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Optical Engineering

Level-Crossing Detection By Photon Statistics

M. Á. Rebolledo

Published Oct 1, 1983• 15 citations
Publisher

Abstract

In this paper several level-crossing detection techniques based on photon statistics are presented. Results on level-crossing detection through the measurement of the normalized second-order factorial moment n(2)(T) are reviewed. Detection by measurement of the normalized intensity correlation function g(2)(r) or the Laplace transform of time-interval probability is studied. The interest of the above mentioned techniques is analyzed.

DOI
10.1117/12.7973200

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In this paper several level-crossing detection techniques based on photon statistics are presented. Results on level-crossing detection through the measurement of the normalized second-order factorial moment n(2)(T) are reviewed. Detection by measurement of the normalized intensity correlation function g(2)(r) or the Laplace transform of time-interval probability is studied. The interest of the above mentioned techniques is analyzed.
A level-crossing detection method is presented and developed based on measurement of the normalized second factorial moment n((2))(T) of the photon-counting distribution of the resultant fluorescence. Expression n((2))(T) is obtained, and the errors expected in the determination of signal width and crossing field are theoretically studied. The validity of the approximations performed to establish the theoretical model is proved by an experiment with a square-wave periodically modulated light beam.
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.