Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optica Acta International Journal of Optics

Photon Statistics of Fluorescence Radiation

Henk F. Arnoldus, Gerard Nienhuis

Published Jun 1, 1986• 15 citations
Publisher

Abstract

We study the general properties of the photon statistics of fluorescence radiation, emitted by a two-level atom in a strong laser field and a perturber bath. We investigate the deviation of the factorial moments from a Poisson distribution, and we show that for long counting times the lowest-order correction can be expressed entirely by the quantity Q, which represents the deviation of the variance from the average. We introduce and evaluate the quantities gn(t), which serve as a measure for the deviation of the higher-order statistics from Poissonian statistics. Subsequently we obtain explicit expressions for the average waiting time for the appearance of the n th photon, after an arbitrary initialization of the counting process. It turns out that the average time delay is again determined by Q. Hence this parameter can be measured in a photon-counting experiment, which involves only the observation of a single photon, rather than an (in principle) infinite number of photons.

DOI
10.1080/713822007

Related papers

Sub-poissonian statistics of fluorescence from a single atom driven by a continuous wave laser field

Игорь Сергеевич Осадько

Statistics of fluorescence photons emitted by a single two-level atom interacting with a continuous wave laser field are analyzed. The photon-counting distribution is calculated for the so-called intermediate fluorescence photons, i.e., those counted during the time interval between instants at which photons are emitted. The result is a sub-Poissonian (narrower than Poisson) distribution, which agrees with experimental observations. This intermediate-photon distribution is used to calculate the average number of fluorescence photons, the second factorial moment of the photon-counting distribution, and Mandel’s Q parameter commonly used to evaluate the deviation of photon statistics from the Poisson distribution. The theoretical expressions obtained for moments of the intermediate-photon distribution are different from well-known Mandel’s formulas.

Journal of Experimental and Theoretical Physics•Jul 1, 2005•14 citations

Waiting times, probabilities and theQfactor of fluorescent photons

Henk F. Arnoldus, Robertsen A. Riehle

Photons in resonance fluorescence from a single atom are correlated, and this affects the photon detection statistics. We consider the time dependence of the variance for the number of counts in a time interval [0, T], and we show that there exist Poisson points for certain values of the atomic parameters. At these points, the variance equals the average, like for a Poisson process. We also show that the conditional probability density for the detection of the nth photon after a detection of a photon at time zero can be obtained from the conditional probability density for the first photon, and we illustrate this by computing several conditional probability densities for a special case of interest. The unconditional probability density for the detection of the nth photon can be obtained from the conditional probability densities and the probability for detecting n photons in [0, T] can subsequently be found from the unconditional probability densities.

Journal of Modern Optics•Jun 12, 2012•4 citations

Statistics of Fluorescent Photons Emitted Near a Phase Conjugator.

Henk F. Arnoldus, Thomas F. George, Chung‐In Um

Abstract : Temporal photon correlations and photon count statistics of fluorescence radiation, emitted by an atom in the vicinity of a phase conjugator, are considered. The fluorescent intensity and the two-photon correlation function are expressed in terms of photon emission operators. An explicit evaluation shows their dependence on the phase-conjugate reflectivity of the surface. The variance of the photon count distribution for long counting times is expressed in terms of the Q-factor, which is evaluated as a function of the reflectivity. It appears that for a reflectivity larger than unity, the photon correlation displays antibunching and the statistics is sub-poissonian.

Unknown eBooks•Jan 1, 1992•0 citations

Photon counting statistics with imperfect detectors

Aleksei Reutov, Сыч Денис Васильевич

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.

Journal of Physics Conference Series•Dec 1, 2021•0 citations

Thermal-field effects of photon statistics in resonance fluorescence

Saad S. M. Hassan, R. Bullough, G. P. Hildred +1 more

The photon counting statistics of the fluorescence of a single atom driven by a resonant coherent field has been calculated and the results checked experimentally. The authors examine the effect of detuning the coherent field and/or the effect of an additional thermal field on the photon counting statistics. They work with a master equation that they have used previously and derive exact results for the probability distribution function P(n, tau ) for the emitted photons and for the normalised second factorial moment Q. The subPoissonian character of the photon statistics, for which Q<0, is most pronounced for weak thermal fields or weak detuned coherent fields. For short counting times tau the statistic is dominated by any spontaneous emission that occurs, as expected. Increasing numbers of black-body photons tend to increase the Q values, as might be expected-especially in the case of an initially excited atom-but no simple rule emerges. The recent experiments in the microwave region on Rydberg atoms interacting with thermal radiation in (low-Q) cavities offers the possibility of observing thermal-field effects on the photon counting statistics.

Journal of Physics B Atomic Molecular and Optical Physics•Mar 28, 1988•7 citations

Photon-number statistics in resonance fluorescence

Daan Lenstra

The theory of photon-number statistics in resonance fluorescence is treated, starting with the general formula for the emission probability of $n$ photons during a given time interval $T$. The results fully confirm formerly obtained results by Cook that were based on the theory of atomic motion in a traveling wave. General expressions for the factorial moments are derived and explicit results for the mean and the variance are given. It is explicitly shown that the distribution function tends to a Gaussian when $T$ becomes much larger than the natural lifetime of the excited atom. The speed of convergence towards the Gaussian is found to be typically slow, that is, the third normalized central moment (or the skewness) is proportional to ${T}^{\ensuremath{-}\frac{1}{2}}$. However, numerical results illustrate that the overall features of the distribution function are already well represented by a Gaussian when $T$ is larger than a few natural lifetimes only, at least if the intensity of the exciting field is not too small and its detuning is not too large.

Physical Review A•Dec 1, 1982•57 citations
We study the general properties of the photon statistics of fluorescence radiation, emitted by a two-level atom in a strong laser field and a perturber bath. We investigate the deviation of the factorial moments from a Poisson distribution, and we show that for long counting times the lowest-order correction can be expressed entirely by the quantity Q, which represents the deviation of the variance from the average. We introduce and evaluate the quantities gn(t), which serve as a measure for the deviation of the higher-order statistics from Poissonian statistics. Subsequently we obtain explicit expressions for the average waiting time for the appearance of the n th photon, after an arbitrary initialization of the counting process. It turns out that the average time delay is again determined by Q. Hence this parameter can be measured in a photon-counting experiment, which involves only the observation of a single photon, rather than an (in principle) infinite number of photons.
Statistics of fluorescence photons emitted by a single two-level atom interacting with a continuous wave laser field are analyzed. The photon-counting distribution is calculated for the so-called intermediate fluorescence photons, i.e., those counted during the time interval between instants at which photons are emitted. The result is a sub-Poissonian (narrower than Poisson) distribution, which agrees with experimental observations. This intermediate-photon distribution is used to calculate the average number of fluorescence photons, the second factorial moment of the photon-counting distribution, and Mandel’s Q parameter commonly used to evaluate the deviation of photon statistics from the Poisson distribution. The theoretical expressions obtained for moments of the intermediate-photon distribution are different from well-known Mandel’s formulas.
Photons in resonance fluorescence from a single atom are correlated, and this affects the photon detection statistics. We consider the time dependence of the variance for the number of counts in a time interval [0, T], and we show that there exist Poisson points for certain values of the atomic parameters. At these points, the variance equals the average, like for a Poisson process. We also show that the conditional probability density for the detection of the nth photon after a detection of a photon at time zero can be obtained from the conditional probability density for the first photon, and we illustrate this by computing several conditional probability densities for a special case of interest. The unconditional probability density for the detection of the nth photon can be obtained from the conditional probability densities and the probability for detecting n photons in [0, T] can subsequently be found from the unconditional probability densities.
Abstract : Temporal photon correlations and photon count statistics of fluorescence radiation, emitted by an atom in the vicinity of a phase conjugator, are considered. The fluorescent intensity and the two-photon correlation function are expressed in terms of photon emission operators. An explicit evaluation shows their dependence on the phase-conjugate reflectivity of the surface. The variance of the photon count distribution for long counting times is expressed in terms of the Q-factor, which is evaluated as a function of the reflectivity. It appears that for a reflectivity larger than unity, the photon correlation displays antibunching and the statistics is sub-poissonian.
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.
The photon counting statistics of the fluorescence of a single atom driven by a resonant coherent field has been calculated and the results checked experimentally. The authors examine the effect of detuning the coherent field and/or the effect of an additional thermal field on the photon counting statistics. They work with a master equation that they have used previously and derive exact results for the probability distribution function P(n, tau ) for the emitted photons and for the normalised second factorial moment Q. The subPoissonian character of the photon statistics, for which Q<0, is most pronounced for weak thermal fields or weak detuned coherent fields. For short counting times tau the statistic is dominated by any spontaneous emission that occurs, as expected. Increasing numbers of black-body photons tend to increase the Q values, as might be expected-especially in the case of an initially excited atom-but no simple rule emerges. The recent experiments in the microwave region on Rydberg atoms interacting with thermal radiation in (low-Q) cavities offers the possibility of observing thermal-field effects on the photon counting statistics.
The theory of photon-number statistics in resonance fluorescence is treated, starting with the general formula for the emission probability of nnn photons during a given time interval TTT. The results fully confirm formerly obtained results by Cook that were based on the theory of atomic motion in a traveling wave. General expressions for the factorial moments are derived and explicit results for the mean and the variance are given. It is explicitly shown that the distribution function tends to a Gaussian when TTT becomes much larger than the natural lifetime of the excited atom. The speed of convergence towards the Gaussian is found to be typically slow, that is, the third normalized central moment (or the skewness) is proportional to ${T}^{\ensuremath{-}\frac{1}{2}}$. However, numerical results illustrate that the overall features of the distribution function are already well represented by a Gaussian when TTT is larger than a few natural lifetimes only, at least if the intensity of the exciting field is not too small and its detuning is not too large.