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arXiv:0906.2662 · Physical Review A

Photon statistics in the macroscopic realm measured without photon counters

Alessandra Andreoni, Maria Bondani

Published Jul 22, 2009• 33 citations
arXivHTMLPDF

Abstract

In a macroscopic realm, in which photons are too many to be counted by any photon-counting detector, photon statistics can be measured by using detectors simply endowed with linear response. We insert one of such detectors in a conventional photon-counting apparatus, which returns a voltage every time the detector responds to light by generating a number of elementary charges via its primary photodetection process. We only assume that, when a single charge is photogenerated, the probability density of the voltages is a distribution that is narrow with respect to its mean value. Under this hypothesis the output voltages can be suitably binned so that their probability distribution is the same as that of the photogenerated charges, that is, of the detected photons.

DOI
10.1103/physreva.80.013819

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In a macroscopic realm, in which photons are too many to be counted by any photon-counting detector, photon statistics can be measured by using detectors simply endowed with linear response. We insert one of such detectors in a conventional photon-counting apparatus, which returns a voltage every time the detector responds to light by generating a number of elementary charges via its primary photodetection process. We only assume that, when a single charge is photogenerated, the probability density of the voltages is a distribution that is narrow with respect to its mean value. Under this hypothesis the output voltages can be suitably binned so that their probability distribution is the same as that of the photogenerated charges, that is, of the detected photons.
We theoretically demonstrate that detectors endowed with internal gain and operated in regimes in which they do not necessarily behave as photon-counters, but still ensure linear input/output responses, can allow a self-consistent characterization of the statistics of the number of detected photons without need of knowing their gain. We present experiments performed with a photo-emissive hybrid detector on a number of classical fields endowed with non-trivial statistics and show that the method works for both microscopic and mesoscopic photon numbers. The obtained detected-photon probability distributions agree with those expected for the photon numbers, which are also reconstructed by an independent method.
Abstract Measurement of photon statistics is an important tool for the verification of quantum properties of light. Due to the various imperfections of real single photon detectors, the observed statistics of photon counts deviates from the underlying statistics of photons. Here we analyze statistical properties of coherent states, and investigate a connection between Poissonian distribution of photons and sub-Poissonian distribution of photon counts due to the detector dead-time corrections. We derive a functional dependence between the mean number of photons and the mean number of photon counts, as well as connection between higher-order statistical moments, for the pulsed or continuous wave coherent light sources, and confirm the results by numerical simulations.
It is well known that photoelectric measurements yield information about the statistical behavior of fluctuating light beams. The probability of n photoelectrons being ejected, in a fixed time interval, from the photosensitive surface of the photoelectric detector, upon which the light beam is normally incident, is a linear (Poisson) transform of the probability density for the intensity of the beam. With the help of some plausible assumptions, the present analysis provides solutions to the problem of inverting the Poisson transform, thus determining the probability density for the intensity from experimentally obtained photocounting distributions. The effectiveness of the method is demonstrated by an actual inversion of a typical experimental counting distribution. The technique is of particular interest in connection with efforts to understand the statistical behavior of optical fields, especially of laser fields.
Photon counting is a cornerstone of quantum optics. Here, we demonstrate precisely counting from 0 to over 9000 photons, beating the Poisson noise limit by at least 4.1 dB4.1~\mathrm{dB}4.1 dB across this range. We achieve sub-single-photon precision up to 276 photons per pulse. To do so, we multiplex eight intrinsically photon-number-resolving superconducting nanowire single-photon detectors across 128 temporal modes. We use a model-informed characterization of each of the 1024 detection bins, for optimal precision. We perform quantum detector tomography to reconstruct the positive operator valued measures (POVMs) of the complete device, which consists of 1.38⋅1081.38\cdot10^81.38⋅108 matrix elements. At the repetition rate of our experiment of 80 kHz80~\mathrm{kHz}80 kHz, we can precisely count photons corresponding to an optical power of approximately 71 pW71~\mathrm{pW}71 pW, bridging the gap from single-photon measurements to high-sensitivity optical power meters. A photon-number-resolving detector of this size, and the tools used to analyze it, will become increasingly important to characterize large quantum states, as well as tasks in precision metrology and optical power standards.