International Journal of Theoretical Physics

, Volume 57, Issue 7, pp 2167–2191 | Cite as

Dynamical Evolution of Properties for Atom and Field in the Process of Two-Photon Absorption and Emission Between Atomic Levels

  • Jian-ming Wang
  • Xue-xiang Xu


Using dressed state method, we cleverly solve the dynamics of atom-field interaction in the process of two-photon absorption and emission between atomic levels. Here we suppose that the atom is initially in the ground state and the optical field is initially in Fock state, coherent state or thermal state, respectively. The properties of the atom, including the population in excited state and ground state, the atom inversion, and the properties for optical field, including the photon number distribution, the mean photon number, the second-order correlation function and the Wigner function, are discussed in detail. We derive their analytical expressions and then make numerical analysis for them. In contrast with Jaynes-Cummings model, some similar results, such as quantum Rabi oscillation, revival and collapse, are also exhibit in our considered model. Besides, some novel nonclassical states are generated.


Two-photon absorption and emission Jaynes-Cummings model Dressed state method Atomic inversion Wigner function 


  1. 1.
    Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  2. 2.
    Walls, D.F., Milburn, G.J.: Quantum optics. Springer, Berlin (2008)CrossRefzbMATHGoogle Scholar
  3. 3.
    Orszag, M.: Quantum optics. Springer, Berlin (2008)Google Scholar
  4. 4.
    Gerry, C.C., Knight, P.: Introductory Quantum Optics. Cambridge University Press, Cambridge (2005)Google Scholar
  5. 5.
    Barnett, S.M., Radmore, P.M.: Methods in Theoretical Quantum Optics. Claredon Press, Oxford (1997)zbMATHGoogle Scholar
  6. 6.
    Haroche, S., Raimond, J.M.: Exploring the quantum: Atoms, Cavities and Photons. Oxford University Press, Oxford (2006)CrossRefzbMATHGoogle Scholar
  7. 7.
    Meystre, P., Sargent, M. III: Element of quantum optics. Springer, Berlin (2007)CrossRefzbMATHGoogle Scholar
  8. 8.
    Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G.: Atom-Photon Interactions. Wiley, New York (1992)Google Scholar
  9. 9.
    Weissbluth, M.: Photon-Atom Interactions. Academic Press, New York (1989)Google Scholar
  10. 10.
    Allen, L., Eberly, J.H.: Optical Resonance and Two-Level Atoms. Wiley, New York (1975)Google Scholar
  11. 11.
    Eberly, J.H., Narozhny, N.B., Sanchez-Mondragon, J.J.: Phys. Rev. Lett. 44, 1323–1326 (1980)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Narozhny, N.B., Sanchez-Mondragon, J.J., Eberly, J.H.: Phys. Rev. A 23, 236–247 (1981)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Jaynes, E.T., Cummings, F.W.: Proc. Inst. Elect. Eng. 51, 89–109 (1963)CrossRefGoogle Scholar
  14. 14.
    Cummings, F.W.: Phys. Rev. 149, A1051–A1056 (1965)CrossRefGoogle Scholar
  15. 15.
    Knight, P.L., Radmore, P.M.: Phys. Rev. A 26, 676–679 (1982)ADSCrossRefGoogle Scholar
  16. 16.
    Rabi, I.I.: Phys. Rev. 51, 652–654 (1937)ADSCrossRefGoogle Scholar
  17. 17.
    Dell’Anno, F., De Siena, S., Illuminati, F.: Phys. Rep. 428, 53–168 (2006)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Yoo, H.J., Eberly, J.H.: Phys. Rep. 118, 239–337 (1985)ADSCrossRefGoogle Scholar
  19. 19.
    Shore, B.W., Knight, P.L.: J. Mod. Opt. 40, 1195–1238 (1993)ADSCrossRefGoogle Scholar
  20. 20.
    Messina, A., Maniscalco, S., Napoli, A.: J. Mod. Opt. 50, 1–49 (2003)ADSGoogle Scholar
  21. 21.
    Schleich, W.P.: Quantum Optics in Phase Space. Wiley-Vch Verlag, Berlin (2001)CrossRefzbMATHGoogle Scholar
  22. 22.
    Knight, P.L., Milonni, P.W.: Phys. Rep. 66, 21–107 (1980)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Allen, L., Knight, P.L.: Concepts of Quantum Optics. Pergamon, Oxford (1983)Google Scholar
  24. 24.
    Wigner, E.P.: Phys. Rev. 40, 749–759 (1932)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Quantum Science and TechnologyJiangxi Normal UniversityNanchangChina
  2. 2.College of Physics Communication ElectronicsJiangxi Normal UniversityNanchangChina

Personalised recommendations