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At least 127 records · Page 7

BatAnalysis - A Comprehensive Python Pipeline for Swift BAT Survey Analysis

The Swift Burst Alert Telescope (BAT) is a coded-aperture gamma-ray instrument with a large field of view that primarily operates in survey mode when it is not triggering on transient events. The survey data consist of 80- channel detector plane histograms that accumulate photon counts over periods of at least 5 minutes. These histograms are processed on the ground and are used to produce the survey data set between 14 and 195 keV. Survey data comprise >90% of all BAT data by volume and allow for the tracking of long-term light curves and spectral properties of cataloged and uncataloged hard X-ray sources. Until now, the survey data set has not been used to its full potential due to the complexity associated with its analysis and the lack of easily usable pipelines. Here, we introduce the BatAnalysis Python package, a wrapper for HEASoftpy, which provides a modern, opensource pipeline to process and analyze BAT survey data. BatAnalysis allows members of the community to use BAT survey data in more advanced analyses of astrophysical sources, including pulsars, pulsar wind nebula, active galactic nuclei, and other known/unknown transient events that may be detected in the hard X-ray band. We outline the steps taken by the Python code and exemplify its usefulness and accuracy by analyzing survey data of the Crab Nebula, NGC 2992, and a previously uncataloged MAXI transient. The BatAnalysis package allows for ~18 yr of BAT survey data to be used in a systematic way to study a large variety of astrophysical sources.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Detector Tilt Considerations in Bragg Coherent Diffraction Imaging: A Simulation Study

This paper addresses the three-dimensional signal distortion and image reconstruction issues in X-ray Bragg coherent diffraction imaging (BCDI) in the event of a general non-orthogonal orientation of the area detector with respect to the diffracted beam. Growing interest in novel BCDI adaptations at fourth-generation synchrotron light sources has necessitated improvisations in the experimental configuration and the subsequent data analysis. One such possibly unavoidable improvisation that is envisioned in this paper is a photon-counting area detector whose face is tilted away from the perpendicular to the Bragg-diffracted beam during the acquisition of the coherent diffraction signal. We describe a likely circumstance in which one would require such a detector configuration, along with the experimental precedent at third-generation synchrotrons. Using physically accurate diffraction simulations from synthetic scatterers in the presence of such tilted detectors, we analyze the general nature of the observed signal distortion qualitatively and quantitatively and provide a prescription to correct for it during image reconstruction. Our simulations and reconstructions are based on an adaptation of the known theory of BCDI sampling geometry, as well as the recently developed projection-based methods of wavefield propagation. Such configurational modifications and their numerical remedies are potentially valuable in realizing unconventional coherent diffraction measurement geometries, eventually paving the way for the integration of BCDI into new material characterization experiments at next-generation light sources.

36 MATERIALS SCIENCE↗

First Results from the Thomson Scattering Diagnostic on the Large Plasma Device

We present the first Thomson scattering measurements of electron density and temperature in the Large Plasma Device (LAPD), a 22 m long magnetized linear plasma device at the University of California Los Angeles (UCLA). The diagnostic spectrally resolves the Doppler shift imparted on light from a frequency-doubled Nd:YAG laser when scattered by plasma electrons. A fiber array coupled to a triple-grating spectrometer is used to obtain high stray light rejection and discriminate the faint scattering signal from a much larger background. In the center of the plasma column, the measured electron density and temperature are about ne≈1.5×1013 cm−3 and Te≈ 3 eV, respectively, depending on the discharge parameters and in good agreement with Langmuir probe data. Optical design considerations to maximize photon count while minimizing alignment sensitivity are discussed in detail and compared to numerical calculations. Raman scattering off of a quartz crystal probe is used for an absolute irradiance calibration of the system.

Kaloyan, Marietta (ORCID:0000000182593038)↗

BatAnalysis - A Comprehensive Python Pipeline for Swift BAT Survey Analysis

The Swift Burst Alert Telescope (BAT) is a coded-aperture gamma-ray instrument with a large field of view that primarily operates in survey mode when it is not triggering on transient events. The survey data consist of 80-channel detector plane histograms that accumulate photon counts over periods of at least 5 minutes. These histograms are processed on the ground and are used to produce the survey data set between 14 and 195 keV. Survey data comprise >90% of all BAT data by volume and allow for the tracking of long-term light curves and spectral properties of cataloged and uncataloged hard X-ray sources. Until now, the survey data set has not been used to its full potential due to the complexity associated with its analysis and the lack of easily usable pipelines. Here, we introduce the BatAnalysis Python package, a wrapper for HEASoftpy, which provides a modern, open-source pipeline to process and analyze BAT survey data. BatAnalysis allows members of the community to use BAT survey data in more advanced analyses of astrophysical sources, including pulsars, pulsar wind nebula, active galactic nuclei, and other known/unknown transient events that may be detected in the hard X-ray band. We outline the steps taken by the Python code and exemplify its usefulness and accuracy by analyzing survey data of the Crab Nebula, NGC 2992, and a previously uncataloged MAXI transient. The BatAnalysis package allows for ~18 yr of BAT survey data to be used in a systematic way to study a large variety of astrophysical sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Extending water vapor measurement capability of photon-limited differential absorption lidars through simultaneous denoising and inversion

Abstract. The micropulse differential absorption lidar (MPD) was developed at Montana State University (MSU) and the National Center for Atmospheric Research (NCAR) to perform range-resolved water vapor (WV) measurements using low-power lasers and photon-counting detectors. The MPD has proven to produce accurate WV measurements up to 6 km altitude. However, the MPD's ability to produce accurate higher-altitude WV measurements is impeded by the current standard differential absorption lidar (DIAL) retrieval methods. These methods are built upon a fundamental methodology that algebraically solves for the WV using the MPD forward models and noisy observations, which exacerbates any random noise in the lidar observations. The work in this paper introduces the adapted Poisson total variation (PTV) specifically for the MPD instrument. PTV was originally developed for a ground-based high spectral resolution lidar, and this paper reports on the adaptations that were required in order to apply PTV on MPD WV observations. The adapted PTV method, coined PTV-MPD, extends the maximum altitude of the MPD from 6 to 8 km and substantially increases the accuracy of the WV retrievals starting above 2 km. PTV-MPD achieves the improvement by simultaneously denoising the MPD noisy observations and inferring the WV by separating the random noise from the non-random WV. An analysis with 130 radiosonde (RS) comparisons shows that the relative root-mean-square difference (RRMSE) of WV measurements between RS and PTV-MPD exceeds 100 % between 6 and 8 km, whereas the RRMSE between RS and the standard method exceeds 100 % near 3 km. In addition, we show that by employing PTV-MPD, the MPD is able to extend its useful range of WV estimates beyond that of the ARM Southern Great Plains Raman lidar (RRMSE exceeding 100 % between 3 and 4 km); the Raman lidar has a power-aperture product 500 times greater than that of the MPD.

54 ENVIRONMENTAL SCIENCES↗

Automatic method of material identification for computed tomography

A method is provided for isolating and labeling discrete features in a spectral radiographic image recorded as a set of images in different energy channels. The disclosed method involves creating a profile for each of at least some pixels in the spectral radiographic image. The profiles are sequences of pixel values, in which each pixel value is a photon count or a similar radiographic exposure value indicative of the attenuation of a portion of the scanning beam in a respective energy channel. Iterative hierarchical clustering is used to cluster the pixels on the basis of their respective profiles. Labels are assigned to one or more of the resulting clusters. In implementations, each label can be associated with an inferred material composition or with an inference that the material composition is unknown.

Jimenez, Jr., Edward Steven↗

The Role of Quantum Science Concepts in Enhancing Sensing and Imaging Technologies: Applications for Biology: Proceedings of a Workshop

Quantum concepts hold the potential to enable significant advances in sensing and imaging technologies that could be vital to the study of biological systems. The workshop Quantum Science Concepts in Enhancing Sensing and Imaging Technologies: Applications for Biology, held online March 8–10, 2021, was organized to examine the research and development needs to advance biological applications of quantum technology. Hosted by the National Academies of Sciences, Engineering, and Medicine, the event brought together experts working on state-of-the-art, quantum-enabled technologies and scientists who are interested in applying these technologies to biological systems. Through talks, panels, and discussions, the workshop facilitated a better understanding of the current and future biological applications of quantum-enabled technologies in fields such as microbiology, molecular biology, cell biology, plant science, mycology, and many others. The workshop was organized around three main themes. The first, quantum in biology, examined quantum concepts that are hypothesized to be important for life processes and that researchers are working to observe through biological imaging and sensing. The second, quantum for biology, addressed ways to use quantum concepts to enhance technologies for biological imaging and sensing. The third, biology for quantum, offered a wider discussion of how the frontiers of biological imaging and sensing could enable future study using quantum concepts, tools, or technologies. Throughout the workshop, participants identified a wide range of emerging approaches and opportunities at the intersection of quantum physics and biological sensing and imaging. During the workshop, there were some differences in how each speaker defined the term quantum. During one of the panels, Prem Kumar offered thoughts on what phenomena are classical versus quantum, explaining that techniques get progressively more quantum as you move from just having superposition to having superposition with measurement and entanglement. Another explanation from Clarice Aiello delineates the definition into several levels. This includes a base level of “quantum-ness,” which reflects that all matter is made of atoms, and when these particles are isolated they behave based on quantum mechanical principles. A second level is related to quantum coherence, where a single quantum object might be found in a coherent superposition state. A final level, which she described as the quantum-entangled level, involves multiple quantum systems which are entangled among themselves. Overall, the workshop touched on concepts such as superposition, entanglement, and squeezing and their potential implications for communication, computing, and simulation, in addition to the workshop’s main focal area, biological sensing and imaging. At the opening of the workshop, Thorsten Ritz of the University of California, Irvine, identified two questions at the heart of quantum biology: Is the machinery of life quantum mechanical, and can quantum mechanics be used to study the machinery of life in new ways? Participants highlighted systems in which researchers have explored these questions, from the vast array of molecular interactions involved in biological processes such as photosynthesis, to the mechanics involved in cellular functions such as differentiation and aggregation, to the role of oscillating magnetic fields in flight orientation among birds. Sensing and imaging technologies are crucial to biological research; these technologies could both enhance the study of quantum effects and be enhanced by quantum concepts. A critical challenge in biological research is to develop imaging and sensing tools that do not damage or interfere with the often fragile and fleeting systems being studied. Attendees discussed a variety of established and emerging technologies that could enhance noninvasive biological imaging, including single- and two-photon spectroscopy, single-molecule spectroscopy, quantum illumination, ghost imaging, and cryo-electron microscopy. One example came from Marlan Scully who gave a keynote address on the first day of the workshop. Scully emphasized the use of different laser technologies, which exhibit coherence and other quantum properties, in moving toward real-world biological applications, such as the detection of SARS-CoV-2. Both tools and theory will play an important role in advancing quantum biology research and applications. Several participants suggested theorists and experimentalists should work in tandem to understand and model biological processes. While physics often reduces systems to their simplest forms for fundamental insights, participants also noted the value of observing and understanding biological systems in all their “messiness,” capturing both the inner workings of biological systems and the complex interactions that occur within and between organisms. In discussions among participants, several attendees stressed the need to match emerging tools with the right scientific questions. Rather than developing quantum technologies as “a hammer looking for a nail,” participants emphasized a focus on exploring the problems these technologies are best suited to address. For example, it is important to consider the size of the phenomenon being studied, the timescales that are important in answering the scientific question, and other relevant considerations. Every tool along the spectrum from classical to quantum involves its own set of trade-offs. For example, Ted Laurence of the Lawrence Livermore National Laboratory said that quantum measurements, such as single photon counting, fluorescence transitions, and lasers, can take longer to produce the same results as classical measurements. These quantum measurements, however, do not require calibration and can enable new research questions to be answered. Prem Kumar, Northwestern University, noted that, despite their promise, quantum approaches should not be used simply for the sake of using quantum, especially in situations where classical approaches better meet the needs of the researcher. Understanding and applying quantum concepts could enable advances in a wide range of application areas including energy, synthetic biology, medicine, and sustainability. For example, Michelle O’Malley, University of California, Santa Barbara, described how improved noninvasive imaging approaches could help capture the complex interactions and functions involved in the breakdown of organic matter by microbial communities and lead to new technologies for capturing valuable products from plant waste. Several other participants discussed needs in tracking the movement of metabolites and molecules in microbial communities for insights into nutrient cycling in environments such as soil. Margaret Ahmad, Sorbonne University, discussed potential opportunities to leverage the magnetic properties of cryptochromes to advance new treatment approaches for diseases such as COVID-19 and cancer. Looking toward the future development of the field, participants discussed challenges to advancing quantum biology that arise from disciplinary disconnects between physicists and biologists. The siloing of academic research disciplines represents a significant barrier to progress. Disconnects in terminology, motivations and priorities, and structural barriers to collaborative work underscore the need for concerted efforts to bridge these divides. Attendees and speakers offered suggestions for resolving these divergences, establishing a shared language, moving the field forward, and fostering meaningful feedback between disciplines. Overall, participants stressed a need for balance, open communication, collaboration, unity, and clear dialogue on trade-offs between quantum and classical approaches. Keiko Torii, The University of Texas at Austin, said that the best collaborations happen when the project provides mutual advantages that can show off everyone’s talents, each team finds the work interesting, and partners develop a camaraderie to pursue new knowledge. To enable near- and long-term opportunities in this space, participants suggested that exploratory, high-risk funding could improve existing instrumentation to explore quantum enhancement collaboratively. They also emphasized the need for collaboration between quantum physicists and sensing/imaging scientists, which could be advanced through a dedicated quantum biology investigator program. People, even more than technology, will be crucial to the future of quantum biology. Participants explored training, education, and workforce needs to further develop this burgeoning field and cultivate the next generation of scientists. While many programs are still in their nascent stages, participants highlighted examples of approaches and programs being developed at various types of institutions to engage students and professional scientists in quantum biology research. Several participants stressed the need for an inclusive approach, spanning disciplines as well as communities to foster a diverse field fueled by the intellectual contributions of a wide range of people, including historically under-resourced schools and students. To increase awareness and excitement about quantum physics and related areas of biology, attendees suggested capitalizing on the “buzz” around quantum. Several participants emphasized the need to start early, introducing students to quantum concepts and their appealing “weirdness” in K–12 education. Engaging students early—before they become entrenched in traditional disciplinary siloes as typically happens in graduate school—could help to galvanize interest in the area and foster a generation of scientists with the interdisciplinary mindset and skills needed to advance this interdisciplinary field. While these efforts could be advanced at many levels and across multiple sectors, several participants suggested a national quantum biology center could be a valuable hub to coordinate and support quantum biology education and workforce development across academia, industry, and government.

59 BASIC BIOLOGICAL SCIENCES↗

Digital encoding algorithm for pixelated detectors

A detector for imaging and efficiently digitizing a spatial distribution of photon flux includes pixel circuits that compressively encode pixel values generated by integrated analog to digital converters (ADCs). On-pixel digital compression circuits (DCCs) implement compression to increase continuous frame rate by reducing the number of bits per pixel while keeping quantization error below Poisson noise. Several mapping algorithms for photon-counting and charge-integrating detectors and compact digital logic implementations are presented.

Hammer, Michael P.↗

On the Speed-up of Wave-like Dark Matter Searches with Entangled Qubits

Qubit-based sensing platforms offer promising new directions for wave-like dark matter searches. Recent proposals demonstrate that entangled qubits can achieve quadratic scaling of the signal in the number of qubits. In this work we expand on these proposals to analyze the bandwidth and scan rate performance of entangled qubit protocols across different error regimes. We find that the phase-based readout of entangled protocols preserves the search bandwidth independent of qubit number, in contrast to power-based detection schemes, thereby achieving a genuine scan-rate advantage. We derive coherence time and error rate requirements for qubit systems to realize this advantage. Applying our analysis to dark photon searches, we find that entangled states of approximately 100 qubits can become competitive with benchmark photon-counting cavity experiments for masses $\gtrsim 30{-}40~μ{\rm eV}$, provided sufficiently low error rates are achieved. The advantage increases at higher masses where cavity volume scaling becomes less favorable.

Bodas, Arushi [Fermilab; Chicago U.] (ORCID:000000↗

Axion dark matter search with a photonic bandgap cavity haloscope and dielectric tuning rod over 10.25-10.45 GHz

We report the development of a new widely tunable cavity and demonstrate its use in a search for dark matter axions. We achieve unloaded quality factors above $10^{5}$, roughly $25\times$ larger than a bare copper cavity at the same frequency, using concentric sapphire shells to reduce Ohmic losses on the cavity barrel. A rotating sapphire rod tunes our cavity mode over the $10.1-11.7$ GHz range, approximately $16\%$ of its resonant frequency. Using an amplified receiver chain, we demonstrate sensitivity to new axion parameter space by tuning the cavity over the $200$ MHz range between $10.25-10.45$ GHz (42.4 - 43.2, $μ$eV) to constrain the axion-to-photon coupling to $|g_{aγγ}|$$\leq$ 1 $\times$$10^{-12}$${GeV}^{-1}$. This cavity can scan its tuning range about $9$ times faster compared to a bare copper cavity when paired with a photon counting device, laying the groundwork for a definitive search for the QCD axion over $10.1-11.7$ GHz.

Lynn, Morgan [Chicago U.]↗

PhotonIDs: ML-Powered Photon Identification System for Dark Count Elimination

Reliable single photon detection is the foundation for practical quantum communication and networking. However, today's superconducting nanowire single photon detector(SNSPD) inherently fails to distinguish between genuine photon events and dark counts, leading to degraded fidelity in long-distance quantum communication. In this work, we introduce PhotonIDs, a machine learning-powered photon identification system that is the first end-to-end solution for real-time discrimination between photons and dark count based on full SNSPD readout signal waveform analysis. PhotonIDs ~demonstrates: 1) an FPGA-based high-speed data acquisition platform that selectively captures the full waveform of signal only while filtering out the background data in real time; 2) an efficient signal preprocessing pipeline, and a novel pseudo-position metric that is derived from the physical temporal-spatial features of each detected event; 3) a hybrid machine learning model with near 98% accuracy achieved on photon/dark count classification. Additionally, proposed PhotonIDs ~ is evaluated on the dark count elimination performance with two real-world case studies: (1) 20 km quantum link, and (2) Erbium ion-based photon emission system. Our result demonstrates that PhotonIDs ~could improve more than 31.2 times of signal-noise-ratio~(SNR) on dark count elimination. PhotonIDs ~ marks a step forward in noise-resilient quantum communication infrastructure.

Linne, Karl C. [Chicago U.] (ORCID:000900091870358↗

Towards a Counting Point Detector for Nanosecond Coherent X-ray Science

We present the technical realization of a high-speed hard X-ray single-photon counting-detection scheme based on a commercial avalanche silicon photodiode and high-speed oscilloscope. The development is motivated by the need to perform pulse-resolved photon-correlation and pump-probe studies at synchrotron sources with densely packed pulse patterns that result in high repetition rate pulses on the order of hundreds of MHz. Commissioning experiments are performed at the 1C PAL-KRISS beamline at PLS-II of South Korea operating at a burst mode maximum repetition rate of 500 MHz. In such a high count-rate measurement, detector dead-time can lead to a distortion of counting statistics. We are able to model the counting behavior of our detector under these conditions with a detector dead-time comparable to time between X-ray pulses, implying that nanosecond X-ray photon correlation spectroscopy should be possible at diffraction-limited light sources.

36 MATERIALS SCIENCE↗

Radiation-Induced Dark Counts for Silicon Single-Photon Detectors in Space

Single-photon detectors operating on satellites for use in a quantum communications network can incur large dark-count-rate increases from the natural radiation environment of space. Displacement damage to the material lattice of a detector from the ionizing radiation can result in a permanent dark-count increase in the detector. In this work, we analyze the radiation-induced dark-count rate of a silicon single-photon avalanche diode onboard a satellite at different orbiting altitudes, as well as, the additional radiation from a nuclear-disturbed environment caused by a high-altitude nuclear explosion. For detectors on low Earth orbit satellites, protons are the biggest source of radiation damage and are best mitigated by choosing an orbit that minimizes exposure when passing through the South Atlantic Anomaly and Polar Cusps. Detectors on medium Earth orbit and geostationary orbit satellites, if shielded by more than 10 mm of aluminum, provide the best platform in terms of the least amount of radiation damage to the detectors. In the event of a high-altitude nuclear explosion, the artificial radiation belts produced by the explosion will cause too much damage to silicon single-photon detectors on low Earth orbit satellites and render them unfit for quantum communications in less than a day. Higher orbit satellites will only suffer minor dark-count-rate increases from the artificial radiation belts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Adversarial autoencoder ensemble for fast and probabilistic reconstructions of few-shot photon correlation functions for solid-state quantum emitters

Second-order photon correlation measurements [g (2) (τ) functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations – such as quantum dots – by evaluating the value of g (2) (τ = 0). Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free g (2) (τ) functions from noise-dominated, few-shot inputs. The model is trained with simulated g (2) (τ) functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of g (2) (τ = 0) that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot g (2) (τ) functions (~100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free g (2) (τ) functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. Furthermore, this work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Approximate Bayesian Computation applied to the Diffuse Gamma-Ray Sky

ABSTRACT Many sources contribute to the diffuse gamma-ray background (DGRB), including star forming galaxies, active galactic nuclei, and cosmic ray interactions in the Milky Way. Exotic sources, such as dark matter annihilation, may also make some contribution. The photon counts-in-pixels distribution is a powerful tool for analysing the DGRB and determining the relative contributions of different sources. However, including photon energy information in a likelihood analysis of the counts-in-pixels distribution quickly becomes computationally intractable as the number of source types and energy bins increase. Here, we apply the likelihood-free method of approximate Bayesian computation (ABC) to the problem. We consider a mock analysis that includes contributions from dark matter annihilation in Galactic subhaloes as well as astrophysical backgrounds. We show that our results using ABC are consistent with the exact likelihood when energy information is discarded, and that significantly tighter parameter constraints can be obtained with ABC when energy information is included. ABC presents a powerful tool for analysing the DGRB and understanding its varied origins.

79 ASTRONOMY AND ASTROPHYSICS↗

Counting of Hong-Ou-Mandel Bunched Optical Photons Using a Fast Pixel Camera

The uses of a silicon-pixel camera with very good time resolution (∼nanosecond) for detecting multiple, bunched optical photons is explored. We present characteristics of the camera and describe experiments proving its counting capabilities. We use a spontaneous parametric down-conversion source to generate correlated photon pairs, and exploit the Hong-Ou-Mandel (HOM) interference effect in a fiber-coupled beam splitter to bunch the pair onto the same output fiber. It is shown that the time and spatial resolution of the camera enables independent detection of two photons emerging simultaneously from a single spatial mode.

47 OTHER INSTRUMENTATION↗

Detection of photon statistics and multimode field correlations by Raman processes

Glauber’s g (2) -function provides a common measure of quantum field statistics through two-photon coincidence counting in Hanbury Brown–Twiss measurements. Here, we propose to use nonlinear optical signals as a tool for the characterization of quantum light. In particular, we show that Raman measurements provide an alternative direct probe for a different component of the four-point correlation function underlying the g (2) -function. We illustrate this capacity for a specific quantum state obtained from a frequency conversion process. Our work points out how the analysis of controlled optical nonlinear processes can provide an alternative window toward the analysis of quantum light sources.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗