散粒噪声在光子计数中的应用
On the use of shot noise for photon counting
摘要：
Lieu等人（2015）最近声称，有可能大幅提高射电天文观测的灵敏度。本质上，他们的建议是利用光子散粒噪声的强度作为光子到达率的度量。Lieu等人（2015）提供了一个使用两个探测器的拟议测量方案的详细量子力学计算，并得出结论，该方案避免了与光子聚束相关的灵敏度下降。如果是正确的，这一结果可能对射电天文学产生深远的影响。在这里，我提出了一个详细的分析，使用散粒噪声测量方案，使用一个或两个探测器，可达到的灵敏度，并证明这两个方案都不能避免光子聚束惩罚。我进行半经典和完全量子计算的灵敏度，获得一致的结果，并提供了一个正式的证明这两种方法的等价性。这些直接的计算进一步表明是一致的间接参数的基础上建立一个独立的限制散粒噪声测量方案的灵敏度的相关方法。总的来说，这些结果最终证明，光子聚束灵敏度惩罚适用于散粒噪声测量方案，就像它适用于普通光子计数一样，这与Lieu等人（2015）提出的基本主张相矛盾。这种矛盾的根源可以追溯到他们论证中的一个逻辑谬误。
英文摘要：
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.
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