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Journal of Russian Laser Research

, Volume 35, Issue 1, pp 101–109 | Cite as

Balance Equations-Based Properties of the Rabi Hamiltonian

  • Antonino Messina
  • Anna Napoli
  • Margarita A. Man’ko
  • Vladimir I. Man’ko
Article
  • 63 Downloads

Abstract

A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper, we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrödinger equation. The knowledge of such properties in the case of the Rabi Hamiltonian is exploited to provide arguments to make easier the variational engineering of the ground state of this model.

Keywords

ground state variational approach Wigner function Rabi model balance equations 

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References

  1. 1.
    V. V. Dodonov and V. I. Man’ko, Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physical Institute, Nauka, Moscow (1987), Vol. 183 [translated by Nova Science, New York (1989)].Google Scholar
  2. 2.
    G. Benivegna and A. Messina, Phys. Rev A, 35, 3313 (1987).ADSCrossRefGoogle Scholar
  3. 3.
    G. Benivegna and A. Messina, Phys. Rev A, 37, 4747 (1988).ADSCrossRefGoogle Scholar
  4. 4.
    G. Benivegna and A. Messina, J. Phys. A: Math. Gen., 27, L453 (1994).ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    G. Benivegna, A. Messina, and E. Paladino, J. Phys. A: Math. Gen., 29, 2485 (1996).ADSCrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    G. Benivegna, A. Messina, and E. Paladino, Nuovo Cim. B, 112, 905 (1997).Google Scholar
  7. 7.
    I. I. Rabi, Phys. Rev., 49, 324 (1936).ADSCrossRefMATHGoogle Scholar
  8. 8.
    D. Braak, Phys. Rev. Lett., 107, 100401 (2011).ADSCrossRefGoogle Scholar
  9. 9.
    L. Yu, S. Zhu, Q. Liang, et al., Phys. Rev. A, 86, 015803 (2012).ADSCrossRefGoogle Scholar
  10. 10.
    H. -P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, Oxford, UK (2002)MATHGoogle Scholar
  11. 11.
    S. Haroche and J. M. Raimond, Exploring the Quantum: Atoms, Cavities and Photons, Oxford University Press, Oxford, UK (2006)CrossRefGoogle Scholar
  12. 12.
    T. Niemczyk, F. Deppe, H. Huebl, et al., Nature Phys., 6, 772 (2010).ADSCrossRefGoogle Scholar
  13. 13.
    P. Forn-Diaz, J. Lisenfeld, D. Marcos, et al., Phys. Rev. Lett., 105, 237001 (2010).ADSCrossRefGoogle Scholar
  14. 14.
    X. Cao, J. Q. You, H. Zheng, et al., Phys. Rev. A, 82, 022119 (2010).ADSCrossRefGoogle Scholar
  15. 15.
    O. Q. You and F. Nori, Nature, 474, 589 (2011).ADSCrossRefGoogle Scholar
  16. 16.
    J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys., 73, 565 (2001).ADSCrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    A. Moroz, Los Alamos ArXiv:1302.2565v3 (2013).Google Scholar
  18. 18.
    G. Gunter, A. A. Anappara, J. Hees, et al., Nature, 458, 178 (2009).ADSCrossRefGoogle Scholar
  19. 19.
    Y. Todorov, A. M. Andrews, R. Colombelli, et al., Phys. Rev. Lett., 105, 196402 (2010).ADSCrossRefGoogle Scholar
  20. 20.
    E. Wigner, Phys. Rev., 40, 749 (1932).ADSCrossRefGoogle Scholar
  21. 21.
    F. J. Narcowich and R. F. O’Connel, Phys. Rev. A, 34, 1 (1986).ADSCrossRefMathSciNetGoogle Scholar
  22. 22.
    W. P. Schleich, Quantum Optics in Phase Space, Wiley, Weinheim, Germany (2005).Google Scholar
  23. 23.
    O. V. Man’ko, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Gen., 35, 699 (2002).ADSCrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., Nuovo Cim. C, 36, Ser. 3, 163 (2013).Google Scholar
  25. 25.
    G. G. Amosov, Ya. A. Korennoy, and V. I. Man’ko, Phys. Rev. A, 85, 052119 (2012).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Antonino Messina
    • 1
  • Anna Napoli
    • 1
  • Margarita A. Man’ko
    • 2
  • Vladimir I. Man’ko
    • 2
    • 3
  1. 1.Dipartimento di Fisica e ChimicaUniversity of PalermoPalermoItaly
  2. 2.P. N. Lebedev Physical Institute, Russian Academy of SciencesMoscowRussia
  3. 3.Moscow Institute of Physics and Technology (State University)DolgoprudnyíRussia

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