On the use of shot noise for photon counting

TL;DR

This paper critically evaluates the use of shot noise for photon counting in radio astronomy, demonstrating that photon bunching limits sensitivity as previously thought, contradicting recent claims of improved measurement schemes.

Contribution

It provides a comprehensive analysis showing that shot-noise measurement schemes cannot bypass the photon bunching sensitivity penalty, refuting recent claims.

Findings

Shot noise schemes are limited by photon bunching sensitivity.

Semiclassical and quantum calculations yield consistent results.

The supposed advantage of two-detector schemes is invalid.

Abstract

Lieu et al. (2015) 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. (2015) 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. 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. (2015). The source of this contradiction is traced to a logical fallacy in their argument.