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Canadian Journal of Physics

PHOTON CORRELATION IN COHERENT LIGHT BEAMS

ERIC BRANNEN, H. I. S. Ferguson, W. H. Wehlau

Published Jul 1, 1958• 18 citations
Publisher

Abstract

Experiments have been carried out in an attempt to detect any correlation between photons in coherent light rays using a coincidence circuit of resolving time 2τ = 8 ×10 −9 second. A Hg 198 electrodeless discharge tube under rf excitation was used to provide an intense monochromatic source of narrow line width (0.006 Å and 0.009 Å) at 5461 Å. A positive correlation was detected and compared with theoretical predictions.

DOI
10.1139/p58-093

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Experiments have been carried out in an attempt to detect any correlation between photons in coherent light rays using a coincidence circuit of resolving time 2τ = 8 ×10 −9 second. A Hg 198 electrodeless discharge tube under rf excitation was used to provide an intense monochromatic source of narrow line width (0.006 Å and 0.009 Å) at 5461 Å. A positive correlation was detected and compared with theoretical predictions.
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.
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.
Measurements have been made of the distribution in time of arrival of photons produced in a low-pressure Hg198{\mathrm{Hg}}^{198}Hg198 discharge. Sufficient calibration was done so that the measurements could be directly compared with the predictions of a calculation of G(2)(x1,x2,x2,x1){G}^{(2)}({x}_{1},{x}_{2},{x}_{2},{x}_{1})G(2)(x1​,x2​,x2​,x1​), the second-order coherence function. Correlations were observed in a mixture of light from two independent sources and between orthogonally polarized components of a beam initially in a pure polarization state.
Two-photon correlation measurement provides a promising way to experimentally demonstrate the statistical nature of a light source, which is very significant for the deep understanding of the photon-generating process and the diagnosing of the coherence property. Quantitatively two- photon correlation is described by second-order coherence. Usually the behavior of the second-order coherence against any of the parameters defining the phase volume is different for different photon statistics. The Poisson photon statistics for coherent light gives its second-order coherence as a flat response; The Bose-Einstein photon statistics for chaotic light gives its second-order coherence as a bunching effect; While the Sub-Poisson photon statistics for non-classical light gives its second-order coherence as an anti-bunching effect. Therefore the measurement of two-photon correlation is proved to be a good finger print to check whether light is in coherent state or incoherent state such as thermal state or non-classical state. Historically the measurement of two-photon correlation was first performed by Hanbury-Brown and Twiss (HBT) in 1956. They used a linear mixer to realize the correlation of the two currents from the photoelectric detectors illuminated by a stationary thermal light souece, a mercury arc, and the photo-bunching effect was first successfully observed in the visible region of 435.8 nm. HBT method is no doubt a good way to extract the small excess two-photon correlation for a stationary light because the background, that is the DC components, has been cut off automatically by the broad band amplifiers, which is in fact the key of the success of HBT experiment. However there exists a general problem, to which no attention has ever been paid, in measuring the two-photon correlation of non-stationary light such as synchrotron radiation (SR) by the HBT method. Here the "non-stationary" means a sense of classical mechanics that the observed intensity has some deterministic time structure. The systematic time structure of SR decided by the bunch distribution of the electric current in a storage ring will give rise to a large amount of unexpected accidental correlation, which in fact has nothing to do with the inherent photon statistics of light source and usually l000～l0000 times larger than the true two-photon correlation due to the short bunch separation length (2ns) and the short coherence time (～0.1ps) which is not comparable to the time resolution (1ns) of the measuring system. The existence of the accidental correlation would severely prevent us from observing the bunching effect of the true two-photon correlation. Therefore to suppress the much larger accidental correlation and to extract the small true two-photon correlation, a novel intensity interferometer has been developed for soft X-ray synchrotron radiation. This intensity interferometer consists of an optical vacuum chamber and an electric correlator. All the essential optical elements which includes a wire scanner, a precise diffraction slit, a grating monochromator with a coherence time modulator, a beam divider and two fast-response photon detectors (microchannel plates) are mounted in this high vacuum chamber. The electric correlator completes the multiplication of the two broad band electric currents coming from the photoelectric detectors. The basic idea to suppress the much larger accidental correlation is to modulate the coherence time by modulating the entrance slit width of the monochromator by a piezoclectric translator. The two sets of light intensity are simultaneously modulated too. When the frequency of modulation is f, the third harmonics 3f is detected with a loch-in amplifier because the 3f components include only the true two-photon correlation. Practically it is difficult to modulate with frequency f without any higher order harmonics distortion which might add some false 3f components. To overcome this difficulty we have used a sharp bandpass filter of l00～350 MHz in each branch of the correlator, which is lower than the RF frequency 500 MHz and much higher than 1.6 MHz, the revolution frequency of the stored beam of the 2.5 GeV storage ring. This new apparatus has been operated successfully in the measurement of the horizontal two-photon correlation for the first harmonic of undulator radiation with photon energy of 70 eV at the Photon Factory, KEK. By narrowing the precise slit width which correspondingly changes the spatial coherence of the incident SR, a bunching effect of the normalized excess two-photon correlation has been clearly observed. This explicit bunching effect implies that synchrotron radiation is chaotic radiation. Further investigation shows that although second-order coherence is completely determined by the first-order coherence for the case of chaotic light, the measured information from the light source is essentially different. The two-photon correlation of synchrotron radiation does not depend on the response time of the detectors but gives the information of instantaneous emittance of the stored beam with the time scale of coherence time τC. By fitting the experimental data, the horizontal instantaneous emittance of the stored beam is estimated to be 40nmrad. This intensity interferometer can be utilized to characterize the coherence properties of incomplete FELs, such as SASE, because if they are fully coherent light sources the normalized excess two-photon correlation would have a flat response, but not showing a photon-bunching effect.
The authors have measured the two-photon correlation function in 632.8-nm single-mode He-Ne laser light which had been amplified by stimulated emission in a long He-Ne discharge tube. For laser light intensities which were comparable with the discharge-tube spontaneous-emission intensity into a single mode, the measured correlations agree well with those predicted for a simple mixture of laser and chaotic light. The results are consistent with the assumption that laser light linearly amplified by stimulated emission has the same statistical properties as unamplified laser light.
An intensity-correlation experiment is proposed to test the second-order coherence of laser light from a cw-operated laser based on the Glauber formalism. The calculation utilizes the known form of the density matrix for radiation from a randomly excited source such as a discharge tube which is equivalent to filtered black-body radiation, and represents the laser radiation field by a coherent state. The intensity correlation calculated exhibits the standard Hanbury Brown-Twiss term and an extra term due to intensity interference between the Fourier components of the thermal field and the laser mode.