Quantum Point Process Model for Photodetection

  • M. D. Srinivas
Conference paper


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].


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    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
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    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
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    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
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Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

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

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