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Optica Acta International Journal of Optics

Antibunching and Sub-poissonian Statistics in Photoelectron-triggered Optical Dead-time Experiments

Eric Jakeman, J. H. Jefferson

Published May 1, 1986• 15 citations
Publisher

Abstract

We investigate the statistical properties of photoelectric events in experiments where dead-times are introduced into a propagating light field by the use of a detection-triggered optical shutter. Theoretical results are derived for various optical arrangements generating both analogue and genuine non-classical effects. The validity of the formulae is tested by numerical simulation.

DOI
10.1080/713821989

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We investigate the statistical properties of photoelectric events in experiments where dead-times are introduced into a propagating light field by the use of a detection-triggered optical shutter. Theoretical results are derived for various optical arrangements generating both analogue and genuine non-classical effects. The validity of the formulae is tested by numerical simulation.
The use of dead time effects to generate sub-Poissonion photo-electron counting statistics is discussed. An experiment is described in which dead times are introduced using an optical shutter triggered by photo-detection events. Although the triggering photo-electron train is sub-Poissonion and antibunched, the light sampled by a second detector gives rise to a super-Poissonion and bunched train of photo-elecrons. A second experiment is proposed which would generate truly sub-Poisson light (ie detector independent). This is based on the use of optical dead times in parametric fluorescence.
An optoelectronic device that can generate either the non-paralysable or the paralysable dead-time effect has been constructed using a feedback scheme in conjunction with the acousto-optic deflector. ‘Semi-classical’ experiments show good agreement with the theory, which predicts antibunching and sub-Poissonian statistics. An expression for the correlation function of an arbitrary order is obtained for a general renewal process. From this general result, exact expressions for autocorrelation functions for both the non-paralysable and the paralysable counters are derived when the dead-time is greater than twice the sample time. The Fano factor is considered for both the non-paralysable and the paralysable counters. It is seen that the Fano factor for the paralysable counter can be smaller than that for the non-paralysable counter for a certain range of the input count rate.
Experiments on nonclassical optical fields have recently been performed. One of the main properties reported is the antibunching effect of photoelectrons, a property that cannot be explained in the framework of the classical theory of optical fields. By carefully studying the random point process of the detection of the optical field, we show that bunching and antibunching effects can be fully explained by a concidence function. In the classical theory, this function is a correlation function which introduces necessarily a bunching effect. But this coincidence function has no reason to be in any case a correlation function. Therefore antibunching effects can simply be derived from the properties of the coincidence function. After having given a precise definition of this coincidence function, some of its properties are discussed and especially its relationship with bunching and antibunching effects. Similarly, its relationship with statistical properties of lifetimes and intervals between points of the process is established. Various examples are presented and analyzed. Several calculations and computer simulations highlight the theoretical results.
A great deal of effort has been devoted during the last decade to the theory of nonclassical states of the radiation field. From a practical point of view some of the most interesting predictions of these theories concern the generation of light with sub-Poissonian photon counting statistics for which Such light is evidently less noisy than laser radiation with obvious implications for the improved performance of optical systems. When the temporal autocorrelation function of the photon counts increases as the delay time increases from zero the light is also said to be antibunched.
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.