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Journal of the Optical Society of America B

Observation of sub-Poisson Franck–Hertz light at 2537 nm

Malvin Carl Teich, Bahaa E. A. Saleh

Published Feb 1, 1985• 146 citations
Publisher

Abstract

We report the generation of ultraviolet (253.7-nm) sub-Poisson light from Hg vapor excited by inelastic collisions with a space-charge-limited (quiet) electron beam. This first stationary sub-Poisson light source is only weakly so, with a Fano factor that is between two and three standard deviations below that for Poisson light. This is principally because of optical losses in the experimental apparatus. There does not appear to be any fundamental limit that impedes the techniques from being used to produce an intense cw light source that is also arbitrarily sub-Poisson.

DOI
10.1364/josab.2.000275

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We report the generation of ultraviolet (253.7-nm) sub-Poisson light from Hg vapor excited by inelastic collisions with a space-charge-limited (quiet) electron beam. This first stationary sub-Poisson light source is only weakly so, with a Fano factor that is between two and three standard deviations below that for Poisson light. This is principally because of optical losses in the experimental apparatus. There does not appear to be any fundamental limit that impedes the techniques from being used to produce an intense cw light source that is also arbitrarily sub-Poisson.
The generation of nonclassical light has recently received a great deal of attention because three forms of it have now been observed in the laboratory: antibunched light, photon-number-squeezed (or sub-Poisson) light, and quadrature-squeezed light. These characteristics may, but need not, accompany each other in any given light source. Nonclassical light has been produced in experiments using resonance fluorescence, the Franck-Hertz effect, parametric interact ions, and semiconductor light sources. It is likely to be useful in providing new insights in various physical and biological processes, and in applications such as lightwave communications. Some of the characteristics, methods of generation, and expected uses of squeezed light will be addressed.
Vacuum ultraviolet light in the range 116 nm to 117 nm was produced by using a two-photon resonant four-wave mixing scheme in Xe. The buildup of coherent cancellation of the two-photon resonant transition employed in the generation of the vacuum ultraviolet, with resulting limitations imposed on the achievable vacuum ultraviolet intensity was investigated. Under certain predicted conditions, increases in the intensity of one of the pumping beams, approx.1500 nm infrared, or tuning this beam towards resonance with the 5p/sup 5/7s(3/2)/sub 1/ level of Xe led, not to increases, but decreases in the vacuum ultraviolet generated. 3 refs., 3 figs.
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.
We call quiet a stationary laser that generates in detectors regular photo-electrons (sub-Poisson statistics). It follows from the law of conservation of energy that this is so when the laser power supply does not fluctuate. Various configurations are analyzed on the basis of the Planck (1907) semi-classical concept: am not seeking the meaning of light quanta in the vacuum but rather in places where emission and absorption occur, and I assume that what happens in the vacuum is rigorously described by Maxwell's equations. Exact agreement with Quantum Optics results is noted. Comments welcome!
A novel method for generating light with sub-Poissonian photoelectron event statistics is described. The method is based on adding photons into an initially Poisson stream of photons, the number added being greater in intervals when the original Poisson stream contains fewer photons. The number of photons present in the original stream is estimated by counting the photoelectron events produced by a replica stream of photons generated by parametric fluorescence. An expression for the probability distribution function of the number of photons is derived and the Fano factor of the resulting photoelectron events is evaluated numerically.