Skip to main content

Advertisement

SpringerLink
Log in

Effect of Disorder Amplitude on the Transport of Bose Einstein Condensates at Lowest Energy

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

Abstract

In this paper, we have presented an analytical and numerical study of a matter wave packet propagation in a disordered optical potential. We have used the self-consistent Born approximation which is well supported in weak disorder to calculate the real part of the self- energy RΣ(ε, p). The difference of 0.1 which appears between the analytical and numerical calculation is very acceptable. The varying of disorder amplitude change the position of the critical energy of the transition which it can be larger or smaller than correlation energy. This analysis gives new insight into numerical result. We propose to analyze the behavior of the energy distribution with this quantum corrected diffusion factor, which is a very important parameter for the mobility edge prediction. Our results open new interesting studies and provide good reference data for future research such as the behavior of the mobility edge in fractal systems and the evolution of the density of condensates in time and space.

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

References

  1. Billy, J., Josse, V., Zuo, Z., Bernard, A., Hambrecht, B., Lugan, P., Clément, D., Sanchez Palencia, L., Bouyer, P., Aspect, A.: Nature (London) 453, 891–894 (2008). https://doi.org/10.1038/nature07000

    Article  ADS  Google Scholar 

  2. Roati, G., D’Errico, C., Fallani, L., Fattori, M., Fort, C., Zaccanti, M., Modugno, G., Modugno, M., Inguscio, M.: Nature (London). 453, 895–898 (2008). https://doi.org/10.1038/nature07071

    Article  ADS  Google Scholar 

  3. Aubry, A., Cobus, L.A., Skipetrov, S.E., van Tiggelen, B., Derode, A., Page, J.H.: Phys. Rev. Lett. 112, 043903 (2014). https://doi.org/10.1103/PhysRevLett.112.043903

    Article  ADS  Google Scholar 

  4. Crosnier de Bellaistre, C., Trefzger, C., Aspect, A., Georges, A., Sanchez-Palencia, L.: Rev. A 97, 013613 (2018). https://doi.org/10.1103/PhysRevA.97.013613

    Article  Google Scholar 

  5. Anderson, P.W.: Phys. Rev. 109, 1492–1505 (1958). https://doi.org/10.1103/PhysRev.109.1492

    Article  ADS  Google Scholar 

  6. John, S.: Phys. Rev. Lett. 53, 2169–2172 (1984). https://doi.org/10.1103/PhysRevLett.53.2169

    Article  ADS  Google Scholar 

  7. Wiersma, D.S.: Nature(London) 390, 671–673 (1997). https://doi.org/10.1038/37757

    Article  ADS  Google Scholar 

  8. Storzer, M., Gross, P., Aegerter, C.M., Maret, G.: Phys. Rev. Lett. 96, 063904 (2006 ). https://doi.org/10.1103/PhysRevLett.96.063904

    Article  ADS  Google Scholar 

  9. Hu, H., Strybulevych, A., Page, J.H., Skipetrov, S.E., van Tiggelen, B.A.: Nature Phys. 4, 845–848 (2008). https://doi.org/10.1038/nphys1101

    Article  Google Scholar 

  10. Jendrzejewski, F., Bernard, A., Muller, K., Cheinet, P., Josse, V., Piraud, M., Pezze, L., Sanchez-Palencia, L., Aspect, A., Bouyer, P.: Nat. Phys. 8, 398 (2012). https://doi.org/10.1038/nphys2256

    Article  Google Scholar 

  11. Kondov, S.S., McGehee, W.R., Zirbel, J.J., DeMarco, B.: Science 334, 66 (2011). https://doi.org/10.1126/science.1209019

    Article  ADS  Google Scholar 

  12. Semeghini, G., Landini, M., Castilho, P., Roy, S., Spagnolli, G., Trenkwalder, A., Fattori, M., Inguscio, M., Modugno, G.: Nat. Phys. 11, 554 (2015). https://doi.org/10.1038/nphys3339

    Article  Google Scholar 

  13. Muller, C.A., Delande, D., Shapiro, B.: Phys. Rev. A 94, 033615 (2016)

    Article  ADS  Google Scholar 

  14. Delande, D., Orso, G.: Phys. Rev. Lett. 113, 060601 (2014)

    Article  ADS  Google Scholar 

  15. Skipetrov, S.E.: Phys. Rev. Lett. 121, 093601 (2018). https://doi.org/10.1103/PhysRevA.94.033615

    Article  ADS  Google Scholar 

  16. Volchkov, V., Pasek, M., Denechaud, V., Mukhtar, M., Aspect, A., Delande, D., Josse, V.: Phys. Rev. Lett. 6, 120 (2018). https://doi.org/10.1103/PhysRevLett.120.060404

    Article  Google Scholar 

  17. Guerin, W., Riou, J.-F., Gaebler, J.P., Josse, V., Bouyer, P., Aspect, A.: Phys. Rev. Lett. 97, 200402 (2006). https://doi.org/10.1103/PhysRevLett.97.200402

    Article  ADS  Google Scholar 

  18. Shapiro, B.: Phys. Rev. Lett. 99, 060602 (2007). https://doi.org/10.1103/PhysRevLett.99.060602

    Article  ADS  Google Scholar 

  19. Yedjour, A., Tiggelen van, B.A.: Eur. Phys. J. D. 59, 249255 (2010). https://doi.org/10.1140/epjd/e2010-00141-5

    Article  Google Scholar 

  20. Yedjour, A., et al.: Journal of Computational Electronics 13, 1 (2017). https://doi.org/10.1007/s10825-017-0953-3

    Article  Google Scholar 

  21. Sanchez-Palencia, L., Lewenstein, M.: Nature Phys. 6, 87–95 (2010). https://doi.org/10.1038/nphys1507

    Article  ADS  Google Scholar 

  22. Shapiro, B.: J. Phys. A: Math. Theory. 45, 143001 (2012). https://doi.org/10.1088/1751-8113/45/14/143001

    Article  ADS  Google Scholar 

  23. Aspect, A., Inguscio, M.: Phys. Today 62, 30 (2009). https://doi.org/10.1063/1.3206092

    Article  Google Scholar 

  24. Aubry, A., Skipetrov, S.E., van Tiggelen, B., Derode, A., Page, J.H.: Phys. Rev. Lett. 112, 043903 (2014). https://doi.org/10.1140/epjst/e2016-60340-3

    Article  ADS  Google Scholar 

  25. Kuhn, R.C., Miniatura, C., Delande, D., Sigwarth, O., Muller, C.M.: Phys. Rev. Lett. 98, 21041 (2007). https://doi.org/10.1103/PhysRevLett.95.250403

    Article  Google Scholar 

  26. Akkermans, E., Montambaux, G.: Mesoscopic Physics of Electrons and Photons . Cambridge University Press, Cambridge (2007)

    Book  Google Scholar 

  27. Castin, Y., Dum, R.: Phys. Rev. Lett. 77, 5315 (1996). https://doi.org/10.1103/PhysRevLett.77.5315

    Article  ADS  Google Scholar 

  28. Ioffe, A.F., Regel, A.R.: Non crystalline, amorphous, and liquid electronic semiconductors. Prog. Semicond. 4, 237–291 (1960)

    Google Scholar 

  29. Vollhardt, D., Wolfle, P.: Selfconsistent theory of anderson localization. In: Hanke, W., Kopaev, Y.V. (eds.) Electronic Phase Transitions. North-Holland, Amsterdam (1992)

  30. Lagendijk, A., van Tiggelen, B.A., Wiersma, D.S.: Physics Today. 62, 24 (2009). https://doi.org/10.1063/1.3206091

    Article  Google Scholar 

  31. Trappe, M.I., Delande, D., Muller, C.A.: J. Phys. A 48, 245102 (2015). https://doi.org/10.1088/1751-8113/4

    Article  ADS  MathSciNet  Google Scholar 

  32. Clément, D., Bouyer, P., Aspect, A., Sanchez-Palencia, L.: Phys. Rev. A. 77, 033631 (2008). https://doi.org/10.1103/PhysRevA.77.033631

    Article  ADS  Google Scholar 

  33. Skipetrov, S.E., Beltukov, Y.M.: Phys. Rev. B 98, 064206 (2018). https://doi.org/10.1103/PhysRevB.98.064206

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculté de Physique, USTO MB, B.p.1505 El M’Naour, 31000, Oran, Algérie

    Yedjour Afifa

  2. Laboratoire d´Instrumentation et Matériaux Avancés, Centre Universitaire Nour Bachir El-Bayadh, El-Bayadh, Algérie

    Mokaddem Allel & Bendouma Doumi

  3. Physics Department, Faculty of Science, University Dr.TaharMoulay of Saida, Saida, Algérie

    Bendouma Doumi

Authors
  1. Yedjour Afifa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mokaddem Allel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bendouma Doumi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yedjour Afifa.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Afifa, Y., Allel, M. & Doumi, B. Effect of Disorder Amplitude on the Transport of Bose Einstein Condensates at Lowest Energy. Int J Theor Phys 59, 3840–3851 (2020). https://doi.org/10.1007/s10773-020-04636-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-020-04636-5

Keywords

Search

Navigation