Skip to main content
SpringerLink
Log in

Landau Quantization for Λ-Type Neutral Atoms in an Homogeneous Spin-Dependent Gauge Potential

  • Condensed Matter
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

We investigate the quantum dynamics of neutral atoms subject to a uniform spin-dependent gauge field. In particular, we analyze a simple experimental scheme to generate the Landau quantization in a two-dimensional atomic gas with internal three-level Λ-type configuration. We show how energy eigenfunctions and eigenvalues are obtained and discuss the experimental conditions for which a variety of physical quantities of the atomic gas can exhibit quantum oscillations.

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

Similar content being viewed by others

References

  1. B. DeMarco, D.S. Jin, Science. 285, 1703 (1999)

    Article  Google Scholar 

  2. M.-O. Mewes, G. Ferrari, F. Schreck, A. Sinatra, C. Salomon, Phys. Rev A. 61(R), 011403 (2000)

    ADS  Google Scholar 

  3. L. Pitaevskii, S. Stringari. Bose-Einstein condensation (Clarendon Press, Oxford, 2003)

    MATH  Google Scholar 

  4. B. Farias, T. Passerat de Silans, M. Chevrollier, M. Oriá, Phys. Rev. Lett. 94, 173902 (2005)

    Article  ADS  Google Scholar 

  5. M. Oriá, B. Farias, T. Sorrentino, M. Chevrollier, J. Opt. Soc. Am. B. 24, 1867 (2007)

    Article  ADS  Google Scholar 

  6. J.R. Anglin, W. Ketterle, Nature (London). 416, 211 (2002)

    Article  ADS  Google Scholar 

  7. U. Leonhardt, T. Kiss, P. Ohberg, Phys. Rev. A. 67, 033602 (2003)

    Article  ADS  Google Scholar 

  8. D. Jaksch, P. Zoller, New J. Phys. 5, 56 (2003)

    Article  ADS  Google Scholar 

  9. Y.J. Lin, et al., Nature (London). 462, 628 (2009)

    Article  ADS  Google Scholar 

  10. G. Juzeliūnas, J. Ruseckas, M. Lindberg, L. Santos, P. Öhberg, Phys. Rev. A. 77(R), 011802 (2008)

    Article  ADS  Google Scholar 

  11. I.I. Satija, D.C. Dakin, J. Y. Vaishnav, C.W. Clark, Phys. Rev. A. 77, 043410 (2008)

    Article  ADS  Google Scholar 

  12. X.-J. Liu, M. F. Borunda, X. Liu, J. Sinova, Phys. Rev. Lett. 102, 046402 (2009)

    Article  ADS  Google Scholar 

  13. D.-W. Zhang, Z.-Y. Xue, H. Yan, 2 Wang Z.D., S.-L. Zhu, Phys. Rev. A. 85, 013628 (2012)

    Article  ADS  Google Scholar 

  14. B. Farias, J. Lemos de Melo, C. Furtado, Eur. Phys. J. D. 68, 77 (2014)

    Article  ADS  Google Scholar 

  15. Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  16. X.-G. He, B.H.J. McKellar, Phys. Rev. A. 47, 3424 (1993)

    Article  ADS  Google Scholar 

  17. M. Wilkens, Phys. Rev. Lett. 72, 5 (1994)

    Article  ADS  Google Scholar 

  18. H. Wei, R. Han, X. Wei, Phys. Rev. Lett. 75, 2071 (1995)

    Article  ADS  Google Scholar 

  19. A.L. Fetter, Rev. Mod. Phys. 81, 647 (2009)

    Article  ADS  Google Scholar 

  20. E.J. Mueller, Phys. Rev. A. 70(R), 041603 (2004)

    Article  ADS  Google Scholar 

  21. G. Juzeliūnas, P. Öhberg, Phys. Rev. Lett. 93, 033602 (2004)

    Article  ADS  Google Scholar 

  22. J. Ruseckas, G. Juzeliūnas, P. Öhberg, M. Fleischhauer, Phys. Rev. Lett. 95, 010404 (2005)

    Article  ADS  Google Scholar 

  23. P. Öhberg, G. Juzeliūnas, J. Ruseckas, M. Fleischhauer, Phys. Rev. A. 72, 053632 (2005)

    Article  ADS  Google Scholar 

  24. A.L. Fetter, Rev. Mod. Phys. 81, 647 (2009)

    Article  ADS  Google Scholar 

  25. M. Ericsson, E. Sjöqvistt, Phys. Rev. A. 65, 013607 (2001)

    Article  ADS  Google Scholar 

  26. L.R. Ribeiro, C. Furtado, J.R. Nascimento, Phys. Lett. A. 348, 135 (2006)

    Article  ADS  Google Scholar 

  27. L.R. Ribeiro, C. Furtado, J.R. Nascimento, Phys. Lett. A. 358, 336 (2006)

    Article  ADS  Google Scholar 

  28. X. -J. Liu, M.F. Borunda, X. Liu, J. Sinova, Phys. Rev. Lett. 102, 046402 (2009)

    Article  ADS  Google Scholar 

  29. A. Jacob, P. Öhberg, G. Juzeliūnas, L. Santos, New J. Phys. 10, 045022 (2008)

    Article  ADS  Google Scholar 

  30. B. Estienne, S. Haaker, K. Schoutens, New J. Phys. 13, 045012 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  31. M.-Y. Ye, X.-M. Lin, e-print arXiv:1207.5369v1

  32. L.S. Brown, W.I. Weisberger, Nucl. Phys. B. 157, 285–326 (1979)

    Article  ADS  Google Scholar 

  33. L.D. Landau, E.M. Lifshitz. Quantum mechanics: Non-relativistic theory, 3rd edn. (Pergamon Press, Oxford, 1977)

    MATH  Google Scholar 

  34. B. Farias, C. Furtado, Physica B. 481, 19 (2016)

    Article  ADS  Google Scholar 

  35. B. Farias, C. Furtado, Eur. Phys. J. Plus. 131, 237 (2016)

    Article  Google Scholar 

  36. B. Padhi, S. Ghosh, Phys. Rev. Lett. 111, 043603 (2013)

    Article  ADS  Google Scholar 

  37. W. Ketterle, Nat. Phys. 11, 90 (2015)

    Article  Google Scholar 

  38. G. Juzeliūnas, P. Öhberg, Phys. Rev. Lett. 93, 033602–1 (2004)

    Article  ADS  Google Scholar 

  39. K. Merloti, R. Dubessy, L. Longchambon, A. Perrin, P.-E. ́ Pottie, V. Lorent, H. Perrin, New J. Phys. 15, 033007 (2013)

    Article  ADS  Google Scholar 

  40. A similar constraint is imposed on the cyclotron frequency once \({\omega } = \frac {B}{m}\)

Download references

Acknowledgments

This work was support by the Brazilian agencies CNPq and CAPES.

Author information

Authors and Affiliations

  1. Centro de Ciências e Tecnologia Agroalimentar, Universidade Federal de Campina Grande, Pombal, PB, 58840-000, Brazil

    B. Farias

  2. Centro de Ciências Exatas e Tecnológicas, Universidade Federal do Reconcavo da Bahia, Cruz das Almas, BA, Brazil

    J. Lemos de Melo

  3. Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, João Pessoa, PB, 58051-970, Brazil

    C. Furtado

Authors
  1. B. Farias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Lemos de Melo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Furtado
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Farias.

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

Farias, B., de Melo, J. & Furtado, C. Landau Quantization for Λ-Type Neutral Atoms in an Homogeneous Spin-Dependent Gauge Potential. Braz J Phys 50, 30–34 (2020). https://doi.org/10.1007/s13538-019-00715-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-019-00715-z

Keywords

Search

Navigation