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Color centers in hexagonal boron nitride (hBN) advantageously combine excellent photophysical properties with a potential for integration in highly compact devices. Progress towards scalable integration necessitates a high quantum efficiency and an efficient photon collection. In this context, we compare the optical characteristics of individual hBN color centers generated by electron irradiation, in two different electromagnetic environments. We keep track of well-identified emitters that we characterize before and after dry transfer of exfoliated crystals. This comparison provides information about their quantum efficiency - which we find close to unity - as well as their vertical position in the crystal with nanometric precision, which we find away from the flake surfaces. Our work suggests hybrid dielectric-metal planar structures as an efficient tool for characterizing quantum emitters in addition to improving the count rate, and can be generalized to other emitters in 2D materials or in planar photonic structures.

Super-Resolution (SR) is the problem that consists in reconstructing images that have been degraded by a zoom-out operator. This is an ill-posed problem that does not have a unique solution, and numerical approaches rely on a prior on high-resolution images. While optimization-based methods are generally deterministic, with the rise of image generative models more and more interest has been given to stochastic SR, that is, sampling among all possible SR images associated with a given low-resolution input. In this paper, we construct an efficient, stable and provably exact sampler for the stochastic SR of Gaussian microtextures. Even though our approach is limited regarding the scope of images it encompasses, our algorithm is competitive with deep learning state-of-the-art methods both in terms of perceptual metric and execution time when applied to microtextures. The framework of Gaussian microtextures also allows us to rigorously discuss the limitations of various reconstruction metrics to evaluate the efficiency of SR routines.

Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by solving numerically the backward SDE or its associated flow ODE. Studying the convergence of these models necessitates to control four different types of error: the initialization error, the truncation error, the discretization and the score approximation. In this paper, we study theoretically the behavior of diffusion models and their numerical implementation when the data distribution is Gaussian. In this restricted framework where the score function is a linear operator, we derive the analytical solutions of the backward SDE and the probability flow ODE. We prove that these solutions and their discretizations are all Gaussian processes, which allows us to compute exact Wasserstein errors induced by each error type for any sampling scheme. Monitoring convergence directly in the data space instead of relying on Inception features, our experiments show that the recommended numerical schemes from the diffusion models literature are also the best sampling schemes for Gaussian distributions.

The sharp Dirac cone of the electronic dispersion confers to graphene a remarkable sensitivity to strain. It is usually encoded in scalar and pseudo-vector potentials, induced by the modification of hopping parameters, which have given rise to new phenomena at the nanoscale such as giant pseudomagnetic fields and valley polarization. Here, we unveil the effect of these potentials on the quantum transport across a succession of strain-induced barriers. We use high-mobility, hBN-encapsulated graphene, transferred over a large (10x10 $\mu$m$^{2}$) crenellated hBN substrate. We show the emergence of a broad resistance ancillary peak at positive energy that arises from Klein tunneling barriers induced by the tensile strain at the trench edges. Our theoretical study, in quantitative agreement with experiment, highlights the balanced contributions of strain-induced scalar and pseudo-vector potentials on ballistic transport. Our results establish crenellated van der Waals heterostructures as a promising platform for strain engineering in view of applications and basic physics.

Under high electrical current, some materials can emit electromagnetic radiation beyond incandescence. This phenomenon, referred to as electroluminescence, leads to the efficient emission of visible photons and is the basis of domestic lighting devices (e.g., light-emitting diodes). In principle, electroluminescence can lead to mid-infrared (mid-IR) emission of confined light-matter excitations called phonon-polaritons, resulting from the coupling of photons with crystal lattice vibrations (optical phonons). In particular, phonon-polaritons arising in the van der Waals crystal hexagonal boron nitride (hBN) exhibit hyperbolic dispersion, which enhances light-matter coupling. For this reason, electroluminescence of hyperbolic phonon-polaritons (HPhPs) has been proposed as an explanation for the peculiar radiative energy transfer within hBN-encapsulated graphene transistors. However, since HPhPs are confined, they are inaccessible in the far-field, so that any hint of electroluminescence is only based on indirect electronic signatures and needs to be confirmed by direct observation. Here, we demonstrate far-field mid-IR ({\lambda} = 6.5 {\mu}m) electroluminescence of HPhPs excited by strongly biased high-mobility graphene within a van der Waals heterostructure, and we quantify the associated radiative energy transfer through the material. The presence of HPhPs is revealed via far-field mid-IR spectroscopy due to their elastic scattering at discontinuities in the heterostructure. The associated radiative flux is quantified by mid-IR pyrometry of the substrate receiving the energy. This radiative energy transfer is shown to be reduced in hBN with nanoscale inhomogeneities, demonstrating the central role of the electromagnetic environment in this process., Comment: 32 pages including Extended Data and Supplementary Material (Main text: 7 pages, 4 figures)

Electroluminescence, a non-thermal radiative process, is ubiquitous in semi-conductors and insulators but fundamentally precluded in metals. We show here that this restriction can be circumvented in high-quality graphene. By investigating the radiative emission of semi-metallic graphene field-effect transistors over a broad spectral range, spanning the near- and mid-infrared, we demonstrate direct far-field electroluminescence from hBN-encapsulated graphene in the mid-infrared under large bias in ambient conditions. Through a series of test experiments ruling out its incandescence origin, we determine that the electroluminescent signal results from the electrical pumping produced by interband tunneling. We show that the mid-infrared electroluminescence is spectrally shaped by a natural quarter-wave resonance of the heterostructure. This work invites a reassessment of the use of metals and semi-metals as non-equilibrium light emitters, and the exploration of their intriguing specificities in terms of carrier injection and relaxation, as well as emission tunability and switching speed., Comment: Main text (8 pages , 3 figures ) + Supplementary Information ( 19 pages , 19 figures)

Super-resolution (SR) is an ill-posed inverse problem which consists in proposing high-resolution images consistent with a given low-resolution one. While most SR algorithms are deterministic, stochastic SR deals with designing a stochastic sampler generating any realistic SR solution. The goal of this paper is to show that stochastic SR is a well-posed and solvable problem when restricting to Gaussian stationary textures. Using Gaussian conditional sampling and exploiting the stationarity assumption, we propose an efficient algorithm based on fast Fourier transform. We also demonstrate the practical relevance of the approach for SR with a reference image. Although limited to stationary microtextures, our approach compares favorably in terms of speed and visual quality to some state of the art methods designed for a larger class of images.

Lead halide perovskite nanocrystals are promising materials for classical and quantum light emission. To understand these outstanding properties, a thorough analysis of the band-edge exciton emission is needed which is not reachable in ensemble and room temperature studies because of broadening effects. Here, we report on a cryogenic-temperature study of the photoluminescence of single CsPbBr$_3$ NCs in the intermediate quantum confinement regime. We reveal the size-dependence of the spectral features observed: the bright-triplet exciton energy splittings, the trion and biexciton binding energies as well as the optical phonon replica spectrum. In addition, we show that bright triplet energy splittings are consistent with a pure exchange model and that the variety of polarisation properties and spectra recorded can be rationalised simply by considering the orientation of the emitting dipoles and the populations of the emitting states.

In view of the extensive use of hexagonal boron nitride (hBN) in 2D material electronics, it becomes important to refine its dielectric characterization in terms of low-field permittivity and high-field strength and conductivity up to the breakdown voltage. The present study aims at filling this gap using DC and RF transport in two Au-hBN-Au capacitor series of variable thickness in the 10--100 nm range, made of large high-pressure, high-temperature (HPHT) crystals and a polymer derivative ceramics (PDC) crystals. We deduce an out-of-plane low field dielectric constant $\epsilon_\parallel=3.4\pm0.2$ consistent with the theoretical prediction of Ohba et al., that narrows down the generally accepted window $\epsilon_\parallel=3$--$4$. The DC-current leakage at high-field is found to obey the Frenkel-Pool law for thermally-activated trap-assisted electron transport with a dynamic dielectric constant $\epsilon_\parallel\simeq3.1$ and a trap energy $\Phi_B\simeq1.3\;\mathrm{eV}$, that is comparable with standard technologically relevant dielectrics., Comment: 10 pages, 2 figures, AM version in Materials Research Express

We develop a Bayesian inference framework to quantify uncertainties in epidemiological models. We use SEIJR and SIJR models involving populations of susceptible, exposed, infective, diagnosed, dead and recovered individuals to infer from covid-19 data rate constants, as well as their variations in response to lockdown measures. To account for confinement, we distinguish two susceptible populations at different risk: confined and unconfined. We show that transmission and recovery rates within them vary in response to facts. A key unknown to predict the evolution of the epidemic is the fraction of the population affected by the virus, including asymptomatic subjects. Our study tracks its time evolution with quantified uncertainty from available official data from the onset of the epidemic, limited, however, by the data quality. We exemplify the technique with data from Spain, country in which late drastic lockdowns were enforced for months. In late actions and in the absence of other measures, spread is delayed but not stopped unless a large enough fraction of the population is confined until the asymptomatic population is depleted. To some extent, confinement could be replaced by strong distancing through masks in adequate circumstances.

Single photon emitters (SPEs) in low-dimensional layered materials have recently gained a large interest owing to the auspicious perspectives of integration and extreme miniaturization offered by this class of materials. However, accurate control of both the spatial location and the emission wavelength of the quantum emitters is essentially lacking to date, thus hindering further technological steps towards scalable quantum photonic devices. Here, we evidence SPEs in high purity synthetic hexagonal boron nitride (hBN) that can be activated by an electron beam at chosen locations. SPE ensembles are generated with a spatial accuracy better than the cubed emission wavelength, thus opening the way to integration in optical microstructures. Stable and bright single photon emission is subsequently observed in the visible range up to room temperature upon non-resonant laser excitation. Moreover, the low-temperature emission wavelength is reproducible, with an ensemble distribution of width 3 meV, a statistical dispersion that is more than one order of magnitude lower than the narrowest wavelength spreads obtained in epitaxial hBN samples. Our findings constitute an essential step towards the realization of top-down integrated devices based on identical quantum emitters in 2D materials., Comment: Main text and supplementary information: 22 pages, 11 figures

We revisit the concept of sphere of gravitational activity, to which we give both a geometrical and physical meaning. This study aims to refine this concept in a much broader context that could, for instance, be applied to exo-planetary problems (in a Galactic stellar disc-Star-Planets system) to define a first order "border" of a planetary system. The methods used in this paper rely on classical Celestial Mechanics and develop the equations of motion in the framework of the 3-body problem (e.g. Star-Planet-Satellite System). We start with the basic definition of planet's sphere of activity as the region of space in which it is feasible to assume a planet as the central body and the Sun as the perturbing body when computing perturbations of the satellite's motion. We then investigate the geometrical properties and physical meaning of the ratios of Solar accelerations (central and perturbing) and planetary accelerations (central and perturbing), and the boundaries they define. We clearly distinguish throughout the paper between the sphere of activity, the Chebotarev sphere (a particular case of the sphere of activity), Laplace sphere, and the Hill sphere. The last two are often wrongfully thought to be one and the same. Furthermore, taking a closer look and comparing the ratio of the star's accelerations (central/perturbing) to that of the planetary acceleration (central/perturbing) as a function of the planeto-centric distance, we have identified different dynamical regimes which are presented in the semi-analytical analysis., Comment: 11 pages, 5 figures

In this article, we study the persistence of properties of a given classical deter-ministic dierential equation under a stochastic perturbation of two distinct forms: external and internal. The rst case corresponds to add a noise term to a given equation using the framework of It\^o or Stratonovich stochastic dierential equations. The second case corresponds to consider a parameters dependent dierential equations and to add a stochastic dynamics on the parameters using the framework of random ordinary dierential equations. Our main concerns for the preservation of properties is stability/instability of equilibrium points and symplectic/Poisson Hamiltonian structures. We formulate persistence theorem in these two cases and prove that the cases of external and internal stochastic perturbations are drastically dierent. We then apply our results to develop a stochastic version of the Landau-Lifshitz equation. We discuss in particular previous results obtain by Etore and al. in [P. 'Etore, S.Labbe, J. Lelong, Long time behaviour of a stochastic nanoparticle, J. Differential Equations 257 (2014), 2115-2135] and we nally propose a new family of stochastic Landau-Lifshitz equations.