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arXiv:0707.2137

A classical model for a photodetector in the presence of electromagnetic vacuum fluctuations

Trevor W. Marshall, Emilio Santos

Published Jul 14, 2007• 0 citations
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Abstract

The main argument against the reality of the electromagnetic vacuum fluctuations is that they do not activate photon detectors. In order to meet this objection we propose a classical model of a photodetector which, in the simple case of a light signal with constant intensity, gives a counting rate which is a non-linear function of the intensity. For sufficiently large signal intensity, the counting rate is proportional to the intensity, in agreement with the standard quantum results, but there is a dark rate when the signal intensity is low.

DOI
10.48550/arxiv.0707.2137

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The main argument against the reality of the electromagnetic vacuum fluctuations is that they do not activate photon detectors. In order to meet this objection we propose a classical model of a photodetector which, in the simple case of a light signal with constant intensity, gives a counting rate which is a non-linear function of the intensity. For sufficiently large signal intensity, the counting rate is proportional to the intensity, in agreement with the standard quantum results, but there is a dark rate when the signal intensity is low.
The main argument against the assumption that quantum fluctuations of the electromagnetic field are real is that they do not activate photon detectors. In order to met this objection I study several models of photon counter compatible with the reality of the fluctuations. The models predict a nonlinear dependence of the counting rate with the light intensity and the existence of a nonthermal dark rate, results which might explain the difficulty for performing loophole-free optical tests of Bell's inequality.
We study in this paper the possible influence of vacuum fluctuations on photo detection and its background noise in Bell tests. We analyze its consequences on the standard statistical analysis of data showing that it is not fulfilled anymore the conventional hypothesis of a Poisson like probability density distribution of single photodetection events. We assume that vacuum fluctuations are due to real and measurable fluctuating fields, as recently confirmed experimentally, and that their non null correlations outside the light cone contribute to photon coincidence rates making them time dependent. We introduce a generalized Bell like correlation function which contains a new term due to supposed vacuum induced photon counting events. We deduce then a generalization of CH-inequality which takes in account the effect of these vacuum electric fields on detector efficiency. We predict an apparatus temperature fluctuations during photon detection which we suggest could be observed by looking for colored noise thermal emission of the photodetectors, generalizing the standard white noise prediction of C.S.L. models on wave function collapse postulate. We discuss an experimental test of this prediction, based on the idea of inducing a thermal wave on the whole quantum detectors, aimed to observe time dependent deviations from standard stationary statistical predictions of Quantum Mechanics.
The basic formulae governing the fluctuations of counts registered by photoelectric detectors in an optical field are derived. The treatment, which has its origin in Purcell's explanation of the Hanbury Brown-Twiss effect, is shown to apply to any quasi-monochromatic light, whether stationary or not, and whether of thermal origin or not. The representation of the classical wave amplitude, of the light by Gabor's complex analytic signal appears naturally in this treatment. It is shown that the correlation of counts registered by N separate photodetectors at N points in space is determined by a 2 N th order correlation function of the complex classical field. The variance of the individual counts is shown to be expressible as the sum of terms representing the effects of classical particles and classical waves, in analogy to a well-known result of Einstein relating to black-body radiation. Since the theory applies to correlation effects obtained with any type of light it applies, in particular, to the output of an optical maser, although, for a maser operating on one mode, correlation effects are likely to be very small.
I assume that everywhere in space there is a real random electromagnetic radiation, or zeropoint field (ZPF), which looks similar for all inertial observers, so that the stochastic properties of the field should be Lorentz invariant. This fixes the spectrum except for a single adjustable parameter measuring the scale, which is identified with Planck's constant, so making the ZPF identical to the quantum electromagnetic vacuum. Photons are just fluctuations of the random field or, equivalently, wavepackets in the form of needles of radiation superimposed to the ZPF. Two photons are "classically correlated" if the correlation involves just the intensity above the average energy of the ZPF, but they are "entangled" if the ZP fields in the neighbourhood of the photons are also correlated. These assumptions may explain all quantum optical phenomena involving radiation and macroscopic bodies, provided the latter may be treated as classical. That is, we have an interpretation of quantization for light but not for matter. Detection of photons involves subtracting the ZPF, which cannot be made without a fundamental uncertainty. This explains why photon counters cannot be manufactured with 100% efficiency and no noise (dark rate), which prevents the violation of a genuine Bell inequality (this is the so-called detection loophole). The theory thus obtained agrees very closely with standard quantum optics if this is formulated in the Wigner representation.
In the Maxwell continuum wave theory of light, a photodetector measures the intensity of the Electro Magnetic wave. The output current of the photodetector is proportional to the intensity of input light. Since the introduction of the concept of photon, or the concept of field quantization, physicists started to premeditate single-photon detection, theoretically and experimentally. Due to slight differences in their optical paths, at certain locations, the radiations superposed constructively, at other locations the field superposed destructively. A sinusoidal modulation is thus observable. However, people found this interpretation may not be appropriate when the experimental physicists improved the sensitivity of their photodetector to the single-photon level. Almost everyone was surprised that the interference was still observable in the observation plane, and the sinusoidal modulation observed from single-photon was exactly the same as before. A single-photon counting detector is able to count photons one by one.