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Journal of Modern Optics

Generation and Statistical Properties of Optical Dead-time Effects

Doo Jin Cho, G. Michael Morris

Published Apr 1, 1988• 2 citations
Publisher

Abstract

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.

DOI
10.1080/09500348814550691

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Journal of the Optical Society of America B•Jun 1, 1984•45 citations
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.
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.
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.
We analyze the quantum statistical properties of light scattered by an acousto-optic modulator. From the perspective of quantum mechanics, the acousto-optic effect arises from a nonlinear interaction between three bosonic fields: the laser light, the Brillouin-scattered light, and an acoustic wave. The Hamiltonian coincides with that of sum-frequency generation, where the sum-frequency mode is known to exhibit sub-Poissonian statistics. We calculate the free temporal evolution of the Fano factor for Brillouin backscattered light and determine that sub-Poissonian statistics are obtained when faint laser light is scattered by a counter-propagating coherent acoustic wave with low average phonon number. The use of sub-Poissonian light would lead to an increase of the security for quantum key distribution.
Summary form only given. In any optical system, quantum and classical theory yield identical predictions for the mean intensity. The quantum mechanical predictions diverge from the classical theory only for higher order correlations. For this reason, typical quantum-interference experiments are performed by measuring coincidence rates between two or more detectors. The usual approximation, following Glauber, is that a single-photon counter fires at a rate proportional to the intensity, or number of incident photons per unit time. This approximation is so good and so entrenched that one routinely assumes that all singles-detection rates are insensitive to quantum effects. However, if one of these detectors fires, it cannot fire again for a characteristic time, called the dead-time. This characteristic of the detectors makes them highly nonlinear over times shorter than the dead-time, and thus sensitive to the higher order intensity correlations. In other words the detector has a different response for two photons arriving at different times, than for two photons arriving at the same time. We use the process of spontaneous parametric-downconversion (SPDC) to create correlated photon-pairs and send them through a polarization-based Hong-Ou-Mander interferometer. This quantum interferometer allows us to change the photon statistics without changing the intensity of the beams.
We examine the coherence properties of stationary light obtained by the superposition of nonstationary independent emissions occurring at random space–time points. The positions of the points are independent and uniformly distributed over the volume of the source. The emission times fluctuate in accordance with a stationary renewal point process. This process admits of super-Poisson, sub-Poisson, or Poisson behavior. The individual emissions are assumed to be in a coherent, chaotic, or n state. The statistical nature of the random-emission space–time points plays an important role in determining the coherence properties and photon statistics of the total field. This is manifested in the normalized second-order correlation function, which turns out to have the usual form for chaotic light with two additional terms. The first of these is determined by the statistical nature of the individual emissions (it is positive for coherent or chaotic, but zero for single-photon, emissions). The second term is governed by the statistics of the primary excitations (it is positive for super-Poisson, zero for Poisson, and negative for sub-Poisson excitations). Both additional terms become small for light with a high degeneracy parameter (many total photons per emission lifetime). The behavior of the light is then asymptotically chaotic. In the opposite limit, when the degeneracy parameter is small (or the emissions are instantaneous), the correlation properties of the primary excitations are directly transferred to the correlation properties of the photons. The first-order spatial-coherence properties of the field turn out to be identical with those of chaotic light (i.e., the van Cittert–Zernike theorem is obeyed), although the second-order properties differ. The photon-counting distribution reflects the character of the correlation function. Thus sub-Poisson primary excitations, together with n-state emissions, can lead to sub-Poisson photon counts under certain conditions. Such nonclassical light may be made arbitrarily intense if interference effects are eliminated by detecting many spatial modes. As an example of our theory, we cite a Franck–Hertz experiment excited by a space-charge-limited electron beam. If the electron excitations are represented as a sub-Poisson renewal point process, and the photon emissions as one-photon states, the light generated should be antibunched and sub-Poisson.