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Physical Review A

Intrinsic and extrinsic statistical dependence in photoemission

G. J. Gabriel

Published Feb 1, 1974• 0 citations
Publisher

Abstract

Preliminary observations of a new effect in photoelectron statistics is reported. By utilizing an AND-gate system, the joint probability of emission of two photoelectrons from a photocathode at times ${t}_{1}$ and ${t}_{2}$ has been measured over a range of intervals, $\ensuremath{\tau}={t}_{2}\ensuremath{-}{t}_{1}$, lying between 4.0 and 50 nsec with a resolution $\ensuremath{\Delta}\ensuremath{\tau}$ at 1.0 nsec, under illumination with a single-mode He-Ne laser and a tungsten lamp. The joint probability of emission as a function of $\ensuremath{\tau}$, under both conditions of illumination, rises to a large peak in the neighborhood of $\ensuremath{\tau}=15$ nsec, and when $\ensuremath{\tau}$ exceeds 25 nsec, it drops rapidly to the constant value predicted by the classical theory of Mandel. In addition, there is a distinct fine structure which becomes more pronounced in the "dark" emission. Significantly, the amplitude of the peak varies linearly with the mean intensity of the incident light, while the constant value obtained at long intervals varies quadratically. To explain the observed phenomena, a generalization of the Mandel theory is formulated on the basis of the axiomatic theory of probability and the following hypotheses: (1) The emission of two photoelectrons separated by a time interval are statistically dependent events owing to intrinsic processes within the cathode as well as extrinsic processes of the radiation field; (2) If the instantaneous intensity of the radiation field is proportional to the square of the field amplitude, then the probability of emission is a function of this amplitude. Both hypotheses are found to be necessary to provide a base for interpreting the linear dependence of the joint probability peak on field intensity. Moreover, the generalized formulation reduces to Mandel's expressions when the following restrictions are imposed: The emission process is statistically independent; the probability of emission is proportional to the intensity of radiation, and the radiation field is a Gaussian random process.

DOI
10.1103/physreva.9.976

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A simple semiclassical derivation is given of the statistics of the photoelectrons emitted from a photosurface illuminated by light with statistically time dependent intensity. Comparison is made with the quantum mechanical expressions. Experiments are described that yield the probability of emission ofnphotoelectrons within a fixed time interval from a photocathode illuminated by a laser below and above threshold. The experimental results are compared with the theory developed in this paper and expressions derived by Glauber.
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In recent papers by Cohen-Tannoudji and Dalibard1 and Zoller et al.2 the statistics of quantum jumps in a three-level atom are analyzed in terms of the joint probability density W(t + τ;t) for a photon emission at time t followed by the next photon emission at time t+ τ. W(t+ τ;t) differs from the second-order correlation function G(2) (t + τ;t) often used to characterize photon statistics; the latter gives the joint emission probability without the condition that there be no emissions in the interval t to t + τ. Alter dividing by the density for single-photon emission, W(t + τ;t) gives the probability density for a delay τ between photon emissions.
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