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Metasurfaces -- ultrathin structures composed of subwavelength optical elements -- have revolutionized light manipulation by enabling precise control over electromagnetic waves' amplitude, phase, polarization, and spectral properties. Concurrently, computational imaging leverages algorithms to reconstruct images from optically processed signals, overcoming limitations of traditional imaging systems. This review explores the synergistic integration of metaoptics and computational imaging, "computational metaoptics," which combines the physical wavefront shaping ability of metasurfaces with advanced computational algorithms to enhance imaging performance beyond conventional limits. We discuss how computational metaoptics addresses the inherent limitations of single-layer metasurfaces in achieving multifunctionality without compromising efficiency. By treating metasurfaces as physical preconditioners and co-designing them with reconstruction algorithms through end-to-end (inverse) design, it is possible to jointly optimize the optical hardware and computational software. This holistic approach allows for the automatic discovery of optimal metasurface designs and reconstruction methods that significantly improve imaging capabilities. Advanced applications enabled by computational metaoptics are highlighted, including phase imaging and quantum state measurement, which benefit from the metasurfaces' ability to manipulate complex light fields and the computational algorithms' capacity to reconstruct high-dimensional information. We also examine performance evaluation challenges, emphasizing the need for new metrics that account for the combined optical and computational nature of these systems. Finally, we identify new frontiers in computational metaoptics which point toward a future where computational metaoptics may play a central role in advancing imaging science and technology.

Stellar occultations provide a powerful tool to explore objects of the outer solar system. The Gaia mission now provides milli-arcsec accuracy on the predictions of these events and makes possible observations that were previously unthinkable. Occultations return kilometric accuracies on the three-dimensional shape of bodies irrespective of their geocentric distances, with the potential of detecting topographic features along the limb. From the shape, accurate values of albedo can be derived, and if the mass is known, the bulk density is pinned down, thus constraining the internal structure and equilibrium state of the object. Occultations are also extremely sensitive to tenuous atmospheres, down to the nanobar level. They allowed the monitoring of Pluto's and Triton's atmospheres in the last three decades, constraining their seasonal evolution. They may unveil in the near future atmospheres around other remote bodies of the solar system. Since 2013, occultations have led to the surprising discovery of ring systems around the Centaur object Chariklo, the dwarf planet Haumea and the large trans-Neptunian object Quaoar, while revealing dense material around the Centaur Chiron. This suggests that rings are probably much more common features than previously thought. Meanwhile, they have raised new dynamical questions concerning the confining effect of resonances forced by irregular objects on ring particles. Serendipitous occultations by km-sized trans-Neptunian or Oort objects has the potential to provide the size distribution of a population that suffered few collisions until now, thus constraining the history of primordial planetesimals in the 1-100 km range., Comment: 76 pages, 22 figures, 7 tables, accepted for publication in The Astronomy and Astrophysics Review

Scintillators have been widely used in X-ray imaging due to their ability to convert high-energy radiation into visible light, making them essential for applications such as medical imaging and high-energy physics. Recent advances in the artificial structuring of scintillators offer new opportunities for improving the energy resolution of scintillator-based X-ray detectors. Here, we present a three-bin energy-resolved X-ray imaging framework based on a three-layer multicolor scintillator used in conjunction with a physics-aware image postprocessing algorithm. The multicolor scintillator is able to preserve X-ray energy information through the combination of emission wavelength multiplexing and energy-dependent isolation of X-ray absorption in specific layers. The dominant emission color and the radius of the spot measured by the detector are used to infer the incident X-ray energy based on prior knowledge of the energy-dependent absorption profiles of the scintillator stack. Through ab initio Monte Carlo simulations, we show that our approach can achieve an energy reconstruction accuracy of 49.7%, which is only 2% below the maximum accuracy achievable with realistic scintillators. We apply our framework to medical phantom imaging simulations where we demonstrate that it can effectively differentiate iodine and gadolinium-based contrast agents from bone, muscle, and soft tissue.

Scintillators are essential for converting X-ray energy into visible light in imaging technologies. Their widespread application in imaging technologies has been enabled by scalable, high-quality, and affordable manufacturing methods. Nanophotonic scintillators, which feature nanostructures at the scale of their emission wavelength, provide a promising approach to enhance emission properties like light yield, decay time, and directionality. However, scalable fabrication of such nanostructured scintillators has been a significant challenge, impeding their widespread adoption. Here, we present a scalable fabrication method for large-area nanophotonic scintillators based on the self-assembly of chalcogenide glass photonic crystals. This technique enables the production of nanophotonic scintillators over wafer-scale areas, achieving a six-fold enhancement in light yield compared to unpatterned scintillators. We demonstrate this approach using a conventional X-ray scintillator material, cerium-doped yttrium aluminum garnet (YAG:Ce). By analyzing the influence of surface nanofabrication disorder, we establish its effect on imaging performance and provide a route towards large-scale scintillation enhancements without decrease in spatial resolution. Finally, we demonstrate the practical applicability of our nanophotonic scintillators through X-ray imaging of biological and inorganic specimens. Our results indicate that this scalable fabrication technique could enable the industrial implementation of a new generation of nanophotonic-enhanced scintillators, with significant implications for advancements in medical imaging, security screening, and nondestructive testing.

Trans-Neptunian objects (TNOs) are considered to be among the most primitive objects in our Solar System. Knowledge of their primary physical properties is essential for understanding their origin and the evolution of the outer Solar System. We predicted a stellar occultation by this TNO for 2020 October 23 UT and ran a specific campaign to investigate this event. We derived the projected profile shape and size from the occultation observations by means of an elliptical fit to the occultation chords. We also performed photometric observations of (143707) 2003 UY117 to obtain the absolute magnitude and the rotational period from the observed rotational light curve. Finally, we combined these results to derive the three-dimensional shape, volume-equivalent diameter, and geometric albedo for this TNO. From the stellar occultation, we obtained a projected ellipse with axes of $(282 \pm 18) \times (184 \pm 32)$ km. The area-equivalent diameter for this ellipse is $D_\textrm{eq,A} = 228 \pm 21$ km. From our photometric $R$ band observations, we derived an absolute magnitude of $H_V = 5.97 \pm 0.07$ mag using $V-R = 0.46 \pm 0.07$ mag, which was derived from a $V$ band subset of these data. The rotational light curve has a peak-to-valley amplitude of $\Delta m = 0.36 \pm 0.13$ mag. We find the most likely rotation period to be $P = 12.376 \pm 0.0033$ hours. By combining the occultation with the rotational light curve results and assuming a triaxial ellipsoid, we derived axes of $a \times b \times c = (332 \pm 24)$ km $\times$ $(216 \pm 24)$ km $\times$ $(180\substack{+28\\-24})$ km for this ellipsoid, and therefore a volume-equivalent diameter of $D_\textrm{eq,V} = 235 \pm 25$ km. Finally, the values for the absolute magnitude and for the area-equivalent diameter yield a geometric albedo of $p_V = 0.139 \pm 0.027$., Comment: 9 pages, 7 figures, accepted for publication in Astronomy and Astrophysics on Sept 13, 2024

Scintillation describes the conversion of high-energy particles into light in transparent media and finds diverse applications such as high-energy particle detection and industrial and medical imaging. This process operates on multiple timescales, with the final radiative step consisting of spontaneous emission, which can be modeled within the framework of quasi-equilibrium fluctuational electrodynamics. Scintillation can therefore be controlled and enhanced via nanophotonic effects, which has been proposed and experimentally demonstrated. Such designs have thus far obeyed Lorentz reciprocity, meaning there is a direct equivalence between scintillation emission and absorption by the scintillator. However, scintillators that do not obey Lorentz reciprocity have not been explored, even though they represent a novel platform for probing emission which is both nonequilibrium and nonreciprocal in nature. In this work, we propose to harness nonreciprocity to achieve directional control of scintillation emission, granting an additional degree of control over scintillation. Such directionality of light output is important in improving collection efficiencies along the directions where detectors are located. We present the design of a nonreciprocal scintillator using a one-dimensional magnetophotonic crystal in the Voigt configuration. Our work demonstrates the potential of controlling nonequilibrium emission such as scintillation by breaking reciprocity and expands the space of nanophotonic design for achieving such control., Comment: 16 pages, 9 figures

Nonlinear optics has become the workhorse for countless applications in classical and quantum optics, from optical bistability to single photon pair generation. However, the intrinsic weakness of optical nonlinearity has meant that large input powers and weak output powers are often a necessity in nonlinear frequency conversion. Here, motivated by recent advances in using non-Hermitian photonics and gain/loss engineering to enable non-reciprocal light transport, we explore how the interplay between non-Hermiticity and optical nonlinearity leads to a fundamentally new regime of nonlinear frequency conversion. We show how non-Hermitian coupling between discrete frequency modes can result in non-reciprocal flow of energy in the frequency dimension, closely resembling the non-Hermitian skin effect (NHSE). Applying our theory to a multimode nonlinear cavity supporting cascaded nonlinear processes, we create an asymmetric infrared (IR) comb that features a ``skin'' frequency mode populated with efficiency exceeding 85\%. Furthermore, we demonstrate how three-wave mixing processes in the non-reciprocal infrared comb we generate enables terahertz (THz) generation exceeding the Manley-Rowe limit. We then show how the non-reciprocal frequency conversion is robust against cavity defects and disorder that cause random fluctuations in the dissipation rate for different modes. Moreover, in certain regimes, the nonlinear, non-Hermitian system supports stable limit cycles that can enable multimode pulsing with picosecond pulse widths and GHz repetition rates. Finally, we explore how the system can be applied to generate simultaneous IR and THz frequency combs, potentially unlocking novel applications in spectroscopy and metrology.

The differential nature of solutions of linear difference equations over the projective line was recently elucidated. In contrast, little is known about the differential nature of solutions of linear difference equations over elliptic curves. In the present paper, we study power series $f(z)$ with complex coefficients satisfying a linear difference equation over a field of elliptic functions $K$,with respect to the difference operator $\phi f(z)=f(qz)$, $2\le q\in\mathbb{Z}$,arising from an endomorphism of the elliptic curve. Our main theoremsays that such an $f$ satisfies, in addition, a polynomial differentialequation with coefficients from $K,$ if and only if it belongs tothe ring $S=K[z,z^{-1},\zeta(z,\Lambda)]$ generated over $K$ by$z,z^{-1}$ and the Weierstrass $\zeta$-function. This is the first elliptic extension of recent theorems of Adamczewski, Dreyfus and Hardouin concerning the differential transcendence of solutions of difference equations with coefficients in $\mathbb{C}(z),$ in which various difference operators were considered (shifts, $q$-differenceoperators or Mahler operators). While the general approach, of usingparametrized Picard-Vessiot theory, is similar, many features, andin particular the emergence of monodromy considerations and the ring$S$, are unique to the elliptic case and are responsible for non-trivial difficulties. We emphasize that, among the intermediate results, we prove an integrability result for difference-differential systems over ellipticcurves which is a genus one analogue of the integrability results obtained by Sch\''afke and Singer over the projective line.

In this study, we propose a novel model describing the coevolution between hosts and pathogens, based on a non-local partial differential equation formalism for populations structured by phenotypic traits. Our objective with this model is to illustrate scenarios corresponding to the evolutionary concept of ''Chase Red Queen scenario'', characterized by perpetual evolutionary chases between hosts and pathogens. First, numerical simulations show the emergence of such scenarios, depicting the escape of the host (in phenotypic space) pursued by the pathogen. We observe two types of behaviors, depending on the assumption about the presence of a phenotypic optimum for the host: either the formation of traveling pulses moving along a straight line with constant speed and constant profiles, or stable phenotypic distributions that periodically rotate along a circle in the phenotypic space. Through rigorous perturbation techniques and careful application of the implicit function theorem in rather intricate function spaces, we demonstrate the existence of the first type of behavior, namely traveling pulses moving with constant speed along a straight line. Just as the Lotka-Volterra models have revealed periodic dynamics without the need for environmental forcing, our work shows that, from the pathogen's point of view, various trajectories of mobile optima can emerge from coevolution with a host species.

Entanglement is a unique feature of quantum mechanics. In coupled systems of light and matter, entanglement manifests itself in the linear superposition of multipartite quantum states (e.g., parametrized by the multiple spatial, spectral, or temporal degrees of freedom of a light field). In bipartite systems, the Schmidt decomposition provides a modal decomposition of the entanglement structure over independent, separable states. Although ubiquitous as a mathematical tool to describe and measure entanglement, there exists no general efficient experimental method to decompose a bipartite quantum state onto its Schmidt modes. Here, we propose a method that relies on bipartite self-configuring optics that automatically ``learns'' the Schmidt decomposition of an arbitrary pure quantum state. Our method is agnostic to the degrees of freedom over which quantum entanglement is distributed and can reconstruct the Schmidt modes and values by variational optimization of the network's output powers or coincidences. We illustrate our method with numerical examples of spectral entanglement analysis for biphotons generated via spontaneous parametric down conversion and provide experimental guidelines for its realization, including the influence of losses and impurities. Our method provides a versatile and scalable way of analyzing entanglement in bipartite integrated quantum photonic systems.

This study focuses on advancing metascintillators to break the 100 ps barrier and approach the 10 ps target. We exploit nanophotonic features, specifically the Purcell effect, to shape and enhance the scintillation properties of the first-generation metascintillator. We demonstrate that a faster emission is achievable along with a more efficient conversion efficiency. This results in a coincidence time resolution improved by a factor of 1.6, crucial for TOF-PET applications.

Optical computing often employs tailor-made hardware to implement specific algorithms, trading generality for improved performance in key aspects like speed and power efficiency. An important computing approach that is still missing its corresponding optical hardware is probabilistic computing, used e.g. for solving difficult combinatorial optimization problems. In this study, we propose an experimentally viable photonic approach to solve arbitrary probabilistic computing problems. Our method relies on the insight that coherent Ising machines composed of coupled and biased optical parametric oscillators can emulate stochastic logic. We demonstrate the feasibility of our approach by using numerical simulations equivalent to the full density matrix formulation of coupled optical parametric oscillators.

Non-Abelian gauge fields provide a conceptual framework for the description of particles having spins. The theoretical importance of non-Abelian gauge fields motivates their experimental synthesis and explorations. Here, we demonstrate non-Abelian lattice gauge fields for photons. In the study of gauge fields, lattice models are essential for the understanding of their implications in extended systems. We utilize the platform of synthetic frequency dimensions, which enables the study of lattice physics in a scalable and programmable way. We observe Dirac cones at time-reversal-invariant momenta as well as the direction reversal of eigenstate trajectories associated with such Dirac cones. Both of them are unique signatures of non-Abelian gauge fields in our lattice system. Our results highlight the implications of non-Abelian gauge field in the study of topological physics and suggest opportunities for the control of photon spins and pseudospins.

Enhancing interactions in many-body quantum systems, while protecting them from environmental decoherence, is at the heart of many quantum technologies. Waveguide quantum electrodynamics is a promising platform for achieving this, as it hosts infinite-range interactions and decoherence-free subspaces of quantum emitters. However, as coherent interactions between emitters are typically washed out in the wavelength-spacing regime hosting decoherence-free states, coherent control over the latter becomes limited, and many-body Hamiltonians in this important regime remain out of reach. Here we show that by incorporating emitter arrays with nonlinear waveguides hosting parametric gain, we obtain a unique class of many-body interaction Hamiltonians with coupling strengths that increase with emitter spacing, and persist even for wavelength-spaced arrays. We then propose to use these Hamiltonians to coherently generate decoherence-free states directly from the ground state, using only global squeezing drives, without the need for local addressing of individual emitters. Interestingly, we find that the dynamics approaches a unitary evolution in the limit of weak intra-waveguide squeezing, and discuss potential experimental realizations of this effect. Our results pave the way towards coherent control protocols in waveguide quantum electrodynamics, with applications including quantum computing, simulation, memory and nonclassical light generation.

The widespread practice of delivering antibiotics through drinking water to livestock leads to considerable variability in exposure levels among animals, raising concerns regarding disease outbreaks and the emergence of antibiotic resistance. This variability is primarily driven by three pivotal factors: fluctuations in drug concentration within water pipes, variances in drinking behavior among animals, and differences in individual pharmacokinetic parameters. This article introduces an approach aimed at improving medication distribution by customizing it according to the drinking patterns of pigs, without escalating the medication dose. As examples, we demonstrate that incorporating the drinking behavior into the delivery of amoxicillin results in an increase in the percentage of piglets reaching an AUC/MIC ratio greater than 25h. Specifically, with Pasteurella multocida, the percentage rises from 30% to at least 60%, while with Actinobacillus pleuropneumoniae, it increases from 20% to more than 70%.

Multimode squeezed light is enticing for several applications, from squeezed frequency combs for spectroscopy to signal multiplexing in optical computing. To generate squeezing in multiple frequency modes, optical parametric oscillators have been vital in realizing multimode squeezed vacuum states through second-order nonlinear processes. However, most work has focused on generating multimode squeezed vacua and squeezing in mode superpositions (supermodes). Bright squeezing in multiple discrete frequency modes, if realized, could unlock novel applications in quantum-enhanced spectroscopy and optical quantum computing. Here, we show how $Q$ factor engineering of a multimode nonlinear cavity with cascaded three wave mixing processes creates strong, spectrally tunable single mode output amplitude noise squeezing over 10 dB below the shot noise limit. In addition, we demonstrate squeezing for multiple discrete frequency modes above threshold. This bright squeezing arises from enhancement of the (noiseless) nonlinear rate relative to decay rates in the system due to the cascaded generation of photons in a single idler "bath" mode. A natural consequence of the strong nonlinear coupling in our system is the creation of an effective cavity in the synthetic frequency dimension that sustains Bloch oscillations in the modal energy distribution. Bloch mode engineering could provide an opportunity to better control nonlinear energy flow in the synthetic frequency dimension, with exciting applications in quantum random walks and topological photonics. Lastly, we show evidence of long-range correlations in amplitude noise between discrete frequency modes, pointing towards the potential of long-range entanglement in a synthetic frequency dimension.

The observation that free electrons can interact coherently with quantized electromagnetic fields and matter systems has led to a plethora of proposals leveraging the unique quantum properties of free electrons. At the heart of these proposals lies the assumption of a strong quantum interaction between a flying free electron and a photonic mode. However, existing schemes are intrinsically limited by electron diffraction, which puts an upper bound on the interaction length and therefore the quantum coupling strength. Here, we propose the use of "free-electron fibers'': effectively one-dimensional photonic systems where free electrons co-propagate with two guided modes. The first mode applies a ponderomotive trap to the free electron, effectively lifting the limitations due to electron diffraction. The second mode strongly couples to the guided free electron, with an enhanced coupling that is orders of magnitude larger than previous designs. Moreover, the extended interaction lengths enabled by our scheme allows for strong single-photon nonlinearities mediated by free electrons. We predict a few interesting observable quantum effects in our system, such as deterministic single-photon emission and complex, nonlinear multimode dynamics. Our proposal paves the way towards the realization of many anticipated effects in free-electron quantum optics, such as non-Gaussian light generation, deterministic single photon emission, and quantum gates controlled by free-electron--photon interactions., Comment: References updated in version 2

Probabilistic machine learning utilizes controllable sources of randomness to encode uncertainty and enable statistical modeling. Harnessing the pure randomness of quantum vacuum noise, which stems from fluctuating electromagnetic fields, has shown promise for high speed and energy-efficient stochastic photonic elements. Nevertheless, photonic computing hardware which can control these stochastic elements to program probabilistic machine learning algorithms has been limited. Here, we implement a photonic probabilistic computer consisting of a controllable stochastic photonic element - a photonic probabilistic neuron (PPN). Our PPN is implemented in a bistable optical parametric oscillator (OPO) with vacuum-level injected bias fields. We then program a measurement-and-feedback loop for time-multiplexed PPNs with electronic processors (FPGA or GPU) to solve certain probabilistic machine learning tasks. We showcase probabilistic inference and image generation of MNIST-handwritten digits, which are representative examples of discriminative and generative models. In both implementations, quantum vacuum noise is used as a random seed to encode classification uncertainty or probabilistic generation of samples. In addition, we propose a path towards an all-optical probabilistic computing platform, with an estimated sampling rate of ~ 1 Gbps and energy consumption of ~ 5 fJ/MAC. Our work paves the way for scalable, ultrafast, and energy-efficient probabilistic machine learning hardware.

Optical phenomena always display some degree of partial coherence between their respective degrees of freedom. Partial coherence is of particular interest in multimodal systems, where classical and quantum correlations between spatial, polarization, and spectral degrees of freedom can lead to fascinating phenomena (e.g., entanglement) and be leveraged for advanced imaging and sensing modalities (e.g., in hyperspectral, polarization, and ghost imaging). Here, we present a universal method to analyze, process, and generate spatially partially coherent light in multimode systems by using self-configuring optical networks. Our method relies on cascaded self-configuring layers whose average power outputs are sequentially optimized. Once optimized, the network separates the input light into its mutually incoherent components, which is formally equivalent to a diagonalization of the input density matrix. We illustrate our method with arrays of Mach-Zehnder interferometers and show how this method can be used to perform partially coherent environmental light sensing, generation of multimode partially coherent light with arbitrary coherency matrices, and unscrambling of quantum optical mixtures. We provide guidelines for the experimental realization of this method, paving the way for self-configuring photonic devices that can automatically learn optimal modal representations of partially coherent light fields.

To keep current global warming below 1.5{\deg}C compared with the pre-industrial era, measures must be taken as quickly as possible in all spheres of society. Astronomy must also make its contribution. In this proceeding, and during the workshop to which it refers, different levers of actions are discussed through various examples: individual efforts, laboratory-level actions, impact evaluation and mitigation in major projects, institutional level, and involvement through collectives., Comment: 5 pages, 0 figures, SF2A conference 2023

Nonlinear systems are important in many areas of modern science and technology. For example, nonlinearity plays an essential role in generating quantum mechanical states of both light and matter. As a result, there has been great interest in understanding the fundamental quantum nature of a variety of nonlinear effects. At the same time, there is currently a large gap between the classical and quantum understanding of nonlinear systems, with the classical understanding being far more developed. To close this gap, we introduce a general new theory which allows us to predict quantum effects in any nonlinear system purely in terms of its classical description. We demonstrate the predictions of our theory in experiments probing quantum fluctuations of intense femtosecond pulses propagating in an optical fiber undergoing soliton-fission supercontinuum generation, a process where broadband radiation is produced by a narrow-band input. Famously, this process is known to be highly noise-sensitive, leading to noisy outputs even from inputs with only quantum fluctuations. In contrast, our experiments uncovered a variety of previously hidden low-noise and noise-robust states arising from quantum correlations and entanglement, in agreement with the predictions of our theory. We also show how the theory points to new design concepts for controlling quantum noise in optics and beyond. We expect that our results will provide a template for discovering quantum effects in a wide variety of complex nonlinear systems.

The question of the origin of the hard X-ray/soft gamma-ray emission in Centaurus A (Cen A) persists despite decades of observations. Results from X-ray instruments suggest a jet origin since the implied electron temperature (kT_e) would cause pair production runaway in the corona. In contrast, instruments sensitive to soft gamma-rays report electron temperatures indicating a corona origin may be possible. In this context, we analyzed archival INTEGRAL/IBIS-ISGRI and SPI data and observations from a 2022 Cen A monitoring program. Our analysis did not find any spectral variability. Thus we combined all observations for long-term average spectra, which were fit with a NuSTAR observation to study the 3.5 keV - 2.2 MeV spectrum. Spectral fits using a CompTT model found kT_e ~ 550 keV, near pair-production runaway. The spectrum was also well described by a log-parabola to model synchrotron self-Compton emission from the jet. Additionally, a spectral fit with the 12-year catalog Fermi/LAT spectrum using a log-parabola can explain the data up to ~ 3 GeV. Above ~ 3 GeV, a power-law excess is present, which has been previously reported in LAT/H.E.S.S. analysis. However, including a corona spectral component can also describe the data well. In this scenario, the hard X-rays/soft gamma-rays are due the corona and the MeV to GeV emission is due to the jet., Comment: 20 pages, 4 figures. Accepted by ApJ

Given a linear differential equation with coefficients in $\mathbb{Q}(x)$, an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions is algebraic. After presenting motivating examples coming from various branches of mathematics, we advertise in an elementary way a beautiful local-global arithmetic approach to these questions, initiated by Grothendieck in the late sixties. This approach has deep ramifications and leads to the still unsolved Grothendieck-Katz $p$-curvature conjecture., Comment: 52 pages, 2 figures, to appear in the Bulletin of the AMS

In this paper, we investigate the large-time behavior of bounded solutions of the Cauchy problem for a reaction-diffusion equation in $\mathbb{R}^N$ with bistable reaction term. We consider initial conditions that are chiefly indicator functions of bounded Borel sets. We examine how geometric transformations of the supports of these initial conditions affect the propagation or extinction of the solutions at large time. We also consider two fragmentation indices defined in the set of bounded Borel sets and we establish some propagation or extinction results when the initial supports are weakly or highly fragmented. Lastly, we show that the large-time dynamics of the solutions is not monotone with respect to the considered fragmentation indices, even for equimeasurable sets.

One of the most important insights of quantum field theory is that electromagnetic fields must fluctuate. Even in the vacuum state, the electric and magnetic fields have a nonzero variance, leading to ubiquitous effects such as spontaneous emission, the Lamb shift, the Casimir effect, and more. These "vacuum fluctuations" have also been harnessed as a source of perfect randomness, for example to generate perfectly random photonic bits. Despite these achievements, many potential applications of quantum randomness in fields such as probabilistic computing rely on controllable probability distributions, which have not yet been realized on photonic platforms. In this work, we show that the injection of vacuum-level "bias" fields into a multi-stable optical system enables a controllable source of "biased" quantum randomness. We demonstrate this concept in an optical parametric oscillator (OPO). Ordinarily, an OPO initiated from the ground state develops a signal field in one of two degenerate phase states (0 and $\pi$) with equal probability. By injecting bias pulses which contain less than one photon on average, we control the probabilities associated with the two output states, leading to the first controllable photonic probabilistic bit (p-bit). We shed light on the physics behind this process, showing quantitative agreement between theory and experiment. Finally, we demonstrate the potential of our approach for sensing sub-photon level fields by showing that our system is sensitive to the temporal shape of bias field pulses far below the single photon level. Our results suggest a new platform for the study of stochastic quantum dynamics in nonlinear driven-dissipative systems, and point toward possible applications in ultrafast photonic probabilistic computing, as well as the sensing of extremely weak fields.

On 2 September 2017 MAXI J1535-571 went into outburst and peaked at ~5 Crab in the 2-20 keV energy range. Early in the flare INTEGRAL performed Target of Opportunity pointings and monitored the source as it transitioned from the hard state to the soft state. Using quasi-simultaneous observations from MAXI/GSC and INTEGRAL/SPI, we studied the temporal and spectral evolution of MAXI J1535-571 in the 2-500 keV range. Early spectra show a Comptonized spectrum and a high-energy component dominant above ~150 keV. CompTT fits to the SPI data found electron temperatures (kTe) evolves from ~31 keV to 18 keV with a tied optical depth (tau ~ 0.85) or tau evolving from ~1.2-0.65 with a tied kTe (~24 keV). To investigate the nature of the high-energy component, we performed a spectral decomposition of the 100-400 keV energy band. The CompTT flux varies significantly during the hard state while the high-energy component flux is consistent with a constant flux. This result suggests that the two components originate from different locations, which favors a jet origin interpretation for the high-energy component over a hybrid corona interpretation. Lastly, two short rebrightenings during the hard-to-soft transition are compared to similar events reported in MAXI J1820+070.

Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. Shift-invariance has deep implications for the design and functionality of optical devices, such as the necessity of free space between components (as in compound objectives made of several curved surfaces). We present a method for nanophotonic inverse design of compact imaging systems whose resolution is not constrained by paraxial shift-invariance. Our method is end-to-end, in that it integrates density-based full-Maxwell topology optimization with a fully iterative elastic-net reconstruction algorithm. By the design of nanophotonic structures that scatter light in a non-shift-invariant manner, our optimized nanophotonic imaging system overcomes the limitations of paraxial shift-invariance, achieving accurate, noise-robust image reconstruction beyond shift-invariant resolution.

Scintillation materials convert high-energy radiation to optical light through a complex multi-stage process. The last stage of the process is light emission via spontaneous emission, which usually governs and limits the scintillator emission rate and light yield. For decades, the quest for faster emission rate and greater light yield motivated the frontier of scintillators research to focus on developing better materials and dopants. Here, we experimentally demonstrate a fundamentally different, recently proposed concept for enhancing the scintillation rate and yield: the Purcell effect. The Purcell effect is a universal enhancement mechanism for spontaneous emission by engineering the optical environment. In scintillators, such an enhancement arises from engineering the nanoscale geometry within the scintillation bulk, which thus applies universally to any scintillating material and dopant. We design and fabricate a thin multilayer nanophotonic scintillator, demonstrating Purcell-enhanced scintillation, achieving a 50% enhancement in emission-rate and an 80% enhancement in light yield. We demonstrate the potential of our device for realizing these enhancements in real-life settings for X-ray applications, also due to the robustness of the nanophotonic design to fabrication disorder. Our results show the bright prospects of bridging nanophotonics and scintillators science, toward reduced radiation dosage and increased resolution for high-energy particles detection.

We propose a model to describe the adaptation of a phenotypically structured population in a $H$-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of this model. We show that the large-time behaviour of the solution (persistence or extinction) depends on the sign of a principal eigenvalue, $\lambda_H$, and we study the dependency of $\lambda_H$ with respect to $H$. This analysis sheds new light on the effect of increasing the number of patches on the persistence of a population, which has implications in agroecology and for understanding zoonoses; in such cases we consider a pathogenic population and the patches correspond to different host species. The occurrence of a springboard effect, where the addition of a patch contributes to persistence, or on the contrary the emergence of a detrimental effect by increasing the number of patches on the persistence, depends in a rather complex way on the respective positions in the phenotypic space of the optimal phenotypes associated with each patch. From a mathematical point of view, an important part of the difficulty in dealing with $H\ge 3$, compared to $H=1$ or $H=2$, comes from the lack of symmetry. Our results, which are based on a fixed point theorem, comparison principles, integral estimates, variational arguments, rearrangement techniques, and numerical simulations, provide a better understanding of these dependencies. In particular, we propose a precise characterisation of the situations where the addition of a third patch increases or decreases the chances of persistence, compared to a situation with only two patches.

When impinging on optical structures or passing in their vicinity, free electrons can spontaneously emit electromagnetic radiation, a phenomenon generally known as cathodoluminescence. Free-electron radiation comes in many guises: Cherenkov, transition, and Smith-Purcell radiation, but also electron scintillation, commonly referred to as incoherent cathodoluminescence. While those effects have been at the heart of many fundamental discoveries and technological developments in high-energy physics in the past century, their recent demonstration in photonic and nanophotonic systems has attracted a lot of attention. Those developments arose from predictions that exploit nanophotonics for novel radiation regimes, now becoming accessible thanks to advances in nanofabrication. In general, the proper design of nanophotonic structures can enable shaping, control, and enhancement of free-electron radiation, for any of the above-mentioned effects. Free-electron radiation in nanophotonics opens the way to promising applications, such as widely-tunable integrated light sources from x-ray to THz frequencies, miniaturized particle accelerators, and highly sensitive high-energy particle detectors. Here, we review the emerging field of free-electron radiation in nanophotonics. We first present a general, unified framework to describe free-electron light-matter interaction in arbitrary nanophotonic systems. We then show how this framework sheds light on the physical underpinnings of many methods in the field used to control and enhance free-electron radiation. Namely, the framework points to the central role played by the photonic eigenmodes in controlling the output properties of free-electron radiation (e.g., frequency, directionality, and polarization). [... see full abstract in paper], Comment: 34 pages; 9 figures

We present measurements of the polarization of X-rays in the $2-8 \thinspace \mathrm{keV}$ band from the nucleus of the radio galaxy Centaurus A (Cen A), using a 100ks observation from the Imaging X-ray Polarimetry Explorer (IXPE). Nearly simultaneous observations of Cen A were also taken with the Swift, NuSTAR, and INTEGRAL observatories. No statistically significant degree of polarization is detected with IXPE. These observations have a minimum detectable polarization at $99 \%$ percent confidence (MDP$_{99}$) of $6.5 \%$ using a weighted, spectral model-independent calculation in the $2-8 \thinspace \mathrm{keV}$ band. The polarization angle $\psi$ is consequently unconstrained. Spectral fitting across three orders of magnitude in X-ray energy ($0.3-400 \thinspace \mathrm{keV}$) demonstrates that the SED of Cen A is well described by a simple power law with moderate intrinsic absorption ($N_H \sim 10^{23} \thinspace \mathrm{cm}^{-2}$) and a Fe K$\alpha$ emission line, although a second unabsorbed power law is required to account for the observed spectrum at energies below $2 \thinspace \mathrm{keV}$. This spectrum suggests that the reprocessing material responsible for this emission line is optically thin and distant from the central black hole. Our upper limits on the X-ray polarization are consistent with the predictions of Compton scattering, although the specific seed photon population responsible for production of the X-rays cannot be identified. The low polarization degree, variability in the core emission, and the relative lack of variability in the Fe K$\alpha$ emission line support a picture where electrons are accelerated in a region of highly disordered magnetic fields surrounding the innermost jet., Comment: Accepted for Publication in ApJ, 15 pages