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Optica Acta International Journal of Optics

Sub-poissonian Photon Statistics by Photon Addition

J.G. Walker

Published Mar 1, 1986• 8 citations
Publisher

Abstract

A novel method for generating light with sub-Poissonian photoelectron event statistics is described. The method is based on adding photons into an initially Poisson stream of photons, the number added being greater in intervals when the original Poisson stream contains fewer photons. The number of photons present in the original stream is estimated by counting the photoelectron events produced by a replica stream of photons generated by parametric fluorescence. An expression for the probability distribution function of the number of photons is derived and the Fano factor of the resulting photoelectron events is evaluated numerically.

DOI
10.1080/713821940

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A novel method for generating light with sub-Poissonian photoelectron event statistics is described. The method is based on adding photons into an initially Poisson stream of photons, the number added being greater in intervals when the original Poisson stream contains fewer photons. The number of photons present in the original stream is estimated by counting the photoelectron events produced by a replica stream of photons generated by parametric fluorescence. An expression for the probability distribution function of the number of photons is derived and the Fano factor of the resulting photoelectron events is evaluated numerically.
Two novel methods of generating light with sub-Poissonian photon-counting statistics are described. Both methods are based on the use of parametric downconversion to generate two beams with simultaneously produced photons. By detecting the photons in one beam a knowledge of the time sequence of the photons in the other beam is obtained and used to modify the initially Poisson statistics. Expressions for the probability distribution functions of the two methods are derived and Fano factors are evaluated.
Sub-Poissonian photoelectron statistics have been produced by using the detection of down-converted photons in a trigger channel, having an electronic dead time, fed back to gate conjugate photoelectrons in a signal channel. With suitable choice of gate width and dead time a second factorial moment of the photo-electron count distribution as low as 0.4 has been achieved with considerable improvements in signal variance over equivalent Poisson sources. Suitable modification of the apparatus to produce sub-Poissonian photons rather than photoelectrons is described.
We show that time distributions of photoelectrons can best be described by a generalized probability-density function which we call the probability-density functional. The probability-density functional gives complete information about the statistical properties of any random-point process, and provides the most natural definitions of the ensemble average and generating functional of a quantity distributed in time. Using this functional, we develop a new approach to photoelectron statistics that systematically relates various joint probability distributions of photoelectrons to one another and to the corresponding generating functionals. We demonstrate that this method can be used to derive previously obtained results and we use it to obtain new results. In particular, the amount of information about the statistical properties of photoelectrons that is contained in a probability distribution can be obtained by comparing the corresponding generating functional with the probability-density functional. Further, we examine time derivatives of the probability distribution for the number of counts and develop new relationships for probability distributions of triggered counting. Finally, we apply our results to obtain an ``inverse'' relationship between photon bunching (antibunching) and super-Poisson (sub-Poisson) statistics.
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.
An analysis of intermittent fluorescence is presented for a single molecule driven by a continuous-wave laser field. The interruptions of fluorescence are caused by transition of the molecule to a triplet state. A method previously developed to calculate photon distribution for continuous-wave fluorescence is applied to analyze photon statistics of fluorescence blinking. The probability w N (T) of counting N photons over a time interval T is derived for intermittent fluorescence. The photons counted over relatively short intervals are found to have a sub-Poissonian (narrower than Poisson) distribution. The photon distribution over intervals longer than the mean off time has a complicated form with two maxima; i.e., a super-Poissonian (wider than Poisson) distribution is obtained.