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arXiv:physics/0411212 · Review of Scientific Instruments

Calibration of second-order correlation functions for nonstationary sources with a multistart, multistop time-to-digital converter

Wonshik Choi, Moonjoo Lee, Ye-Ryoung Lee, Changsoon Park, Jai-Hyung Lee, Kyungwon An, Christopher M. Fang-Yen, Ramachandra Rao Dasari, Michael S. Feld

Published Jul 21, 2005• 9 citations
arXivHTMLPDF

Abstract

A novel high-throughput second-order correlation measurement system is developed that records and makes use of all the arrival times of photons detected at both start and stop detectors. This system is suitable, particularly for a light source having a high photon flux and a long coherence time, since it is more efficient than conventional methods by an amount equal to the product of the count rate and the correlation time of the light source. We have used this system in carefully investigating the dead time effects of detectors and photon counters on the second-order correlation function in the two-detector configuration. For a nonstationary light source, a distortion of the original signal was observed at high photon flux. A systematic way of calibrating the second-order correlation function has been devised by introducing the concept of an effective dead time of the entire measurement system.

DOI
10.1063/1.1986969

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A novel high-throughput second-order correlation measurement system is developed that records and makes use of all the arrival times of photons detected at both start and stop detectors. This system is suitable, particularly for a light source having a high photon flux and a long coherence time, since it is more efficient than conventional methods by an amount equal to the product of the count rate and the correlation time of the light source. We have used this system in carefully investigating the dead time effects of detectors and photon counters on the second-order correlation function in the two-detector configuration. For a nonstationary light source, a distortion of the original signal was observed at high photon flux. A systematic way of calibrating the second-order correlation function has been devised by introducing the concept of an effective dead time of the entire measurement system.
Photonic quantum technologies require single photon sources and detectors operating at high efficiency, but at high rates detector imperfections can lead to inaccurate measurements. We show that the combination of the detector deadtime and the source statistics together determine the saturation level of a single photon detector, with anti-bunched sources leading to a greater detection rate than coherent or thermal light of the same intensity. At high photon rates this behavior distorts second-, third- and fourth- order correlation measurements, in agreement with our numerical simulations. Finally, we discuss the implications for entangled light detection and photonic logic.
A novel technique for photon correlation measurements, based on the excitation of a resonant system by photon-detector single pulses, analog/digital sampling, and deconvolution, has been developed and analyzed experimentally and by computer simulations. The measured correlation function is expressed by a convolution of the true photon correlation function of the optical field and a well-defined, noiseless resonator correlation function. The effect of detector statistics is reduced to the contribution of two integral parameters—the total single-pulse charge and the jitter of single-pulse centers. Good performance of this technique is demonstrated at high photon rates and resolutions, where the well-known photon-counting or single-quantum methods are ineffective. The novel technique offers linear recording of photocount time series without dead-time effects. The temporal resolution is defined by the sampling step of the analog/digital converter. The retrieval error does not exceed 1 to 3% at count rates higher than 1 GHz and single-pulse durations larger than the resolution cell. This technique can be effectively applied in photon correlation measurements of high dynamic optical fields.
A new approach to measure the second order correlation function g(2) and the coherence time was investigated. The g(2) was calculated from the photon pair time interval distribution by direct numerical self-convolution with the high order correction. The accuracy of this method was examined using an optical fiber based Hanbury-Brown-Twiss interferometer with a pseudo-thermal light source. We found that the significance of the high order correction is related to the factor Īτc, which is the overlapping of the photon wave packets. A novel technique was also demonstrated to measure the coherence time τc of a light source using the random phase modulation. This method is more suitable for a weak light source with a long coherence time using a simple experimental setup.
We observe the three-photon correlation in nonclassical light sources by using an indirect measurement scheme based on the dead-time effect of photon-counting detectors. We first develop a general theory which enables us to extract the three-photon correlation from the two-photon correlation of an arbitrary light source measured with detectors with finite dead times. We then confirm the validity of our measurement scheme in experiments done with a cavity-QED microlaser operating with a large intracavity mean photon number exhibiting both sub- and super-Poissonian photon statistics. The experimental results are in good agreement with the theoretical expectation. Our measurement scheme provides an alternative approach for NNN-photon correlation measurement employing $(N\ensuremath{-}1)$ detectors and thus a reduced measurement time for a given signal-to-noise ratio, compared to the usual scheme requiring NNN detectors.
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 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.