Photon Counting Distribution Research Articles

Quantum jump photodetector for narrowband photon counting with a single atom

Using a single neutral Rb87 atom held in an optical trap, and “quantum jump” detection of single-photon-initiated state changes, we demonstrate a single-photon quantum jump photodetector (QJPD) with intrinsically narrow bandwidth and strong rejection of out-of-band photons, of interest for detecting weak optical signals in the presence of a strong broadband background. By analyzing fluorescence photon count distributions for the bright and dark states with and without excitation, we measure quantum efficiency of 2.9(2)×10−3, a record for single-pass quantum jump production, and signal-photon-unprovoked “dark jump” rate—analogous to the dark count rate of other detectors —of 3(10)×10−3jumps/s during passive accumulation plus 4.0(4)×10−3 jumps per readout, orders of magnitude below those of traditional single-photon detectors. Available methods can substantially improve QJPD quantum efficiency, dark jump rate, bandwidth, and tunability. Published by the American Physical Society 2024

Photon-counting statistics-based support vector machine with multi-mode photon illumination for quantum imaging

We propose a photon-counting-statistics-based imaging process for quantum imaging where background photon noise can be distinguished and eliminated by photon mode estimation from the multi-mode Bose–Einstein distribution. Photon-counting statistics show multi-mode behavior in a practical, low-cost single-photon-level quantum imaging system with a short coherence time and a long measurement time interval. Different mode numbers in photon-counting probability distributions from single-photon illumination and background photon noise can be classified by a machine learning technique such as a support vector machine (SVM). The proposed photon-counting statistics-based support vector machine (PSSVM) learns the difference in the photon-counting distribution of each pixel to distinguish between photons from the source and the background photon noise to improve the image quality. We demonstrated quantum imaging of a binary-image object with photon illumination from a spontaneous parametric down-conversion (SPDC) source. The experiment results show that the PSSVM applied quantum image improves a peak signal-to-noise ratio (PSNR) gain of 2.89dB and a structural similarity index measure (SSIM) gain of 27.7% compared to the conventional direct single-photon imaging.

Error rates of arbitrary order optical wireless pulse-position modulation: An efficient approach

We present analytical results on the bit-error probability (BEP) of arbitrary order pulse-position modulation (PPM) of optically pre-amplified receivers. We use the Laguerre photon counting distribution so as to model the statistic of the optical noise, in order to accurately model the effects of signal and spontaneous noise beating at the optical detector. The great advantage of our proposed results is that they are exact and only require a finite summation over the optical noise modes and the modulation order. In addition, this approach enables the efficient calculation of the BEP in optical wireless communication links, under the presence of atmospheric scintillations and pointing errors.

Neural simulation-based inference approach for characterizing the Galactic Center γ -ray excess

The nature of the Fermi gamma-ray Galactic Center Excess (GCE) has remained a persistent mystery for over a decade. Although the excess is broadly compatible with emission expected due to dark matter annihilation, an explanation in terms of a population of unresolved astrophysical point sources e.g., millisecond pulsars, remains viable. The effort to uncover the origin of the GCE is hampered in particular by an incomplete understanding of diffuse emission of Galactic origin. This can lead to spurious features that make it difficult to robustly differentiate smooth emission, as expected for a dark matter origin, from more "clumpy" emission expected for a population of relatively bright, unresolved point sources. We use recent advancements in the field of simulation-based inference, in particular density estimation techniques using normalizing flows, in order to characterize the contribution of modeled components, including unresolved point source populations, to the GCE. Compared to traditional techniques based on the statistical distribution of photon counts, our machine learning-based method is able to utilize more of the information contained in a given model of the Galactic Center emission, and in particular can perform posterior parameter estimation while accounting for pixel-to-pixel spatial correlations in the gamma-ray map. This makes the method demonstrably more resilient to certain forms of model misspecification. On application to Fermi data, the method generically attributes a smaller fraction of the GCE flux to unresolved point sources when compared to traditional approaches. We nevertheless infer such a contribution to make up a non-negligible fraction of the GCE across all analysis variations considered, with at least $38^{+9}_{-19}\%$ of the excess attributed to unresolved point sources in our baseline analysis.

Photon counting statistics with imperfect detectors

Measurement of photon statistics is an important tool for the verification of quantum properties of light. Due to the various imperfections of real single photon detectors, the observed statistics of photon counts deviates from the underlying statistics of photons. Here we analyze statistical properties of coherent states, and investigate a connection between Poissonian distribution of photons and sub-Poissonian distribution of photon counts due to the detector dead-time corrections. We derive a functional dependence between the mean number of photons and the mean number of photon counts, as well as connection between higher-order statistical moments, for the pulsed or continuous wave coherent light sources, and confirm the results by numerical simulations.

A 1064 nm single-photon lidar for three-dimensional imaging

Single-photon light detection and ranging system has been widely used in three-dimensional (3D) imaging for its advantages in weak echo detection and high resolution. However, long-range imaging is a great challenge due to the device performance limits and strong solar irradiance. In this paper, we experimentally demonstrate a single-photon imaging system with an operation wavelength of 1064 nm in daytime. An all-fiber optical system with a two-dimensional rotation platform is designed to realize a wide scanning. And a sub-pixel scanning method is used to improve spatial resolution. Image reconstruction is based on the iterative shrinkage-threshold algorithm; herein the noise threshold is self-adaptive to the received photon-counting distribution. Multi-range information can be retrieved from each pixel and 3D point cloud is finally generated. Results show that the range resolution is 38 cm and the spatial resolution is about 7.4 cm at the distance of 2.13km, three times of the diffraction limit of the optical system.

Enhanced UnaG With Minimal Labeling Artifact for Single-Molecule Localization Microscopy.

We introduced enhanced UnaG (eUnaG), a ligand-activatable fluorescent protein, for conventional and super-resolution imaging of subcellular structures in the mammalian cells. eUnaG is a V2L mutant of UnaG with twice brighter bulk fluorescence. We previously discovered the reversible fluorescence switching behavior of UnaG and demonstrated the high photon outputs and high localization numbers in single-molecule localization microscopy (SMLM). In this study, we showed that the fluorescence of eUnaG can be switched off under blue-light illumination, while a high concentration of fluorogenic ligands in the buffer can efficiently restore the fluorescence, as in UnaG. We demonstrated the capacity of eUnaG as an efficient protein label in mammalian cells, as well as for SMLM by utilizing its photoswitchable nature. While cytosolic UnaG proteins showed aggregated patches and fluorescence reduction at high expression levels, eUnaG-labeled protein targets successfully formed their proper structures in mammalian cells without notable distortion from the endogenous structure in the majority of transiently expressing cells. In particular, eUnaG preserved the vimentin filament structures much better than the UnaG. eUnaG provided similarly high single-molecule photon count distribution to UnaG, thus also similarly high resolution in the super-resolution images of various subcellular structures. The sampling coverage analysis of vimentin filaments in SMLM images showed the improvement of labeling efficiency of eUnaG. eUnaG is a high-performance fluorescent protein for fluorescence and single-molecule localization imaging in green emission with minimal labeling artifact.

Photon-counting distribution for arrays of single-photon detectors

We derive a computationally efficient expression of the photon counting distribution for a uniformly illuminated array of single photon detectors. The expression takes the number of single detectors, their quantum efficiency, and their dark-count rate into account. Using this distribution we compute the error of the array detector by comparing the output to that of a ideal detector. We conclude from the error analysis that the quantum efficiency must be very high in order for the detector to resolve a hand-full of photons with high probability. Furthermore, we conclude that in the worst-case scenario the required array size scales quadratically with the number of photons that should be resolved. We also simulate a temporal array and investigate how large the error is for different parameters and we compute optimal size of the array that yields the smallest error.

Improvement of the safe transmission distance via optimization of the photon number distribution for the faint optical pulse in practical quantum key distribution systems

With practical quantum key distribution (QKD) systems, estimating the safe transmission distance and the safe bit rate under some transmission distance is quite important. For the practical QKD setup, with decoy states, the photon count distribution of the faint laser pulse with signal states can be optimized to acquire the maximum transmission distance. With this goal, we implement a method combining mathematical derivation and numerical simulation to find the optimal photon count distribution under realistic conditions; the numerical simulation results show that the new distributions can be employed in the decoy QKD system to reach safe transmission distances farther than those reached by systems with the Poisson distribution.

Implications of disturbed photon-counting statistics of Eiger detectors for X-ray speckle visibility experiments.

This paper reports on coherent scattering experiments in the low-count regime with less than one photon per pixel per acquisition on average, conducted with two detectors based on the Eiger single-photon-counting chip. The obtained photon-count distributions show systematic deviations from the expected Poisson-gamma distribution, which result in a strong overestimation of the measured speckle contrast. It is shown that these deviations originate from an artificial increase of double-photon events, which is proportional to the detected intensity and inversely proportional to the exposure time. The observed miscounting effect may have important implications for new coherent scattering experiments emerging with the advent of high-brilliance X-ray sources. Different correction schemes are discussed in order to obtain the correct photon distributions from the data. A successful correction is demonstrated with the measurement of Brownian motion from colloidal particles using X-ray speckle visibility spectroscopy.

A Deep Learning Approach to Galaxy Cluster X-Ray Masses

Abstract We present a machine-learning (ML) approach for estimating galaxy cluster masses from Chandra mock images. We utilize a Convolutional Neural Network (CNN), a deep ML tool commonly used in image recognition tasks. The CNN is trained and tested on our sample of 7896 Chandra X-ray mock observations, which are based on 329 massive clusters from the simulation. Our CNN learns from a low resolution spatial distribution of photon counts and does not use spectral information. Despite our simplifying assumption to neglect spectral information, the resulting mass values estimated by the CNN exhibit small bias in comparison to the true masses of the simulated clusters (−0.02 dex) and reproduce the cluster masses with low intrinsic scatter, 8% in our best fold and 12% averaging over all. In contrast, a more standard core-excised luminosity method achieves 15%–18% scatter. We interpret the results with an approach inspired by Google DeepDream and find that the CNN ignores the central regions of clusters, which are known to have high scatter with mass.

Sub-microsecond-resolved multi-speckle X-ray photon correlation spectroscopy with a pixel array detector.

Small-angle X-ray photon correlation spectroscopy (XPCS) measurements spanning delay times from 826 ns to 52.8 s were performed using a photon-counting pixel array detector with a dynamic range of 0-3 (2 bits). Fine resolution and a wide dynamic range of time scales was achieved by combining two modes of operation of the detector: (i) continuous mode, where data acquisition and data readout are performed in parallel with a frame acquisition time of 19.36 µs, and (ii) burst mode, where 12 frames are acquired with frame integration times of either 2.56 µs frame-1 or 826 ns frame-1 followed by 3.49 ms or 1.16 ms, respectively, for readout. The applicability of the detector for performing multi-speckle XPCS was demonstrated by measuring the Brownian dynamics of 10 nm-radius gold and 57 nm-radius silica colloids in water at room temperature. In addition, the capability of the detector to faithfully record one- and two-photon counts was examined by comparing the statistical distribution of photon counts with expected probabilities from the negative binomial distribution. It was found that in burst mode the ratio of 2 s to 1 s is markedly smaller than predicted and that this is attributable to pixel-response dead-time.

Hypothesis Test of the Photon Count Distribution for Dust Discrimination in Dynamic Light Scattering.

Users of dynamic light scattering (DLS) are challenged when a sample of nanoparticles (NPs) contains dust. This is a frequently inevitable scenario and a major problem that critically affects the reproducibility and accuracy of DLS measurements. Current methods approach this problem via photon correlation spectroscopy, but remedy exists only for a few special cases. We introduce here a general criterion and a clearly defined measure to discriminate between NPs and dust particles. The experimental results show that, in contrast to photon correlation spectroscopy, hypothesis testing and the statistical moment analysis of the photon count distribution provides an accurate and precise way to characterize NPs and Brownian dynamics in the presence of dust. To demonstrate, analyses of silica, iron oxide, and gold NPs of low polydispersity are presented.

Thicknesses optimization of two- and three-junction photovoltaic cells with matched currents and matched lattice constants

Maximizing the conversion of sunlight to electricity by theoretically optimizing the utilization of lattice-matched multi-junction photovoltaic cells of the incident solar radiation was attempted. The lattice constant matching among the layers is important to avoid the internal thermal stress. In the proposed model the current mismatching, the thermalization losses, and the fill factor were all introduced to the conversion efficiency equation. The current matching can be achieved not only by suitable choice of bandgap energies, which directly decides the photon count distribution among the junctions, but also, by the absorbed amounts of those photons that could be controlled effectively by optimal choice of thicknesses; which is the significance of this research since such additional design freedom is essential to overcome the possible imperfect choice of bandgap energies that is dictated by the lattice matching requirement. Numerical search method was employed to find the optimal thicknesses for two- and three-junction PV solar cells in order to maximize the conversion efficiency. The performance of the proposed model is tested for various lattice-matched MJ samples. The results revealed that employing well-chosen bandgap energies for the active media in these samples leads to promising and efficient electricity generation using MJ solar cells. For example, 41.6% and 46.7% solar to electricity conversion efficiency can be obtained from double and triple junction solar cells, respectively, under concentrated sun regime.

Artifact reduction in the CSPAD detectors used for LCLS experiments.

The existence of noise and column-wise artifacts in the CSPAD-140K detector and in a module of the CSPAD-2.3M large camera, respectively, is reported for the L730 and L867 experiments performed at the CXI Instrument at the Linac Coherent Light Source (LCLS), in low-flux and low signal-to-noise ratio regime. Possible remedies are discussed and an additional step in the preprocessing of data is introduced, which consists of performing a median subtraction along the columns of the detector modules. Thus, we reduce the overall variation in the photon count distribution, lowering the mean false-positive photon detection rate by about 4% (from 5.57 × 10-5 to 5.32 × 10-5 photon counts pixel-1 frame-1 in L867, cxi86715) and 7% (from 1.70 × 10-3 to 1.58 × 10-3 photon counts pixel-1 frame-1 in L730, cxi73013), and the standard deviation in false-positive photon count per shot by 15% and 35%, while not making our average photon detection threshold more stringent. Such improvements in detector noise reduction and artifact removal constitute a step forward in the development of flash X-ray imaging techniques for high-resolution, low-signal and in serial nano-crystallography experiments at X-ray free-electron laser facilities.

Basis material decomposition method for material discrimination with a new spectrometric X-ray imaging detector

Energy sensitive photon counting X-ray detectors provide energy dependent information which can be exploited for material identification. The attenuation of an X-ray beam as a function of energy depends on the effective atomic number Zeff and the density. However, the measured attenuation is degraded by the imperfections of the detector response such as charge sharing or pile-up. These imperfections lead to non-linearities that limit the benefits of energy resolved imaging. This work aims to implement a basis material decomposition method which overcomes these problems. Basis material decomposition is based on the fact that the attenuation of any material or complex object can be accurately reproduced by a combination of equivalent thicknesses of basis materials. Our method is based on a calibration phase to learn the response of the detector for different combinations of thicknesses of the basis materials. The decomposition algorithm finds the thicknesses of basis material whose spectrum is closest to the measurement, using a maximum likelihood criterion assuming a Poisson law distribution of photon counts for each energy bin. The method was used with a ME100 linear array spectrometric X-ray imager to decompose different plastic materials on a Polyethylene and Polyvinyl Chloride base. The resulting equivalent thicknesses were used to estimate the effective atomic number Zeff. The results are in good agreement with the theoretical Zeff, regardless of the plastic sample thickness. The linear behaviour of the equivalent lengths makes it possible to process overlapped materials. Moreover, the method was tested with a 3 materials base by adding gadolinium, whose K-edge is not taken into account by the other two materials. The proposed method has the advantage that it can be used with any number of energy channels, taking full advantage of the high energy resolution of the ME100 detector. Although in principle two channels are sufficient, experimental measurements show that the use of a high number of channels significantly improves the accuracy of decomposition by reducing noise and systematic bias.

On the Distribution of Photon Counts with Censoring in Two-Photon Laser Scanning Microscopy

We address the problem of counting emitted photons in two-photon laser scanning microscopy. Following a laser pulse, photons are emitted after exponentially distributed waiting times. Modeling the counting process is of interest because photon detectors have a dead period after a photon is detected that leads to an underestimate of the count of emitted photons. We describe a model which has a Poisson \((\alpha )\) number N of photons emitted, and a dead period \(\Delta \) that is standardized by the fluorescence time constant \(\tau (\delta = \Delta /\tau )\), and an observed count D. The estimate of \(\alpha \) determines the intensity of a single pixel in an image. We first derive the distribution of D and study its properties. We then use it to estimate \(\alpha \) and \(\delta \) simultaneously by maximum likelihood. We show that our results improve the signal-to-noise ratio, hence the quality of actual images.

Investigating the uniformity of the excess gamma rays towards the galactic center region

We perform a composite likelihood analysis of subdivided regions within the central 26° × 20° of the Milky Way, with the aim of characterizing the spectrum of the gamma-ray galactic center excess in regions of varying galactocentric distance. Outside of the innermost few degrees, we find that the radial profile of the excess is background-model dependent and poorly constrained. The spectrum of the excess emission is observed to extend upwards of 10 GeV outside ∼5° in radius, but cuts off steeply between 10–20 GeV only in the innermost few degrees. If interpreted as a real feature of the excess, this radial variation in the spectrum has important implications for both astrophysical and dark matter interpretations of the galactic center excess. Single-component dark matter annihilation models face challenges in reproducing this variation; on the other hand, a population of unresolved millisecond pulsars contributing both prompt and secondary inverse Compton emission may be able to explain the spectrum as well as its spatial dependency. We show that the expected differences in the photon-count distributions of a smooth dark matter annihilation signal and an unresolved point source population are an order of magnitude smaller than the fluctuations in residuals after fitting the data, which implies that mismodeling is an important systematic effect in point source analyses aimed at resolving the gamma-ray excess.

Detecting the spatial quantum uncertainty of bosonic systems

We present the quantum theory of direct detection of bosonic particles by multipixel detectors. For the sake of clarity, we specialize on beams of photons, and we study the measurement of different spatial beam characteristics, as position and width. The limits of these measurements are set by the quantum nature of the light field. We investigate how both, detector imperfections and finite pixel size affect the photon counting distribution. An analytic theory for the discretized detection setup is derived. We discuss the results and compare them to the theory presented by Chille et al 2015 Opt. Express 23 32777, which investigates the beam width noise independently of the measurement system. Finally, we present numerical simulations that furnish realistic and promising predictions for possible experimental studies.

Improving z-tracking accuracy in the two-photon single-particle tracking microscope.

Here, we present a method that can improve the z-tracking accuracy of the recently invented TSUNAMI (Tracking of Single particles Using Nonlinear And Multiplexed Illumination) microscope. This method utilizes a maximum likelihood estimator (MLE) to determine the particle's 3D position that maximizes the likelihood of the observed time-correlated photon count distribution. Our Monte Carlo simulations show that the MLE-based tracking scheme can improve the z-tracking accuracy of TSUNAMI microscope by 1.7 fold. In addition, MLE is also found to reduce the temporal correlation of the z-tracking error. Taking advantage of the smaller and less temporally correlated z-tracking error, we have precisely recovered the hybridization-melting kinetics of a DNA model system from thousands of short single-particle trajectories in silico. Our method can be generally applied to other 3D single-particle tracking techniques.