A hierarchy of statistics of increasing sophistication and accuracy is proposed, to exploit an interesting and fundamental arithmetic structure in the photon bunching noise of incoherent light of large photon occupation number, with the purpose of suppressing the noise and rendering a more reliable and unbiased measurement of the light intensity. The method does not require any new hardware, rather it operates at the software level, with the help of high precision computers, to reprocess the intensity time series of the incident light to create a new series with smaller bunching noise coherence length. The ultimate accuracy improvement of this method of flux measurement is limited by the timing resolution of the detector, the precision of the computer in manipulating numbers, and the photon occupation number of the beam (the higher the photon number the better the performance). The principal application is sensitivity enhancement of radio astronomical observations.
A hierarchy of statistics of increasing sophistication and accuracy is proposed, to exploit an interesting and fundamental arithmetic structure in the photon bunching noise of incoherent light of large photon occupation number, with the purpose of suppressing the noise and rendering a more reliable and unbiased measurement of the light intensity. The method does not require any new hardware, rather it operates at the software level, with the help of high precision computers, to reprocess the intensity time series of the incident light to create a new series with smaller bunching noise coherence length. The ultimate accuracy improvement of this method of flux measurement is limited by the timing resolution of the detector, the precision of the computer in manipulating numbers, and the photon occupation number of the beam (the higher the photon number the better the performance). The principal application is sensitivity enhancement of radio astronomical observations.
Lieu et al. (2015) have recently claimed that it is possible to substantially improve the sensitivity of radio astronomical observations. In essence, their proposal is to make use of the intensity of the photon shot noise as a measure of the photon arrival rate. Lieu et al. (2015) provide a detailed quantum-mechanical calculation of a proposed measurement scheme that uses two detectors and conclude that this scheme avoids the sensitivity degradation that is associated with photon bunching. If correct, this result could have a profound impact on radio astronomy. Here I present a detailed analysis of the sensitivity attainable using shot-noise measurement schemes that use either one or two detectors, and demonstrate that neither scheme can avoid the photon bunching penalty. I perform both semiclassical and fully quantum calculations of the sensitivity, obtaining consistent results, and provide a formal proof of the equivalence of these two approaches. These direct calculations are furthermore shown to be consistent with an indirect argument based on a correlation method that establishes an independent limit to the sensitivity of shot-noise measurement schemes. Collectively, these results conclusively demonstrate that the photon bunching sensitivity penalty applies to shot noise measurement schemes just as it does to ordinary photon counting, in contradiction to the fundamental claim made by Lieu et al. (2015). The source of this contradiction is traced to a logical fallacy in their argument.
A proposed method of suppressing the effect of background noise in an optical communication system would exploit the transmission and reception of correlated photons at the receiver. The method would not afford any advantage in a system in which performance is limited by shot noise. However, if the performance of the system is limited by background noise (e.g., sunlight in the case of a free-space optical communication system or incoherently scattered in-band photons in the case of a fiber-optic communication system), then the proposed method could offer an advantage: the proposed method would make it possible to achieve a signal-to-noise ratio (S/N) significantly greater than that of an otherwise equivalent background- noise-limited optical communication system based on the classical transmission and reception of uncorrelated photons. The figure schematically depicts a classical optical-communication system and a system according to the proposed method. In the classical system, a modulated laser beam is transmitted along an optical path to a receiver, the optics of which include a narrow-band-pass filter that suppresses some of the background noise. A photodetector in the receiver detects the laser-beam and background photons, most or all of which are uncorrelated. In the proposed system, correlated photons would be generated at the transmitter by making a modulated laser beam pass through a nonlinear parametric down-conversion crystal. The sum of frequencies of the correlated photons in each pair would equal the frequency of the incident photon from which they were generated. As in the classical system, the correlated photons would travel along an optical path to a receiver, where they would be band-pass filtered and detected. Unlike in the classical system, the photodetector in the receiver in this system would be one that intrinsically favors the detection of pairs of correlated photons over the detection of uncorrelated photons. Even though there would be no way of knowing the precise location and time of creation of a given pair of correlated signal photons in the nonlinear down-conversion crystal, the fact that the photons are necessarily created at the same time and place makes it possible to utilize conventional geometrical imaging optics to reunite the photons in coincidence in the receiving photodetector. Because most or all of the signal photons would be correlated while most or all of the noise photons would be uncorrelated, the S/N would be correspondingly enhanced in the photodetector output. An additional advantage to be gained by use of a correlated-photon detector is that it could be capable of recovering the signal even in the presence of background light so bright that a classical uncorrelated-photon detector would be saturated. A blocked-impurity-band (BIB) photodetector that preferentially detects pairs of correlated photons over uncorrelated ones and that operates at a quantum efficiency of 88 percent is commercially available. This detector must be cooled to the temperature of liquid helium to obtain the desired low-noise performance. It is planned to use this detector in a proof-of-principle demonstration. In addition, it may be possible to develop GaN-based photodetectors that could offer the desired low-noise performance at room temperature.
Characterization of the photon statistics of an optical field is central to identifying light sources in various quantum-enabled technologies, from super-resolved quantum imaging to precise quantum sensing and spectroscopy. In practice, however, estimating photon-correlation functions with sufficient accuracy requires long acquisition times and computationally intensive statistical estimators, severely limiting real-time operation and the study of rapidly varying or weak sources. Here, we show that learned inference based on artificial neural networks enables rapid estimation of second-order coherence directly from photon-number-resolved measurements, outperforming the precision of conventional statistical methods with processing times three orders of magnitude shorter. Our approach is source-agnostic and remains accurate in few-photon illumination regimes where the statistics of coherent, partially coherent, thermal, and super-thermal light become nearly indistinguishable. We experimentally validate the method across more than 4000 distinct classical light sources, demonstrating equal or improved precision with drastically reduced data and computational requirements. These results establish machine-learning-enabled photon-statistics inference as a new operational route to rapid optical-coherence diagnostics, enabling real-time monitoring of classical light sources in regimes previously inaccessible to conventional estimators.
Amplitude interferometry and intensity interferometry are methods for processing the complex amplitude and the intensity, respectively, of an electromagnetic field to estimate the mutual intensity of the field at two spatial locations. Whereas complex amplitude measurements allow for the direct estimation of the mutual-intensity phase, intensity measurements do not. We consider applications for which the estimation of the magnitude or the squared magnitude of the mutual intensity is adequate, and we provide fundamental limits on the estimation accuracy of any unbiased estimator of the squared magnitude of the mutual intensity from coherent (complex amplitude) or incoherent (intensity) measurements. Our analysis is performed for the high-light-level (classical-noise-limit) case and quantifies the advantages of making the more difficult coherent measurements.
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 accuracy of optical measurements at low light levels is limited by the quantum noise of the source and by the random nature of the interaction with the measured object. The source noise may be reduced by use of nonclassical photon-number squeezed light. We consider the use of two photon-correlated beams (generated, for example, by spontaneous parametric downconversion) to measure the optical transmittance of an object. The photons of each beam obey a random Poisson process but are synchronized in time. One beam is used to probe the object, and the other is used as a reference providing information on the realization of the random arrival of photons at the object. The additional information available by such measurement may be exploited to improve the accuracy of the measurement. Various estimators, including the maximum-likelihood estimator, are considered, and their performance is evaluated and compared with the measurement based on a single-beam conventional (Poissonian) source and a maximally squeezed (fixed-photon-number) source. The performance advantage that is established depends on parameters such as the intensity of the source, the transmittance of the object, the quantum efficiency of the detectors, the background noise, and the degree of correlation of the photon numbers in the two beams.