Quantum Point Process Model for Photodetection
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). 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].
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- see also L. Mandel in Progress in Optics, Vol. II, ed. E. Wolf ( North-Holland, Amsterdam, 1963 ).Google Scholar
- 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
- 5.P.L. Kelley and W.H. Kleiner, Phys. Rev. 136A, 316 (1964).Google Scholar
- 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
- 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
- 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
- (c) See also E.B. Davies, Quantum Theory of Open Systems ( Academic Press, New York, 1976 ).Google Scholar
- 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
- 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
- 15.M.D. Srinivas, “Conditional Probabilities and Statistical Independence in Quantum Theory”, Jour. Math. Phys. (in press).Google Scholar
- 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
- 17.Our arguments can also be presented in more formal terms on the basis of the formalism outlined in Section 3.Google Scholar
- 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 has indicated how the QPP framework can be suitably generalised in the case of such unbounded Jt.Google Scholar