Atom–Field Interactions

  • André Xuereb
Part of the Springer Theses book series (Springer Theses)


I begin this chapter with a very brief review of atomic structure, covering the fine and hyperfine structures as well as the magnetic sublevels within the hyperfine manifold; these ideas will be used later to discuss trapping and cooling of atoms. The following sections describe the density matrix approach and build up to a derivation of the Optical Bloch Equations. These equations are the tools necessary to examine the interaction between an atom and the electromagnetic field and, ultimately, to derive an expression for the forces acting on an atom, as parametrised by the polarisability of that atom. The chapter continues with a note on the fluctuation–dissipation theorem and shows how the calculation of the full force acting on the atom allows the prediction of the equilibrium temperature a population of such atoms will tend to, and concludes with a short discussion on multi-level atoms. The reader is referred to Refs. [1, 2, 3, 4, 5, 6, 7], and references therein, for a more in-depth and complete treatment of certain parts of this chapter.


Density Matrix Hyperfine Structure Rabi Frequency Magnetic Sublevel Dissipation Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Cohen-Tannoudji, C., Diu, B. & Lalöe, F. Quantum Mechanics, Volume 1 (Wiley, 1978).Google Scholar
  2. 2.
    Cohen-Tannoudji, C. Quantum Mechanics, Volume 2 (Wiley, 1978).Google Scholar
  3. 3.
    Shore, B. W. The Theory of Coherent Atomic Excitation: Simple Atoms and Fields, Volume 1 (Wiley VCH, 1990).Google Scholar
  4. 4.
    Shore, B. W. The Theory of Coherent Atomic Excitation: Simple Atoms and Fields, Volume 2 (Wiley VCH, 1990).Google Scholar
  5. 5.
    Woodgate, G. K. Elemetary Atomic Structure (Oxford University Press, 2000), seventh edn.Google Scholar
  6. 6.
    Cohen-Tannoudji, C., Dupont-Roc, J. & Grynberg, G. Atom-Photon Interactions: Basic Processes and Applications (Wiley, 1992).Google Scholar
  7. 7.
    Foot, C. J. Atomic Physics (Oxford Master Series in Atomic, Optical and Laser Physics) (Oxford University Press, USA, 2005).Google Scholar
  8. 8.
    Arimondo, E., Inguscio, M. & Violino, P. Experimental determinations of the hyperfine structure in the alkali atoms. Rev. Mod. Phys. 49, 31 (1977).Google Scholar
  9. 9.
    Steck, D. A. Rubidium 85 D Line Data (2008). Rubidium 85 D Line Data
  10. 10.
    Schrödinger, E. An undulatory theory of the mechanics of atoms and molecules. Phys. Rev. 28,1049 (1926).Google Scholar
  11. 11.
    Gardiner, C. W. & Zoller, P. Quantum Noise (Springer, 2004), third edn.Google Scholar
  12. 12.
    Lindblad, G.On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976).Google Scholar
  13. 13.
    Domokos, P., Horak, P. & Ritsch, H. Semiclassical theory of cavity-assisted atom cooling. J. Phys. B 34,187 (2001).Google Scholar
  14. 14.
    Gardiner, C. W. Handbook of stochastic methods: for physics, chemistry and the natural sciences (Springer, 1996), second edn.Google Scholar
  15. 15.
    Xuereb, A., Horak, P. & Freegarde, T.Atom cooling using the dipole force of a single retroflected laser beam. Phys. Rev. A 80, 013836 (2009).Google Scholar
  16. 16.
    Xuereb, A., Domokos, P., Asbóth, J., Horak, P. & Freegarde, T.Scattering theory of cooling and heating in optomechanical systems. Phys. Rev. A 79, 053810 (2009).Google Scholar
  17. 17.
    Gardiner, C. W. Adiabatic elimination in stochastic systems. I. Formulation of methods and application to few-variable systems. Phys. Rev. A 29, 2814 (1984).Google Scholar
  18. 18.
    Jackson, J. D. Classical Electrodynamics (Wiley, 1998), third edn.Google Scholar
  19. 19.
    Hecht, E. Optics (Addison Wesley, 2001), fourth edn.Google Scholar
  20. 20.
    Springer Handbook of Atomic, Molecular, and Optical Physics (Springer, 2005), second edn.Google Scholar
  21. 21.
    Deutsch, I. H., Spreeuw, R. J. C., Rolston, S. L. & Phillips, W. D. Photonic band gaps in optical lattices. Phys. Rev. A 52, 1394 (1995).Google Scholar
  22. 22.
    Tey, M. K. et al. Interfacing light and single atoms with a lens. New J. Phys. 11, 043011 (2009).Google Scholar
  23. 23.
    Toll, J. S. Causality and the dispersion relation: Logical foundations. Phys. Rev. 104, 1760 (1956).Google Scholar
  24. 24.
    Wang, D.-w., Li, A.-j., Wang, L.-g., Zhu, S.-y. & Zubairy, M. S. Effect of the counterrotating terms on polarizability in atom-field interactions. Phys. Rev. A 80, 063826 (2009).Google Scholar
  25. 25.
    Dalibard, J. & Cohen-Tannoudji, C. Laser cooling below the Dopplerlimit by polarization gradients: simple theoretical models. J. Opt. Soc. Am. B 6, 2023 (1989).Google Scholar
  26. 26.
    Cohen-Tannoudji, C. Atomic motion in laser light. In Dalibard, J., Zinn-Justin, J.& Raimond, J. M. (eds.) Fundamental Systems in Quantum Optics, Proceedings of the Les Houches Summer School, Session LIII, 1(North Holland, 1992).Google Scholar
  27. 27.
    Gordon, J. P.& Ashkin, A. Motion of atoms in a radiation trap. Phys. Rev. A 21, 1606 (1980).Google Scholar
  28. 28.
    Risken, H. The Fokker-Planck Equation: Methods of Solutions and Applications. Springer Series in Synergetics (Springer, 1996), third edn.Google Scholar
  29. 29.
    Einstein, A. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeitensuspendierten Teilchen. Ann. Phys. 322, 549 (1905).Google Scholar
  30. 30.
    Metcalf, H. J. & van der Straten, P. Laser Cooling and Trapping (Springer, 1999), first edn.Google Scholar
  31. 31.
    Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155 (2010).Google Scholar
  32. 32.
    Onsager, L. Reciprocal relations in irreversible processes.Phys. Rev. 38, 2265 (1931).Google Scholar
  33. 33.
    Ford, G. W. & O’Connell, R. F. There is no quantum regression theorem. Phys. Rev. Lett. 77, 798 (1996).Google Scholar
  34. 34.
    Lax, M. The Lax-Onsager regression ‘theorem’ revisited. Opt. Commun. 179, 463 (2000).Google Scholar
  35. 35.
    Dalibard, J., Reynaud, S. & Cohen-Tannoudji, C. Potentialities of a new \(\sigma _+\)-\(\sigma _-\) laser configuration for radiative cooling and trapping. J. Phys. B 17, 4577 (1984).Google Scholar
  36. 36.
    Bateman, J., Xuereb, A.& Freegarde, T. Stimulated raman transitions via multiple atomic levels. Phys. Rev. A 81, 043808 (2010).Google Scholar
  37. 37.
    Kasevich, M.& Chu, S. Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer. Applied Physics B: Lasers and Optics 54, 321 (1992).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.University of SouthamptonBelfastUK

Personalised recommendations