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American Journal of Physics

Photon counting statistics—Undergraduate experiment

P. Koczyk, Piotr P. Wiewior, Czesław Radzewicz

Published Mar 1, 1996• 31 citations
Publisher

Abstract

A photon counting experiment for student physics laboratory is described. It is designed to illustrate the probabilistic nature of the photodetection process itself as well as statistical fluctuations of light. The setup enables the student to measure photon count distributions for both coherent and pseudothermal light sources yielding Poisson and Bose–Einstein distributions, respectively.

DOI
10.1119/1.18211

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A photon counting experiment for student physics laboratory is described. It is designed to illustrate the probabilistic nature of the photodetection process itself as well as statistical fluctuations of light. The setup enables the student to measure photon count distributions for both coherent and pseudothermal light sources yielding Poisson and Bose–Einstein distributions, respectively.
We present a photon counting experiment designed for an undergraduate physics laboratory. The statistics of the number of photons of a pseudo-thermal light source is studied in two limiting cases: much longer and much shorter than the coherence time, giving Poisson and Bose-Einstein distributions, respectively. The experiment can be done in a reasonable time using a digital oscilloscope without the need of counting boards. The use of the oscilloscope has the advantage of allowing the storage of the data for further processing. The stochastic nature of the detection phenomena adds additional value because students are forced to do data processing and analysis.
We present a photon counting experiment designed for an undergraduate physics laboratory. The statistics of the number of photons of a pseudo thermal light source is studied in two limiting cases: well above and well below the coherence time, giving Poisson and Bose-Einstein distributions, respectively. We show that using a digital oscilloscope the experiment can be done in a reasonable time, without need of counting boards. The use of the oscilloscope has the additional advantage of allowing the storage of the data for further processing. Hence, using the same set of data, the analysis of the statistics of the occurrence of n photons as a function of the time windows adds important evidence to determine accurately the nature of the light source. The stochastic nature of the detection phenomena adds an additional value to this type of experiments, since the student is forced to a thorough visit through data processing and statistics.
Abstract We report on a step-by-step-series of experiments from statistical optics with classical light to undergraduate quantum optics with single-photon states, particularly suitable to paving an introductory way to quantum phenomena. We build up a progressive process analysing temporal variations of the irradiance of light discerned by measuring the value of the non-delayed second-order correlation function g (2) ( τ = 0). We demonstrate how Poisson distributed photoelectron counts from constant irradiance ( g (2) (0) = 1) can be used to calibrate the apparatus. Measurements with harmonically modulated irradiance of Poissonian light give an introduction to g (2) (0) correlation analysis. After these introductory steps, we demonstrate photon bunching with (pseudo-) thermal light ( g (2) (0) ≈ 2), and finally show quantum antibunching of photons in Fock states ( g (2) (0) ≈ 0). All measurements are in excellent agreement with the theoretical predictions.
Light emitted from a thermal source has a fluctuating intensity; these fluctuations are a direct illustration of the elementary principles of statistical and quantum physics. We describe here a student experiment demonstrating these ideas. First the probability density for the intensity of thermal light inhabiting s coherence volumes is derived, using the Bose–Einstein distribution for photons in phase space. Then a simple method is shown for measuring this probability density using a quasithermal light source and a multichannel analyzer. Data are presented and a scheme for fitting the data to the theory is outlined.
We describe photon statistics experiments using pseudothermal light that can be performed in an undergraduate physics laboratory. We examine the light properties in terms of a second-order coherence function, as determined either by measuring the light intensity as a function of time or via coincidence analysis of a pair of photon detectors. We determine the coherence time and intensity distribution of the pseudothermal light source that exhibits either Gaussian or non-Gaussian statistics as a function of their optical parameters, and then compare the results with theoretical predictions. The simple photodiode method can be used for the qualitative analysis of the coherence time, but more accurate measurements are achieved using the coincidence method.
While the classical, wavelike behavior of light (interference and diffraction) has been easily observed in undergraduate laboratories for many years, explicit observation of the quantum nature of light (i.e., photons) is much more difficult. For example, while well-known phenomena such as the photoelectric effect and Compton scattering strongly suggest the existence of photons, they are not definitive proof of their existence. Here we present an experiment, suitable for an undergraduate laboratory, that unequivocally demonstrates the quantum nature of light. Spontaneously downconverted light is incident on a beamsplitter and the outputs are monitored with single-photon counting detectors. We observe a near absence of coincidence counts between the two detectors—a result inconsistent with a classical wave model of light, but consistent with a quantum description in which individual photons are incident on the beamsplitter. More explicitly, we measured the degree of second-order coherence between the outputs to be g(2)(0)=0.0177±0.0026, which violates the classical inequality g(2)(0)⩾1 by 377 standard deviations.