Skip to main content
SpringerLink
Log in

Two- and Four-Level Systems in Magnetic Fields Restricted in Time

  • Particles and Fields
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

We describe some new exact solutions for two- and four-level systems. In all the cases, external fields have a restricted behavior in time. First, we consider a method to construct new solutions for one-spin equation and give some explicit examples: One of them is in a external magnetic field that acts during a finite time interval. Then we show how these solutions can be used to solve the two-spin equation problem. A solution for two interacting spins is analyzed in the case when the field difference between the external fields in each spin varies adiabatically, vanishing on the time infinity. The latter system can be identified with a quantum gate realized by two coupled quantum dots. The probability of the Swap operation for such a gate can be explicitly expressed in terms of special functions. Using the obtained expressions, we construct plots for the Swap operation for some parameters of the external magnetic field and interaction function.

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

Similar content being viewed by others

Notes

  1. The operators \(R_{i}\left( \beta\right) \) in (8) are rotation of an angle β along the i-axis and the functions φ,θ ,α can be identify with the Euler angles. In a similar manner, the functions p i in (7) can be identify with the Euler parameters.

References

  1. H.M. Nussenzveig, Introduction to Quantum Optics (Gordon and Breach, New York, 1973)

    Google Scholar 

  2. L. Allen, J.H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975)

    Google Scholar 

  3. I.I. Rabi, N.F. Ramsey, J. Schwinger, Rev. Mod. Phys. 26, 167 (1945)

    Article  ADS  Google Scholar 

  4. J.C. Barata, D.A. Cortez, Phys Lett. A 301, 350 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. V.V. Shamshutdinova, B.F. Samsonov, D.M. Gitman, Ann. Phys. 322, 1043 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. D. Loss, D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998)

    Article  ADS  Google Scholar 

  7. V.G. Bagrov, D.M. Gitman, M.C. Baldiotti, A. Levin, Ann. Phys. 14, 764 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. V.G. Bagrov, M.C. Baldiotti, D.M. Gitman, A.D. Levin, Ann. Phys. 16, 274 (2007)

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  10. M.J. Bremner, C.M. Dawson, J.L. Dodd, A. Gilchrist, A.W. Harrow, D. Mortimer, M.A. Nielsen, T.J. Osborne, Phys. Rev. Lett. 89, 247902 (2002)

    Article  ADS  Google Scholar 

  11. P.W. Shor,in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science (IEEE Computer Society, Los Alamitos, 1994)

    Google Scholar 

  12. R.P. Feynman, Int. J. Theor. Phys. 21, 467 (1982)

    Article  MathSciNet  Google Scholar 

  13. M.C. Baldiotti, V.G. Bagrov, D.M. Gitman, Phys. Part. Nucl. Lett. 6(7), 559 (2009)

    Article  Google Scholar 

  14. M.C. Baldiotti, D.M. Gitman, Ann. Phys. (Berlin) 17(7), 450 (2008)

    Article  ADS  MATH  Google Scholar 

  15. C.F. Destefani, S.E. Ulloa, Braz. J. Phys. 36, 443 (2006)

    Article  Google Scholar 

  16. G. Burkard, D. Loss, D.P. DiVincenzo, J.A. Smolin, Phys. Rev. B 60, 11404 (1999)

    Article  ADS  Google Scholar 

  17. V.N. Golovach, D. Loss, Semicond. Sci. Technol. 17, 355 (2002)

    Article  ADS  Google Scholar 

  18. G. Medeiros-Ribeiro, E. Ribeiro, H. Westfahl Jr., Appl. Phys. A 77, 725 (2003)

    Article  ADS  Google Scholar 

  19. J.R. Petta, A.C. Johnson, J.M. Taylor, E.A. Laird, A. Yacoby, M.D. Lukin, C.M. Marcus, M.P. Hanson, A.C. Gossard, Science 309, 2180 (2005)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

V.G.B. thanks grant SS-871.2008.2 of the President of Russia and RFBR grant 06-02-16719 for partial support; M.C.B. thanks FAPESP; D.M.G. thanks FAPESP and CNPq for permanent support.

Author information

Authors and Affiliations

  1. Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, CEP 05315-970, São Paulo, São Paulo, Brazil

    Mario Cesar Baldiotti

  2. Tomsk Institute of High Current Electronics, Tomsk State University, Tomsk, Russia

    V. G. Bagrov

  3. Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, CEP 05315-970, São Paulo, São Paulo, Brazil

    D. M. Gitman

  4. Dexter Research Center, Dexter, MI, USA

    A. D. Levin

Authors
  1. Mario Cesar Baldiotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. G. Bagrov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. M. Gitman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. D. Levin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Cesar Baldiotti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baldiotti, M.C., Bagrov, V.G., Gitman, D.M. et al. Two- and Four-Level Systems in Magnetic Fields Restricted in Time. Braz J Phys 41, 71–77 (2011). https://doi.org/10.1007/s13538-011-0001-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-011-0001-x

Keywords

Search

Navigation