scholar 

  13. Simon, R.: Peres-Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2726 (2000)

    Article  ADS  Google Scholar 

  14. Taghiabadi, R., Akhtarshenas, S.J., Sarbishaei, M.: Revealing quantum correlation by negativity of the Wigner function. Quantum Inf. Proc. 15, 1999 (2016)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Mari, A., Eisert, J.: Positive Wigner functions render classical simulation of quantum computation efficient. Phys. Rev. Lett. 109, 230503 (2012)

    Article  ADS  Google Scholar 

  16. Veitch, V., Wiebe, N., Ferrie, C., Emerson, J.: Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation. New J. Phys. 15, 013037 (2013)

    Article  ADS  MATH  Google Scholar 

  17. Nazir, A., Brendon, W., Lovett, Sean D., Barrett, John H., Reina, G., Andrew, D.: Anticrossings in Förster coupled quantum dots. Briggs Phys. Rev. B 71, 045334 – Published 27 January (2005)

  18. Shinkai, G., Hayashi, T., Ota, T., Fujisawa, T.: Correlated coherent oscillations in coupled semiconductor charge qubits. Phys. Rev. Lett. 103, 056802 (2009)

    Article  ADS  Google Scholar 

  19. Chen, G., Bonadeo, N.H., Steel, D.G., Gammon, D., Katzer, D.S., Park, D., Sham, L.J.: Optically induced entanglement of excitons in a single quantum dot. Science 289, 1906 (2000)

    Article  ADS  Google Scholar 

  20. Fanchini, F.F., Castelano, L.K., Caldeira, A.O.: Entanglement versus quantum discord in two coupled double quantum dots. New J. Phys. 12, 073009 (2010)

    Article  ADS  Google Scholar 

  21. Shojaei, S., Mahdian, M., Yousefjani, R.: Electric field effects on quantum correlations in three coupled semiconductor quantum dots. Int. J. Quantum Inf. 11(01), 1350009 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Mansour, H. A., Siyouri, F. Z., Faqir, M., Baz, M. E.: Quantum Correlations Dynamics In Two Coupled Semiconductor InAs Quantum Dots. arXiv preprint arXiv:2003.01158 (2020)

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

    MATH  Google Scholar 

  24. Nishibayashi, K., Kawazoe, T., Ohtsu, M., Akahane, K., Yamamoto, N.: Observation of interdot energy transfer between inas quantum dots. Appl. Phys. Lett. 93, 042101 (2008)

    Article  ADS  Google Scholar 

  25. Forster, T.: Intermolecular energy transfer and fluorescence. Ann. Phys. Leipzig. 6, 55–57 (1948)

  26. Gerry, C., Knight, P.: Introductory Quantum Optics. Cambridge University Press, Cambridge (2005)

    Google Scholar 

  27. Dodonov, V.V.J.: Nonclassical’states in quantum optics: asqueezed’review of the first 75 years. Opt. B Quantum Semiclass Opt. 4, R1–R33 (2002)

    Article  ADS  Google Scholar 

  28. Barenco, A., Deutsch, D., Ekert, A., Jozsa, R.: Conditional quantum dynamics and logic gates. Phys. Rev. Lett 74, 4083 (1995)

    Article  ADS  Google Scholar 

  29. He-jun, W., Fan, H.: Two-mode Wigner operator in \(\left\langle \eta \right| representation\). Mod. Phys. Lett. B 11, 544 (1997)

    MathSciNet  Google Scholar 

  30. Jiang, N.Q.: The n-partite entangled Wigner operator and its applications in Wigner function. J. Opt. B Quantum Semiclass Opt. 7, 264 (2005)

    Article  ADS  Google Scholar 

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Correspondence to Fatima-Zahra. Siyouri.

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Siyouri, FZ., Mansour, H.A. Robustness of Wigner function negativity under the exciton-exciton interaction effects inside two coupled semiconductor quantum dots. Quantum Inf Process 20, 136 (2021). https://doi.org/10.1007/s11128-021-03074-4

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