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Photon counting statistics using a digital oscilloscope

María Luz Martínez Ricci, Javier Mazzaferri, Andrea V. Bragas, Oscar E. Martínez

Published Nov 6, 2006• 11 citations
OpenAlex

Abstract

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.

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Photon counting statistics using a digital oscilloscope

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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.

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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.

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Statistics of doubly stochastic light : An experimental investigation of photon arrival statistics

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If a beam of light is coherent, then the photons constituting the beam arrive at random moments in time. Consequently, the photon counting statistics in a given time interval below the coherence time, should in theory follow a Poissonian distribution. When the measurement interval exceeds the coherence time, the distribution should broaden and become a super-Poissonian distribution. The aim of this study is to experimentally demonstrate the Poissonian nature of light, as well as quantifying the transition to a super-Poissonian distribution. In the experiment, a low-intensity laser beam was measured with single-photon detectors, able to capture individual photons. The arrival time of the photons was detected with an oscilloscope, and the data further analysed with our own Python code. The probability distribution of the arrival time of photons was constructed and fitted with a Poissonian distribution for different time intervals. The results showed a clear Poissonian distribution for all intervals from 0.2 μs up to 2000 μs. We did however, observe tendencies of randomness for the longest measured intervals. A Poissonian distribution is defined by the variance being equal to the mean, whilst for a super-Poissonian distribution the variance is higher. The biggest measured ratio between the variance and the mean in our experiment was 1.06 for interval time 2000 μs, which is too small to infer super-Poissonian. Due to limited data memory, our dataset was restricted in length and resolution. Therefore, longer intervals could not be studied without statistical uncertainty. To cross-check the result we also calculated the probability distribution for the arrival time itself. The result perfectly fitted an exponential distribution which was in accordance with the theory of coherent light. Hence, within the given measurement accuracy and statistical uncertainty, it is safe to conclude that the laser beam is coherent for all tested time intervals. However, this does not allow us to conclude that it is a single-mode laser.

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Undergraduate quantum optics: experimental steps to quantum physics

Ruediger Scholz, Gunnar Friege, Kim-Alessandro Weber

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.

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Fluctuations in light beams: A simple student experiment

R. P. Wolf, Peter P. Crooker

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.

American Journal of Physics•May 1, 1982•1 citation
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.
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 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.
If a beam of light is coherent, then the photons constituting the beam arrive at random moments in time. Consequently, the photon counting statistics in a given time interval below the coherence time, should in theory follow a Poissonian distribution. When the measurement interval exceeds the coherence time, the distribution should broaden and become a super-Poissonian distribution. The aim of this study is to experimentally demonstrate the Poissonian nature of light, as well as quantifying the transition to a super-Poissonian distribution. In the experiment, a low-intensity laser beam was measured with single-photon detectors, able to capture individual photons. The arrival time of the photons was detected with an oscilloscope, and the data further analysed with our own Python code. The probability distribution of the arrival time of photons was constructed and fitted with a Poissonian distribution for different time intervals. The results showed a clear Poissonian distribution for all intervals from 0.2 μs up to 2000 μs. We did however, observe tendencies of randomness for the longest measured intervals. A Poissonian distribution is defined by the variance being equal to the mean, whilst for a super-Poissonian distribution the variance is higher. The biggest measured ratio between the variance and the mean in our experiment was 1.06 for interval time 2000 μs, which is too small to infer super-Poissonian. Due to limited data memory, our dataset was restricted in length and resolution. Therefore, longer intervals could not be studied without statistical uncertainty. To cross-check the result we also calculated the probability distribution for the arrival time itself. The result perfectly fitted an exponential distribution which was in accordance with the theory of coherent light. Hence, within the given measurement accuracy and statistical uncertainty, it is safe to conclude that the laser beam is coherent for all tested time intervals. However, this does not allow us to conclude that it is a single-mode laser.
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.