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Physical Review

Accuracy of Measurement for Counting and Intensity-Correlation Experiments

M. L. Goldberger, Kenneth Watson

Published Oct 25, 1965• 4 citations
Publisher

Abstract

A quantum-mechanical analysis is made of the experimental accuracy to be expected for particle-counting and intensity-correlation experiments. The mean-square fluctuation for an ensemble, consisting of a large number of experiments each conducted over a time interval $T$, is calculated.

DOI
10.1103/physrev.140.b500

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A quantum-mechanical analysis is made of the experimental accuracy to be expected for particle-counting and intensity-correlation experiments. The mean-square fluctuation for an ensemble, consisting of a large number of experiments each conducted over a time interval TTT, is calculated.
A commonly used quantum mechanical formulation of the mean square displacement δx2(t) is based on the quantum correlation function of the position operator. While this quantity yields the classically expected result δx2(t)∝t2 for a ballistic particle in the interval topology, it is found here to diverge at essentially all times, when evaluated on infinitely large rings. A somewhat different formulation of the mean square displacement in quantum mechanics was proposed in a previous work (R. Marquardt, Mol. Phys. 119, e1971315 (2021)) and yielded the result δx2(t)∝t for the ballistic particle on an infinitely large ring. Here, it is shown analytically that that formulation yields δx2(t)≡0 for the ballistic particle on an infinitely long interval. The two formulations define two different, topology dependent quantities that have the dimension of an area and that could in principle be determined from the same experiment, following a measurement idea proposed in the aforementioned work. That idea is critically reviewed here.
Abstract A theoretical analysis is given of the correlation to be expected between the fluctuations in the outputs of two photoelectric detectors when these detectors are illuminated with partially coherent light. It is shown how this correlation depends upon the parameters of the equipment and upon the geometry of the experiment. The correlation may be detected either by linear multiplication of the fluctuations in the two outputs or by a coincidence counter which counts the simultaneous arrival of photons at the detectors. The theory is given for both these techniques and it is shown that they are closely equivalent. A laboratory test is described in which two photomultipliers were illuminated with partially coherent light and the correlation between the fluctuations in their outputs measured as a function of the degree of coherence. The results of this experiment are compared with the theory and it is shown that they agree within the limits of accuracy of the test; it is concluded that if there is any systematic error in the theory it is unlikely to exceed a few parts per cent.