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Physical Review

Fluctuations of Beam Intensity in Space and Time

John M. Conway

Published Apr 25, 1967• 0 citations
Publisher

Abstract

The fluctuations in the counting rate of a particle detector are studied. The density matrix for the beam is arbitrary and the limiting cases of a coherent and an incoherent beam are treated in detail. The effect of a measurement on the wave function of a beam is treated in a fashion similar to that of Goldberger, Lewis, and Watson. The results for the correlation experiments performed by Hanbury Brown and Twiss and by Armstrong and Smith are developed.

DOI
10.1103/physrev.156.1365

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The fluctuations in the counting rate of a particle detector are studied. The density matrix for the beam is arbitrary and the limiting cases of a coherent and an incoherent beam are treated in detail. The effect of a measurement on the wave function of a beam is treated in a fashion similar to that of Goldberger, Lewis, and Watson. The results for the correlation experiments performed by Hanbury Brown and Twiss and by Armstrong and Smith are developed.
The distribution of counts from a photoelectric detector illuminated by light of bandwidth Δν 0 is analysed by associating the photons with Gaussian random waves. This is shown to lead to a full statistical description of the counts. It is shown that the number n T in a time interval T << 1/Δν 0 obeys pure Bose-Einstein statistics, and that the fluctuations in longer intervals T >> 1/Δν 0 are simply the density fluctuations of a boson assembly in a phase space of ~ Δν 0 T cells. The correlation coefficient ρ of the fluctuations of counts from two detectors illuminated by partially coherent beams is found to be proportional to the local time average of the square of the coherence function ⟨γ 12 2 ⟩. The correlation is shown to depend on the degeneracy of the beams in such a way that ρ → 2⟨γ 12 2 ⟩ for highly degenerate beams. The results are all consistent with those obtained by Hanbury Brown and Twiss in 1957.
IMeasurements of space-time correlations in the intensity of a beam of scattereq particles yield information about the scatterer.Goldberger and Watson have developed a theory of such measl~ementG appropriate to the case of ne~rly elastic scattering; in this paper we extend their theory to the case of inelastic scattering.The main result of our work is that under certain experimental conditions the correlated counting rate in an inelastic scattering experiment is of a form equivalent to the correlated counting rate for an incoherent beam of particles emitted by a source.This result applies, in particular, to Raman or Brillouin scattering of light by phonons in an extended target.However, estimates of the signal to noise ratio for this case indicate that it may not be possible to observe intensity correlations in Raman or Brillouin lines using presently available light sources. ABSTRACT OF PART IIThe coherent excitation of several atomic status by inelastic electron' scattering and their subsequent radia ti ve decay is considered.General expressions for the photon counting rate in a quantum beat experiment, and the total number of photons counted. in a le,vel crossing experiment are d.erived.The general results are used to calculate the phase of the oscillatory part of the photon counting rate in the Radeishi-Nierenberg quantum beat experiment.
The basic formulae governing the fluctuations of counts registered by photoelectric detectors in an optical field are derived. The treatment, which has its origin in Purcell's explanation of the Hanbury Brown-Twiss effect, is shown to apply to any quasi-monochromatic light, whether stationary or not, and whether of thermal origin or not. The representation of the classical wave amplitude, of the light by Gabor's complex analytic signal appears naturally in this treatment. It is shown that the correlation of counts registered by N separate photodetectors at N points in space is determined by a 2 N th order correlation function of the complex classical field. The variance of the individual counts is shown to be expressible as the sum of terms representing the effects of classical particles and classical waves, in analogy to a well-known result of Einstein relating to black-body radiation. Since the theory applies to correlation effects obtained with any type of light it applies, in particular, to the output of an optical maser, although, for a maser operating on one mode, correlation effects are likely to be very small.