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Journal of Modern Optics

Sub-Poissonian Photon Statistics by Photon Counting and Shuttering and by Photon-Interval Filling

John Walker

Published Jun 1, 1987• 2 citations
Publisher

Abstract

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.

DOI
10.1080/09500348714550761

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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.
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.
In parametric downconversion the quantum effects arise because two photons are created from one pump photon. Detection of photons in one train can be used to modify the quantum statistics of the other train to produce antibunched and/or sub-poissonian light. This chapter reports on two experiments of this type. The first employs single photon detection techniques and a fast optical shutter to create antibunched and slightly sub-poissonian light. The second uses analogue detection and feedback to produce sub-poissonian light at picowatt power levels with a Fano factor of 0.78 over a limited bandwidth. Sub-poissonian light is potentially useful in finite dose transmission measurements and the high degree of temporal coincidence of the downconverted photon pairs can be exploited in absolute measurement of detector quantum efficiency. The detailed shape of the fourth order interference effect can be related to the fourier transform of the photon bandwidth determined by the phase matching uncertainty and aperture size.
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.
States with sub-Poissonian photon-number statistics obtained by post-selection from twin beams are experimentally generated. States with Fano factors down to 0.62 and mean photon numbers around 12 are reached. Their quasi-distributions of integrated intensities attaining negative values are reconstructed. An intensified CCD camera with a quantum detection efficiency exceeding 20% is utilized both for post-selection and beam characterization. Experimental results are compared with theory that provides the optimum experimental conditions.
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.