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Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical Sciences

X.—Remarks on Coincidence Experiments with Visible Light

Zoltan Bay, Péter Faragó

Published Jan 1, 1962• 0 citations
Publisher

Abstract

Synopsis After the detection of correlations in two coherent light beams by Hanbury Brown and Twiss, objections were raised by Brannen and Ferguson on the basis of the experiments of Adam, Janossy and Varga and their own experiments in which no correlations were detected. It is pointed out here that the different groups were looking for two entirely different effects, one being quadratic, the other one linear in the number of photons involved; the quadratic effect (discovered by Hanbury Brown and Twiss) is in agreement with quantum theory while the linear effect is not. It was shown by Purcell and by Hanbury Brown and Twiss that the choice of parameters in the experiments which gave negative results was inadequate to show the quadratic effect. It is shown in this paper that their experiments were also inadequate to decide between the existence or nonexistence of the linear effect.

DOI
10.1017/s0080454100007743

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Synopsis After the detection of correlations in two coherent light beams by Hanbury Brown and Twiss, objections were raised by Brannen and Ferguson on the basis of the experiments of Adam, Janossy and Varga and their own experiments in which no correlations were detected. It is pointed out here that the different groups were looking for two entirely different effects, one being quadratic, the other one linear in the number of photons involved; the quadratic effect (discovered by Hanbury Brown and Twiss) is in agreement with quantum theory while the linear effect is not. It was shown by Purcell and by Hanbury Brown and Twiss that the choice of parameters in the experiments which gave negative results was inadequate to show the quadratic effect. It is shown in this paper that their experiments were also inadequate to decide between the existence or nonexistence of the linear effect.
In 1956, Hanbury Brown and Twiss performed their famous intensity-correlation experiment with two 'coherent' beams of light from a thermal source. They argued that such intensity-correlation must entail an excess of photon arrival-time coincidences over chance ones for the two beams, and went on (with Little) to demonstrate this in an experiment (Twiss, Little and Hanbury Brown 1957). About the same time, Brannen and Ferguson (1956) performed a photon-coincidence experiment with coherent thermal light, and obtained a null result (due to lack of sensitivity).
The Hanbury Brown-Twiss effect is one of the celebrated phenomenologies of modern physics that accommodates equally well classical (interferences of waves) and quantum (correlations between indistinguishable particles) interpretations. The effect was discovered in the late thirties with a basic observation of Hanbury Brown that radio-pulses from two distinct antennas generate signals on the oscilloscope that wiggle similarly to the naked eye. When Hanbury Brown and his mathematician colleague Twiss took the obvious step to propose bringing the effect in the optical range, they met with considerable opposition as single-photon interferences were deemed impossible. The Hanbury Brown-Twiss effect is nowadays universally accepted and, being so fundamental, embodies many subtleties of our understanding of the wave/particle dual nature of light. Thanks to a novel experimental technique, we report here a generalized version of the Hanbury Brown-Twiss effect to include the frequency of the detected light, or, from the particle point of view, the energy of the detected photons. Our source of light is a polariton condensate, that allows high-resolution filtering of a spectrally broad source with a high degree of coherence. In addition to the known tendencies of indistinguishable photons to arrive together on the detector, we find that photons of different colors present the opposite characteristic of avoiding each others. We postulate that fermions can be similarly brought to exhibit positive (boson-like) correlations by frequency filtering.
The Hanbury Brown-Twiss effect is one of the celebrated phenomenologies of modern physics that accommodates equally well classical (interferences of waves) and quantum (correlations between indistinguishable particles) interpretations.The effect was discovered in the late thirties with a basic observation of Hanbury Brown that radio-pulses from two distinct antennas generate signals on the oscilloscope that wiggle similarly to the naked eye.When Hanbury Brown and his mathematician colleague Twiss took the obvious step to propose bringing the effect in the optical range, they met with considerable opposition as single-photon interferences were deemed impossible.The Hanbury Brown-Twiss effect is nowadays universally accepted and, being so fundamental, embodies many subtleties of our understanding of the wave/particle dual nature of light.Thanks to a novel experimental technique, we report here a generalized version of the Hanbury Brown-Twiss effect to include the frequency of the detected light, or, from the particle point of view, the energy of the detected photons.Our source of light is a polariton condensate, that allows high-resolution filtering of a spectrally broad source with a high degree of coherence.In addition to the known tendencies of indistinguishable photons to arrive together on the detector, we find that photons of different colors present the opposite characteristic of avoiding each others.We postulate that fermions can be similarly brought to exhibit positive (bosonlike) correlations by frequency filtering.
From quantum point of view, Hanbury Brown-Twiss effect is a result of constructive-destructive two-photon interference. There should be no Hanbury Brown-Twiss effect if there was no two-photon interference. In this paper, we observed Hanbury Brown- Twiss effect in a specially designed experiment, in which two-photon interference is impossible by keeping only one two-photon probability amplitude in the experimental scheme. However, our experimental results can still be interpreted by Glauber's quantum optical coherence theory. The researches in our paper are helpful to understand the physics of the second-order coherence of light, especially the physics of Hanbury Brown-Twiss effect.
Since the first observation of two-point correlation effects in optical fields (Hanbury, Brown, and Twiss, 1957) there has been continuous theoretical and experimental interest in photon correlation. In this paper we examine the possibility of measuring similar effects involving massive particles. We first discuss the theory of correlations between noninteracting massive particles by using the formalism of second quantization. This theory is considerably simpler than that for light because we can treat particles in the strictly nonrelativistic limit. However, the theory provides a particularly interesting contrast with the photon case because we may choose particles that are either fermions or bosons. We then apply the theory to the case of beams of atoms and neutrons and consider the experimental parameters of existing beams. In particular, we consider the case of experiments with laser-cooled metastable helium.
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.