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Published November 1, 2015 | Published
Journal Article Open

On the Use of Shot Noise for Photon Counting

Abstract

Lieu et al. have recently claimed that it is possible to substantially improve the sensitivity of radio-astronomical observations. In essence, their proposal is to make use of the intensity of the photon shot noise as a measure of the photon arrival rate. Lieu et al. provide a detailed quantum-mechanical calculation of a proposed measurement scheme that uses two detectors and conclude that this scheme avoids the sensitivity degradation that is associated with photon bunching. If correct, this result could have a profound impact on radio astronomy. Here I present a detailed analysis of the sensitivity attainable using shot-noise measurement schemes that use either one or two detectors, and demonstrate that neither scheme can avoid the photon bunching penalty. I perform both semiclassical and fully quantum calculations of the sensitivity, obtaining consistent results, and provide a formal proof of the equivalence of these two approaches. These direct calculations are furthermore shown to be consistent with an indirect argument based on a correlation method that establishes an independent limit to the sensitivity of shot-noise measurement schemes. Furthermore, these calculations are directly applicable to the regime of interest identified by Lieu et al. Collectively, these results conclusively demonstrate that the photon-bunching sensitivity penalty applies to shot-noise measurement schemes just as it does to ordinary photon counting, in contradiction to the fundamental claim made by Lieu et al. The source of this contradiction is traced to a logical fallacy in their argument.

Additional Information

© 2015. The American Astronomical Society. Received 2015 January 13; accepted 2015 September 8; published 2015 October 22. I thank Jim Moran and John Kovac at Harvard for bringing this interesting problem to my attention, and Richard Lieu, Tom Kibble, and Lingze Duan for extensive discussions. This paper is dedicated to the memory of my father, Jonas Stasys Zmuidzinas, who first introduced me to coherent-state integrals.

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