The Quantum Jump Approach and Some of Its Applications

  • Gerhard C. HegerfeldtEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 789)


Modern techniques allow experiments on a single-driven atom or a single system. The quantum jump approach was originally developed for the description of the temporal development of such a driven system and was later extended to more general situations like a moving particle coupled to a spatially confined laser beam or to spin-boson baths. In this chapter the underlying ideas are presented and illustrated by simple examples. Applications include the spectacular macroscopic light and dark periods in the fluorescence of a single atom, quantum counting processes and arrival times.


Density Matrix Pure State Dark Period Markov Property Rabi Frequency 
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  1. 1.
    The projection postulate as commonly used nowadays is due to G. Lüders, Ann. Phys. 8, 323 (1951). For observables with degenerate eigenvalues his formulation differs from that of J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer (Berlin 1932) (English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955), Chapter V.1. The projection postulate intends to describe the effects of an ideal measurement on the state of a system, and it has been widely regarded as a useful tool.Google Scholar
  2. 2.
    For a simplified case one can see this directly as follows. The \(\omega^{2}\) inherent in \(d^{3} k\) and the \(\omega_{k}\) in \(\kappa \) give a factor of \(\omega^{3}\). If this \(\omega^{3}\) is omitted in the definition of \(\kappa \) then the result can be seen by a straightforward calculation of the double integral in (6.22). The general case can be reduced to this by partial integration. We note that for \(\omega_{0}\) in the microwave range the condition \(t^{\prime}\, - \,t_i \gg \,\omega _0^{ - 1}\) does not hold. However, the radiative coupling of such levels is extremely small and is usually neglected in applications.Google Scholar
  3. 3.
    D. Alonso, I. de Vega, Phys. Rev. Lett. 94, 200403 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    A. Beige, Doctoral Dissertation, Universität Göttingen, Germany (1997)Google Scholar
  5. 5.
    A. Beige, G.C. Hegerfeldt, Phys. Rev. A 53, 53 (1996)ADSCrossRefGoogle Scholar
  6. 6.
    A. Beige, G.C. Hegerfeldt, J. Mod. Opt. 44, 345 (1997)ADSGoogle Scholar
  7. 7.
    A. Beige, G.C. Hegerfeldt, J. Phys. A: Math. Gen. 30, 1323 (1997)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Beige, G.C. Hegerfeldt, D.G. Sondermann, Quantum Semiclass. Opt. 8, 999 (1996)ADSCrossRefGoogle Scholar
  9. 9.
    A. Beige, G.C. Hegerfeldt, D.G. Sondermann, Found. Phys. 27, 1671 (1997)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    J.C. Bergquist, R.G. Hulet, W.M. Itano, D.J. Wineland, Phys. Rev. Lett. 57, 1699 (1986)ADSCrossRefGoogle Scholar
  11. 11.
    Th. Sauter, R. Blatt, W. Neuhauser, P.E. Toschek, Opt. Commun. 60, 287 (1986)ADSCrossRefGoogle Scholar
  12. 12.
    W. Nagourney, J. Sandberg, H. Dehmelt, Phys. Rev. Lett. 56, 2797 (1986)ADSCrossRefGoogle Scholar
  13. 13.
    J.C. Bergquist, W.M. Itano, R.G. Hulet, D.J. Wineland, Phys. Script. T22, 79 (1988)ADSCrossRefGoogle Scholar
  14. 14.
    H. Carmichael, An Open Systems Approach to Quantum Optics, Lect. Notes Phys. (Springer, Berlin, 1993)zbMATHGoogle Scholar
  15. 15.
    C. Cohen-Tannoudji, J. Dalibard, Europhys. Lett. 1, 441 (1986)ADSCrossRefGoogle Scholar
  16. 16.
    C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions (John Wiley & Sons, New York, 1992)Google Scholar
  17. 17.
    J. Dalibard, Y. Castin, K. Mølmer, Phys. Rev. Lett. 68, 580 (1992)ADSCrossRefGoogle Scholar
  18. 18.
    J.A. Damborenea, I.L. Egusquiza, G.C. Hegerfeldt, J.G. Muga, Phys. Rev. A 66, 052104 (2002)ADSCrossRefGoogle Scholar
  19. 19.
    H.G. Dehmelt, Bull. Am. Phys. Soc. 20, 60Google Scholar
  20. 20.
    P.A.M. Dirac, The Principles of Quantum Mechanics, 4th edn (Clarendon Press, Oxford, 1959), p. 181Google Scholar
  21. 21.
    B. Gaveau, L.S. Schulman, J. Stat. Phys. 58, 1209 (1990)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    N. Gisin, I.C. Percival, J. Phys. A: Math. Gen. 25, 5677 (1992)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    G.C. Hegerfeldt, Phys. Rev. A 47, 449 (1993)ADSCrossRefGoogle Scholar
  24. 24.
    G.C. Hegerfeldt, Fortschr. Phys. 46, 596 (1998)MathSciNetCrossRefGoogle Scholar
  25. 25.
    G.C. Hegerfeldt, in Irreversible Quantum Dynamics, F. Benatti, R. Floreanini (eds.), Springer Lect. Notes Phys. 622, 233 (2003)Google Scholar
  26. 26.
    G.C. Hegerfeldt, in preparationGoogle Scholar
  27. 27.
    G.C. Hegerfeldt, J.T. Neumann, L.S. Schulman, J. Phys. A 39, 14447 (2006)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    G.C. Hegerfeldt, J.T. Neumann, L.S. Schulman, Phys. Rev. A 75, 012108 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    G.C. Hegerfeldt, M.B. Plenio, Phys. Rev. A 46, 373 (1992)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    G.C. Hegerfeldt, M.B. Plenio, Phys. Rev. A 47, 2186 (1993)ADSCrossRefGoogle Scholar
  31. 31.
    G.C. Hegerfeldt, M.B. Plenio, Quantum Opt. 6, 15 (1994)ADSCrossRefGoogle Scholar
  32. 32.
    G.C. Hegerfeldt, M.B. Plenio, Z. Phys. B 96, 533 (1995)ADSCrossRefGoogle Scholar
  33. 33.
    G.C. Hegerfeldt, M.B. Plenio, Phys. Rev. A 53, 1164 (1996)ADSCrossRefGoogle Scholar
  34. 34.
    G.C. Hegerfeldt, D.G. Sondermann, Quantum Semiclass. Opt. 8, 121 (1996)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    G.C. Hegerfeldt, T.S. Wilser, in Classical and Quantum Systems. Proceedings of the II International Wigner Symposium, July 1991, H.D. Doebner, W. Scherer, and F. Schroeck (eds.) (World Scientific, Singapore, 1992), p. 104Google Scholar
  36. 36.
    W.M. Itano, D.J. Heinzen, J.J. Bollinger, D.J. Wineland, Phys. Rev. A 41, 2295 (1990)ADSCrossRefGoogle Scholar
  37. 37.
    R. Loudon, The Quantum Theory of Light, 3rd edn (Clarendon, London, 2000)zbMATHGoogle Scholar
  38. 38.
    P.W. Milonni, Phys. Rep. 25 C, 1 (1976)ADSCrossRefGoogle Scholar
  39. 39.
    B. Misra, E.C.G. Sudarshan, J. Math. Phys. 18, 756 (1977)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    J.G. Muga, R. Sala, I.L. Egusquiza (eds.), Time in Quantum Mechanics (Springer, Berlin, 2002), cf. also articles in the present bookzbMATHGoogle Scholar
  41. 41.
    J.T. Neumann, Doctoral Dissertation, Universität Göttingen, Germany (2007)Google Scholar
  42. 42.
    M.B. Plenio, P.L. Knight, Rev. Mod. Phys. 70, 101 (1998)ADSCrossRefGoogle Scholar
  43. 43.
    M. Porrati, S. Putterman, Phys. Rev. A 39, 3010 (1989)ADSCrossRefGoogle Scholar
  44. 44.
    R. Reibold, J. Phys. A: Math. Gen. 26, 179 (1993)ADSCrossRefGoogle Scholar
  45. 45.
    C. Schön, A. Beige, Phys. Rev. A 64, 023806 (2001)ADSCrossRefGoogle Scholar
  46. 46.
    D.G. Sondermann, in Nonlinear, Deformed and Irreversible Quantum Systems, H.-D. Doebner, V.K. Dobrev, P. Nattermann (eds.) (World Scientific, Singapore, 1995), p. 273Google Scholar
  47. 47.
    M.D. Srinivas, E.B. Davies, Opt. Acta 28, 981 (1981)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    M.D. Srinivas, E.B. Davies, Opt. Acta 29, 235 (1982)ADSCrossRefGoogle Scholar
  49. 49.
    T.S. Wilser, Doctoral Dissertation, University of Göttingen, Germany (1991)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany

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