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Annual Meeting Optical Society of America

Transition from Maxwell-Boltzmann to Bose-Einstein partition statistics by stochastic splitting of degenerate light

F. De Martini, R. Coluzzi, S. Di Fonzo

Published Jan 1, 1989• 1 citation
Publisher

Abstract

The first experimental verification of the Tersoff-Bayer interstatistics transition theory has been reported.1-3 A novel difference photon-counting method of detection, which reveals the field's particle fluctuations, is used to gain information on the beam splitting process of a highly Bose degenerate chaotic (and coherent) photon beam emitted from an ultrastable He-Ne laser. The splitting device consists of an electrooptic Pockels cell which acts as a stationary beam splitter or a chaotic beam splitter depending on the output properties of a driving noise generator. We found that the quantum Bose statistics in a splitting (i.e., scattering) process corresponds to a fully stochastic splitting process. This conclusion has been experimentally verified for two-way splitting and for general multichannel scattering induced by microscopic particles.

DOI
10.1364/oam.1989.wq1

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The first experimental verification of the Tersoff-Bayer interstatistics transition theory has been reported.1-3 A novel difference photon-counting method of detection, which reveals the field's particle fluctuations, is used to gain information on the beam splitting process of a highly Bose degenerate chaotic (and coherent) photon beam emitted from an ultrastable He-Ne laser. The splitting device consists of an electrooptic Pockels cell which acts as a stationary beam splitter or a chaotic beam splitter depending on the output properties of a driving noise generator. We found that the quantum Bose statistics in a splitting (i.e., scattering) process corresponds to a fully stochastic splitting process. This conclusion has been experimentally verified for two-way splitting and for general multichannel scattering induced by microscopic particles.
The results of an experiment show that the quantum-particles optical photons obey either Maxwell-Boltzmann or intermediate, or Bose-Einstein statistics depending on the degree of randomness of the scattering cross-section. This suggests a consistent model for the (most mysterious) interparticle quantum-correlation process. To accomplish that, we have adopted a novel quantum-optics method that, being sensitive to the field particle fluctuations, reveals the "quantum signature" of any Bose field. The intertatistics transition process is investigated both theoretically and experimentally.
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.
This is a review of a very interesting (in the authors' view) phenomenon — the operation of a nonlinear light beam splitter. The beam splitter is a flat interface between two transparent dielectrics, at least one of which exhibits Kerr nonlinearity, i.e., its refractive index depends on the transmitted radiation intensity. Interestingly, quantum and classical theories make directly opposite predictions about the phase fluctuations of the output radiation of this device. In classical theory, the phases remain unchanged; in quantum theory, the phases fluctuate in accordance with the amplitude–phase uncertainty relation. The origin of this difference is established at the fundamental level. A further remarkable point about this quantum paradox is that not only is the source beam split in two but one can also create conditions where the two split parts are respectively dominated by amplitude noise and phase noise, thus allowing the selection of photon fluctuations. Results of original studies are summarized and further developed.
The realization of the optical stochastic (or nonstationary) field interferometer (Sto-IF) is reported. By this device, whose properties are determined by those of the stochastic beam splitter (Sto-BS), relevant Bose-Einstein correlations are generated within the investigated particle field. A very general quantum theory of Sto-BS and Sto-IF is reported. Because it accounts for any distribution function of the Sto-BS driving field, this theory embodies the formal content and the results of previous interferometry theories. All theoretical results are substantiated by an experiment carried out with a Mach-Zehnder Sto-IF. Basic considerations on Bohr's complementarity in stochastic interferometry are expressed on the basis of Shannon's information theory applied to the particle welcher weg problem.