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Annual Meeting Optical Society of America

Testing particle indistinguishability in quantum statistics by optical interferometry and diffraction

F. De Martini

Published Jan 1, 1986• 0 citations
Publisher

Abstract

We have discovered from Michelson and Young interferometry experiments, carried out with the use of an argon laser (working at λ = 5145 Å, with intracavity etalon, cw, 1-W power) that the standard application of quantum electrodynamics (QED) to this problem is incorrect. Photons belonging to a chaotic mixture of |n〉 states behave as Bose-Einstein (BE) particles showing a large reduction of the interference-fringe visibility V ( n ¯ ) = ( I max − I min ) / ( I max + I min ) for increasing average photon number per radiation mode 〈 n 〉 = n ¯ , where I ( n ¯ ) is the photodetected intensity. This effect, never investigated or anticipated before, is a manifestation of the quantum interparticle correlations inherent BE statistics. Photons belonging to a superimposition of coherent, Glauber, |α〉 states (i.e., a laser beam) follow Maxwell-Boltzmann (MB) statistics leading to V ( n ¯ ) = 1 for any n ¯ , owing to absence of interparticie correlations.

DOI
10.1364/oam.1986.thh7

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Annual Meeting Optical Society of America•Jan 1, 1986•0 citations
We have discovered from Michelson and Young interferometry experiments, carried out with the use of an argon laser (working at λ = 5145 Å, with intracavity etalon, cw, 1-W power) that the standard application of quantum electrodynamics (QED) to this problem is incorrect. Photons belonging to a chaotic mixture of |n〉 states behave as Bose-Einstein (BE) particles showing a large reduction of the interference-fringe visibility V ( n ¯ ) = ( I max − I min ) / ( I max + I min ) for increasing average photon number per radiation mode 〈 n 〉 = n ¯ , where I ( n ¯ ) is the photodetected intensity. This effect, never investigated or anticipated before, is a manifestation of the quantum interparticle correlations inherent BE statistics. Photons belonging to a superimposition of coherent, Glauber, |α〉 states (i.e., a laser beam) follow Maxwell-Boltzmann (MB) statistics leading to V ( n ¯ ) = 1 for any n ¯ , owing to absence of interparticie correlations.
Abstract It is shown by a quantum-mechanical treatment that the emission times of photoelectrons at different points illuminated by a plane wave of light are partially correlated, and identical results are obtained by a classical theory in which the photocathode is regarded as a square-law detector of suitable conversion efficiency. It is argued that the phenomenon exemplifies the wave rather than the particle aspect of light and that it may most easily be interpreted as a correlation between the intensity fluctuations at different points on a wavefront which arise because of interference between different frequency components of the light. From the point of view of the corpuscular picture the interpretation is much less straight­forward but it is shown that the correlation is directly related to the so-called bunching of photons which arises because light quanta are mutually indistinguishable and obey Bose-Einstein statistics. However, it is stressed that the use of the photon concept before the light energy is actually detected is highly misleading since, in an interference experiment, the electromagnetic field behaves in a manner which cannot be explained in terms of classical particles. The quantitative predictions of the theory have been confirmed by laboratory experi­ments and the phenomenon has been used, in an interferometer, to measure the apparent angular diameter of Sirius: these results, together with further applications to astronomy, will be discussed in detail in later papers. It is shown that the classical and quantum treatments give identical results when applied to find the fluctuations in the photoemission current produced by a single light beam, and the connexion between these fluctuations and the correlation between photons in coherent beams is pointed out. The results given here are in full agreement with those obtained by Kahn from an analysis based on quantum statistics: however, they differ from those derived on thermodynamical grounds by Fellgett and by Clark Jones and the reasons for this discrepancy are discussed.
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.
"Quantum interferometry uses the quantum properties of light to surpass the Rayleigh diffraction limit inherent in classical interferometry. We have used Fock and coherent states, which describe the electromagnetic input field, a multi-photon counting apparatus, and an operator-based approach to a multi-slit Young’s experiment to present the principles behind quantum interferometry. Our calculations show interference fringes that depend on the wavelength of the source h, the number of slits in the Young’s screen-both characteristics present in the classical scheme-, and the number of photons m, that the measurement apparatus detects. The latter dependence generates an effective de Broglie wavelength, h/m, a phenomenon that can only be observed by taking advantage of the quantum properties of light."
Classical electromagnetics in free space leaves no room for accommodation of a light particle. To underline this, it is sufficient to remember that Einstein in order to reach his lightquantum (energy-quantum) hypothesis had to mix classical theoretical physics with a piece of experimental information that defies description in classical terms. In his 1905-paper Einstein concluded [60]:Monochromatic radiation of low density (within the range of validity of Wien’s radiation formula) behaves thermodynamically as though it consisted of a number of mutually independent energy quanta of magnitude hν. The introduction of light quanta in the Wien regime (the high-frequency part of the Planck blackbody radiation law) is the first step toward the concept of electromagnetic radiation as a Bose gas of photons [180, 39, 68, 69]. Although a photon gas obeys Bose-Einstein statistics for all frequencies the statistical independence assumed by Einstein in 1905 is not true in general. Einstein used Boltzmann statistics when he conjectured the existence of light quanta. In the Wien regime Boltzmann and Bose-Einstein statistics lead to the same conclusion since the mean number of particles (photons) with a given energy is much less than one. The circumstance that the light quanta are not statistically independent in Bose-Einstein counting finds its explanation in quantum mechanics. Hence, the statistical correlation is induced by the requirement of totally symmetric wave functions.
Interference experiments characterized by the degree of first-order coherence (Young’s fringes, Fresnel, and Fraunhofer diffraction, etc.) have been performed with massive particles, in particular electrons and neutrons, as well as with light. Optical intensity interference or correlation experiments characterized by the degree of second-order coherence have not yet been performed with particles. The theory for such experiments shows striking differences in the behavior of electrons compared with that of light deriving from the differences in quantum statistics and charge. Photons are neutral bosons. They can be prepared in states that exhibit bunching, no bunching, or antibunching; they are unaffected by the presence of electromagnetic potentials. Electrons are charged fermions. Theory indicates that they exhibit antibunching regardless of the coherence of the source, and that their degree of second-order coherence can be influenced by electromagnetic fields through which they do not pass. A remarkable example is the Hanbury Brown-Twiss experiment with electrons that have interacted locally with the vector potential of an inaccessible magnetic field. The electron intensity correlation at two detectors is shown to be sensitive to the confined magnetic flux; experimental conditions differ considerably from those of the well-known Aharonov-Bohm effect.