Advertisement

Quantum Point Process Model for Photodetection

  • M. D. Srinivas
Conference paper

Abstract

In classical physics, phenomena which involve a random sequence of events in time have been successfully investigated by means of the theory of classical point processes (CPP)[1]. Hence, it is not surprising that most of the theoretical approaches [2–6] to the photon-counting problem are also based on the theory of CPP. The central objective of these investigations is to derive an expression (referred to as the counting formula) for the probability p((t,t+T],m) that m counts are observed in the time interval (t,t+T]. This naturally leads to the study of a situation where the detector performs continuous measurements on the electromagnetic field in the interval (t,t+T].

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    See for example, Stochastic Point Processes: Statistical Analysis, Theory and Applications, ed. P.A.W. Lewis ( Wiley, New York, 1972 ).zbMATHGoogle Scholar
  2. 2.
    L. Mandel, Proc. Phys. Soc. (London) 72, 1037 (1958);ADSCrossRefGoogle Scholar
  3. see also L. Mandel in Progress in Optics, Vol. II, ed. E. Wolf ( North-Holland, Amsterdam, 1963 ).Google Scholar
  4. 3.
    R.J. Glauber, Phys. Rev. Lett. 10, 84 (1963);ADSCrossRefMathSciNetGoogle Scholar
  5. 3.
    see also R.J. Glauber in Quantum Optics and Electronics, ed. C. deWitt, A. Blandin and C. Cohen-Tannoudji ( Gordon and Breach, New York, 1965 ).Google Scholar
  6. 4.
    L. Mandel, E.C.G. Sudarshan and E. Wolf, Proc. Phys. Soc. (London) 84, 435 (1964).ADSCrossRefMathSciNetGoogle Scholar
  7. 5.
    P.L. Kelley and W.H. Kleiner, Phys. Rev. 136A, 316 (1964).Google Scholar
  8. 6.
    M. Lax and M. Zwanziger, Phys. Rev. A 7, 750 (1973); see also Appendix A of a preliminary version of this paper.Google Scholar
  9. 7.
    E.B. Davies and J.T. Lewis, Commun. Math. Phys. 17, 239 (1970).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  10. 8.
    M.D. Srinivas, Jour. Math. Phys. 16,1672 (1975)(to be reprinted in The Logic-Algebraic Approach to Quantum Theory, Vol. II,ed. C.A. Hooker (Dordrecht, Netherlands, 1977)).Google Scholar
  11. 9.
    In fact the study of QPP (and much of the quantum probability framework) originated from the consideration of photon-counting experiments by Davies [see Ref. 10]). The so-called ‘quantum stochastic processes’, introduced by Davies for this purpose, are nothing but a particular class of QPP.Google Scholar
  12. 10.
    (a) E.B. Davies, Commun. Math. Phys. 15, 277 (1969);ADSCrossRefzbMATHGoogle Scholar
  13. (b)E.B. Davies, ibid. 19, 83 (1970);zbMATHGoogle Scholar
  14. (c) See also E.B. Davies, Quantum Theory of Open Systems ( Academic Press, New York, 1976 ).Google Scholar
  15. 11.
    M.D. Srinivas, Jour. Math. Phys. 18, 2138 (1977).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  16. 12.
    See for example, Refs. 5 and 6. Unfortunately, it has been the case with several other investigations of this problem, that there is no clear statement of the basic probability relations employed.Google Scholar
  17. 13.
    O. Macchi, Adv. Appl. Prob. 1, 83 (1975).CrossRefMathSciNetGoogle Scholar
  18. 14.
    For the sake of simplicity, we have suppressed all the vector indices and we have also restricted ourselves to the case of a single detector only. Another generalisation, which can also be easily carried out, involves replacing (2.5) by the relation where K(r,r’) is sometimes interpreted as a correlation function characterizing the detector. A similar change can also be effected in Egs.(2.9) and (2.18).Google Scholar
  19. 15.
    M.D. Srinivas, “Conditional Probabilities and Statistical Independence in Quantum Theory”, Jour. Math. Phys. (in press).Google Scholar
  20. 16.
    This is in marked contrast with the situation in classical theory where the CPD are the same, irrespective of whether or not any experiments are performed during the intervening periods.Google Scholar
  21. 17.
    Our arguments can also be presented in more formal terms on the basis of the formalism outlined in Section 3.Google Scholar
  22. 18.
    It should be noted that, since Jt as given by (3.14) is not a bounded operator on V, our model does not strictly correspond to a regular QPP as per conditions of IV. However, Davies[10] has indicated how the QPP framework can be suitably generalised in the case of such unbounded Jt.Google Scholar
  23. 19.
    L. Mandel, Phys. Rev. 152, 438 (1966).ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • M. D. Srinivas
    • 1
  1. 1.University of MadrasMadrasIndia

Personalised recommendations