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Australian Journal of Physics

The Detection of Time-correlated Photons by a Coincidence Counter

R. Q. Twiss, A. G. Little

Published Mar 1, 1959• 37 citations
Publisher

Abstract

The existence of a correlation between the arrival times of photons has been confirmed by measurements with a coincidence counter having a resolving time of 3·5 X 10-9 sec in three different experiments. In the first experiment it was found that the number of coincidence counts recorded from two photomultipliers, the apertures of which were optically superimposed, was significantly greater than when the light beams were incoherent. Furthermore, the number of these correlated counts was in satisfactory agreement with that predicted by theory. In the second experiment the change in the number of excess coincidences was measured as the degree of coherence of the light was altered by increasing the apparent separation of the photocathodes, and in this case also there was reasonable agreement between theory and experiment. In the final experiment it was shown that there was a significant difference between the number of coincidences observed when the light beams were in identical as opposed to orthogonal polarizations, and this last result especially makes it extremely improbable that the correlation could be caused by some spurious effect, such as plasma oscillations in the source, since the light source itself was found to be completely unpolarized.

DOI
10.1071/ph590077

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The existence of a correlation between the arrival times of photons has been confirmed by measurements with a coincidence counter having a resolving time of 3·5 X 10-9 sec in three different experiments. In the first experiment it was found that the number of coincidence counts recorded from two photomultipliers, the apertures of which were optically superimposed, was significantly greater than when the light beams were incoherent. Furthermore, the number of these correlated counts was in satisfactory agreement with that predicted by theory. In the second experiment the change in the number of excess coincidences was measured as the degree of coherence of the light was altered by increasing the apparent separation of the photocathodes, and in this case also there was reasonable agreement between theory and experiment. In the final experiment it was shown that there was a significant difference between the number of coincidences observed when the light beams were in identical as opposed to orthogonal polarizations, and this last result especially makes it extremely improbable that the correlation could be caused by some spurious effect, such as plasma oscillations in the source, since the light source itself was found to be completely unpolarized.
Summary form only given. In any optical system, quantum and classical theory yield identical predictions for the mean intensity. The quantum mechanical predictions diverge from the classical theory only for higher order correlations. For this reason, typical quantum-interference experiments are performed by measuring coincidence rates between two or more detectors. The usual approximation, following Glauber, is that a single-photon counter fires at a rate proportional to the intensity, or number of incident photons per unit time. This approximation is so good and so entrenched that one routinely assumes that all singles-detection rates are insensitive to quantum effects. However, if one of these detectors fires, it cannot fire again for a characteristic time, called the dead-time. This characteristic of the detectors makes them highly nonlinear over times shorter than the dead-time, and thus sensitive to the higher order intensity correlations. In other words the detector has a different response for two photons arriving at different times, than for two photons arriving at the same time. We use the process of spontaneous parametric-downconversion (SPDC) to create correlated photon-pairs and send them through a polarization-based Hong-Ou-Mander interferometer. This quantum interferometer allows us to change the photon statistics without changing the intensity of the beams.
Abstract A theoretical analysis is given of the correlation to be expected between the fluctuations in the outputs of two photoelectric detectors when these detectors are illuminated with partially coherent light. It is shown how this correlation depends upon the parameters of the equipment and upon the geometry of the experiment. The correlation may be detected either by linear multiplication of the fluctuations in the two outputs or by a coincidence counter which counts the simultaneous arrival of photons at the detectors. The theory is given for both these techniques and it is shown that they are closely equivalent. A laboratory test is described in which two photomultipliers were illuminated with partially coherent light and the correlation between the fluctuations in their outputs measured as a function of the degree of coherence. The results of this experiment are compared with the theory and it is shown that they agree within the limits of accuracy of the test; it is concluded that if there is any systematic error in the theory it is unlikely to exceed a few parts per cent.
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.
Synopsis Methods which are widely used in the mathematical analysis of random noise are used here to obtain expressions for the coincidence-counting rates which could be obtained in studies of the intensity correlations between plane-polarized, parallel beams of nearly monochromatic light. It is shown that, with presently available circuit techniques, delayed coincidence measurements could provide information about the breadths of lines radiated by atomic beam light sources, and in prompt coincidence experiments it should be possible to observe interference between beams of incoherent light from sources whose line widths are comparable with those of the Hg198 electrodeless discharge.
A new method for detecting a squeezed state by coincidence counting or cross correlation of the signals from two photodetectors is proposed. The two light beams falling on the two detectors are obtained from the two outputs of a homodyne beam splitter, whose inputs are the squeezed light and the local oscillator beam. With fast detectors the squeezing gives rise to excess photon coincidence counts. When a spectral analysis of the photoelectric currents is made, squeezing shows up as a positive cross correlation between the two signals, whereas unsqueezed light always produces negative correlations. Although the technique does not always cause the effects of local oscillator fluctuations to cancel out, as does the method of Yuen and Chan [Opt. Lett. B8R, 177 (1983)], they cancel in special cases, and the method has the advantage of being largely unaffected by detector after-pulsing. A simple combination of autocorrelation and cross-correlation measurements yields the degree of squeezing.
Interference fringes produced by the superposition of light beams from two independent lasers have been investigated under conditions where the light flux was so low that one photon was usually received at the detector before the next one was emitted by one or the other source. Because the average number of photons detected in each observation was only about 10, a photon correlation technique was used to demonstrate the presence of interference fringes. The measurement procedure was automated, and this led to much greater statistical accuracy than was previously reported. The effect of varying the observation time and the number of interference fringes sampled was investigated, and found to be in good agreement with theory.