Advertisement

Theoretical and Mathematical Physics

, Volume 144, Issue 1, pp 975–984 | Cite as

Quantum Integrable Multiatom Matter-Radiation Models With and Without the Rotating-Wave Approximation

  • A. Kundu
Article

Abstract

New integrable multiatom matter-radiation models with and without the rotating-wave approximation (RWA) are constructed and exactly solved via the algebraic Bethe ansatz. The models with the RWA are generated using the ancestor model approach in a unified way. The rational case yields the standard type of matter-radiation models, while the trigonometric case corresponds to their q-deformations. The models without the RWA are obtained from the elliptic case in the limit of the Gaudin model and high spin.

Keywords

integrable multiatom models rotating-wave approximation matter-radiation interaction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    G. Rempe, H. Walther, and N. Klein, Phys. Rev. Lett., 58, 353 (1987); G. Rempe, F. Schmidt-Kaler, and H. Walther, Phys. Rev. Lett., 64, 2783 (1990).PubMedGoogle Scholar
  2. 2.
    M. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett., 63, 240 (1989).PubMedGoogle Scholar
  3. 3.
    C. A. Blockley, D. F. Walls, and H. Risken, Europhys. Lett., 17, 509 (1992).Google Scholar
  4. 4.
    W. Vogel and R. de Mitos Filho, Phys. Rev. A, 52, 4214 (1995).CrossRefPubMedGoogle Scholar
  5. 5.
    E. T. Jaynes and F. W. Cummings, Proc. IEEE, 51, 89 (1963).Google Scholar
  6. 6.
    B. Buck and C. V. Sukumar, Phys. Lett. A, 81, 132 (1981).CrossRefGoogle Scholar
  7. 7.
    R. Angelo, M. K. Furuya, M. C. Nemes, and G. Q. Pellegrino, Phys. Rev. A, 64, 043801 (2001).CrossRefGoogle Scholar
  8. 8.
    V. Buzek, J. Modern Opt., 39, 949 (1992).Google Scholar
  9. 9.
    M. Chaichian, D. Ellinas, and P. Kulish, Phys. Rev. Lett., 65, 980 (1990).PubMedGoogle Scholar
  10. 10.
    H.-S. Zeng, L.-M. Kuang, and K.-L. Gao, “Jaynes-Cummings model dynamics in two trapped ions,” quant-ph/0106020 (2001).Google Scholar
  11. 11.
    G. S. Agarwal, Phys. Rev. Lett., 53, 1732 (1984).CrossRefGoogle Scholar
  12. 12.
    M. Tavis and F. W. Cummings, Phys. Rev., 170, 379 (1968); W. R. Mallory, Phys. Rev., 188, 1976 (1969).CrossRefGoogle Scholar
  13. 13.
    N. M. Bogoliubov, R. K. Bullough, and J. Timonen, J. Phys. A, 29, 6305 (1996).Google Scholar
  14. 14.
    A. Rybin, G. Kastelewicz, J. Timonen, and N. Bogoliubov, J. Phys. A, 31, 4705 (1998).Google Scholar
  15. 15.
    L. Amico and K. Hikami, Eur. Phys. J. B, 43, 387 (2005); cond-mat/0309680 (2003).MathSciNetGoogle Scholar
  16. 16.
    J. Dukelsky, G. G. Dussel, C. Esebbag, and S. Pittel, Phys. Rev. Lett., 93, 050403 (2004).PubMedGoogle Scholar
  17. 17.
    P. Kulish and E. K. Sklyanin, “Quantum spectral transform method: Recent developments,” in: Integrable Quantum Field Theories (Lect. Notes Phys., Vol. 151, J. Hietarinta and C. Montonen, eds.), Springer, Berlin (1982), p. 61; A. G. Izergin and V. E. Korepin, Lett. Math. Phys., 8, 259 (1984); V. O. Tarasov, Theor. Math. Phys., 63, 440 (1985); L. D. Faddeev, Internat. J. Mod. Phys. A, 10, 1845 (1995).Google Scholar
  18. 18.
    A. Kundu, Phys. Rev. Lett., 82, 3936 (1999).CrossRefGoogle Scholar
  19. 19.
    A. Kundu, J. Phys., 37, L281 (2004).Google Scholar
  20. 20.
    L. Takhtajan, “Introduction to algebraic Bethe ansatz,” in: Exactly Solvable Problems in Condensed Matter and Relativistic Field Theory (Lect. Notes Phys., Vol. 242, B. S. Shastry, S. S. Jha, and V. Singh, eds.), Springer, Berlin (1985), p. 175.Google Scholar
  21. 21.
    V. Pasquier and H. Saleur, Nucl. Phys. B, 330, 523 (1990).CrossRefGoogle Scholar
  22. 22.
    E. K. Sklyanin, Funct. Anal. Appl., 16, 263 (1983); 17, 273 (1983).CrossRefGoogle Scholar
  23. 23.
    E. K. Sklyanin and T. Takebe, Phys. Lett. A, 219, 217 (1996).CrossRefGoogle Scholar
  24. 24.
    A. Kundu, “Integrable multi atom matter-radiation models without rotating wave approximation,” cond-mat/0411166 (2004).Google Scholar
  25. 25.
    L. A. Takhtadzhyan and L. D. Faddeev, Russ. Math. Surveys, 34, 11 (1979).Google Scholar
  26. 26.
    T. Takebe, J. Phys. A, 25, 1071 (1992); 28, 6675 (1995).Google Scholar
  27. 27.
    K. An, J. J. Childs, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett., 73, 3375 (1994); K. An, J. Phys. Soc. Japan, 72, 811 (2003).PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. Kundu
    • 1
  1. 1.Theory GroupSaha Institute of Nuclear PhysicsCalcuttaIndia

Personalised recommendations