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This article is a continuation of arXiv:2401.14977. We study the concentration properties of spectral projectors on manifolds, in connection with the uncertainty principle. In arXiv:2401.14977, the second author proved an optimal uncertainty principle for the spectral projector of the Laplacian on the hyperbolic half-plane. The aim of the present work is to generalize this condition to surfaces with hyperbolic ends. In particular, we tackle the case of cusps, in which the volume of balls of fixed radius is not bounded from below. We establish that spectral estimates hold from sets satisfying a thickness condition, with a proof based on propagation of smallness estimates of Carleman and Logunov--Malinnikova type. We also prove the converse, namely the necessary character of the thickness condition, on any smooth manifold with Ricci curvature bounded from below., Comment: 29 pages, 4 figures. Comments welcome. v2: Significant overhaul of the proof of Theorem 1. v3: minor corrections

Exciton-polaritons, hybrid light-matter elementary excitations arising from the strong coupling regime between excitons in semiconductors and photons in photonic nanostructures, offer a fruitful playground to explore the physics of quantum fluids of light as well as to develop all-optical devices. However, achieving room temperature propagation of polaritons with a large excitonic fraction, which would be crucial, e.g., for nonlinear light transport in prospective devices, remains a significant challenge. } Here we report on experimental studies of exciton-polariton propagation at room temperature in resonant metasurfaces made from a sub-wavelength lattice of perovskite pillars. Thanks to the large Rabi splitting, an order of magnitude larger than the optical phonon energy, the lower polariton band is completely decoupled from the phonon bath of perovskite crystals. The long lifetime of these cooled polaritons, in combination with the high group velocity achieved through the metasurface design, enables long-range propagation regardless of the polariton excitonic fraction. Remarkably, we observed propagation distances exceeding hundreds of micrometers at room temperature, even when the polaritons possess a very high excitonic component, approximately {80}$\%$. Furthermore, the design of the metasurface introduces an original mechanism for directing uni-directional propagation through polarization control. This discovery of a ballistic propagation mode, leveraging high-speed cooled polaritons, heralds a promising avenue for the development of advanced polaritonic devices.

We obtain a central limit theorem for bulk counting statistics of free fermions in smooth domains of $\mathbb{R}^n$ with an explicit description of the covariance structure. This amounts to a study of the asymptotics of norms of commutators between spectral projectors of semiclassical Schr\"odinger operators and indicator functions supported in the bulk. In the spirit of the Widom conjecture, we show that the squared Hilbert-Schmidt norm of these commutators is of order $\hbar^{-n+1}\log(\hbar)$ as the semiclassical parameter $\hbar$ tends to $0$. We also give a new upper bound on the trace norm of these commutators and applications to estimations of the entanglement entropy for free fermions.

Exciton-polaritons represent a promising platform that combines the strengths of both photonic and electronic systems for future optoelectronic devices. However, their application is currently limited to laboratory research due to the high cost and complexity of fabrication methods, which are not compatible with the mature CMOS technology developed for microelectronics. In this work, we develop an innovative, low-cost, and CMOS-compatible method for fabricating large surface polaritonic devices. This is achieved by direct patterning of a halide-perovskite thin film via thermal nanoimprint. As a result, we observe highly homogeneous polaritonic modes of quality factor $Q\approx 300$ at room temperature across a centimetric scale. Impressively, the process provides high reproducibility and fidelity, as the same mold can be reused more than 10 times to imprint the perovskite layer on different types of substrates. Our results could pave the way for the production of low-cost integrated polaritonic devices operating at room temperature.

We build a general theory of microlocal (homogeneous) Fourier Integral Operators in real-analytic regularity, following the general construction in the smooth case by H\"ormander and Duistermaat. In particular, we prove that the Boutet-Sj\"ostrand parametrix for the Szeg\H{o} projector at the boundary of a strongly pseudo-convex real-analytic domain can be realised by an analytic Fourier Integral Operator. We then study some applications, such as FBI-type transforms on compact, real-analytic Riemannian manifolds and propagators of one-homogeneous (pseudo)differential operators.

We consider the determinantal point processes associated with the spectral projectors of a Schr\"odinger operator on $\mathbb{R}$, with a smooth confining potential. In the semiclassical limit, where the number of particles tends to infinity, we obtain a Szeg\H{o}-type central limit theorem (CLT) for the fluctuations of smooth linear statistics. More precisely, the Laplace transform of any statistic converges without renormalization to a Gaussian limit with a $H^{1/2}$-type variance, which depends on the potential. In the one-well (one-cut) case, using the quantum action-angle theorem and additional micro-local tools, we reduce the problem to the asymptotics of Fredholm determinants of certain approximately Toeplitz operators. In the multi-cut case, we show that for generic potentials, a similar result holds and the contributions of each wells are independent in the limit.

Friedrich-Wintgen (FW) interference is an atypical coupling mechanism that grants loss exchange between leaky resonances in non-Hermitian classical and quantum systems. Intriguingly, such an mechanism makes it possible for destructive interference scenario in which a radiating wave becomes a bound state in the continuum (BIC) by giving away all of its losses. Here we propose and demonstrate experimentally an original concept to tailor FW-BICs as polarization singularity at on-demand wavevectors in optical metasurface. As a proof-of-concept, using hybrid organic-inorganic halide perovskite as active material, we empower this novel polarization singularity to obtain lasing emission exhibiting both highly directional emission at oblique angles and polarization vortex in momentum space. Our results pave the way to steerable coherent emission with tailored polarization pattern for applications in optical communication/manipulation in free-space, high-resolution imaging /focusing and data storage.

We prove the convergence of quantized Bergman geodesics to the Mabuchi geodesics for the initial value problem, in the case of real-analytic initial data and in short time. This partially solves a conjecture of Y. Rubinstein and the last author. We also argue against the existence of a solution to the boundary value problem, generically in real-analytic regularity.

Exciton-polaritons are mixed light-matter excitations that result from the strong coupling regime between an active excitonic material and photonic resonances. Harnessing these hybrid excitations provides a rich playground to explore fascinating fundamental features, such as out-of-equilibrium Bose-Einstein condensation and quantum fluids of light, as well as novel mechanisms to be exploited in optoelectronic devices. Here, we investigate experimentally the formation of exciton-polaritons arising from the mixing between hybrid inorganic-organic perovskite excitons and an optical Bound state In a Continuum (BIC) of a subwavelength-scale metasurface, at room temperature. These polaritonic eigenmodes, hereby called polariton BICs (pol-BICs) are revealed in both reflectivity, resonant scattering, and photoluminescence measurements. Although pol-BICs only exhibit a finite quality factor that is bounded by the non-radiative losses of the excitonic component, they fully inherit BIC peculiar features: a full uncoupling from the radiative continuum in the vertical direction, which is associated to a locally vanishing farfield radiation in momentum space. Most importantly, our experimental results confirm that the topological nature of the photonic BIC is perfectly transferred to the pol-BIC. This is evidenced with the observation of a polarization vortex in the farfield of polaritonic emission. Our results pave the way to engineer BIC physics of interacting bosons, as well as novel room temperature polaritonic devices.

Defect engineering is applied to hybrid (CH$_3$NH$_3$)PbI$_3$ organic-inorganic perovskites. These materials have become one of the most promising low-cost alternatives to traditional semiconductors in the field of photovoltaics and light emitting devices. We use here Helium ion irradiation at low energy as a tool for the controlled introduction of point defects in both single crystals and polycrystalline thin films. The irradiation defects modify the opto-electronic properties as probed using photoluminescence spectroscopy from 10K to room-temperature. 2 Contrary to usual semiconductors, we observe a very good resilience of the PL properties with irradiation, even associated to an enhancement of the optical emission at low temperature. We discuss these results in relation with the tetragonal to orthorhombic low-temperature phase transition below T=160 K. A comparison between spectra from single crystals and polycrystalline films, both with and without irradiation defects, allow a better understanding of the light emission mechanisms in both kinds of samples. We thereby evidence radiation hardness of these materials and the specificity of defects and their impact over light emission properties.

We study local asymptotics for the spectral projector associated to a Schr\"odinger operator $-\hbar^2\Delta+V$ on $\mathbb{R}^n$ in the semiclassical limit as $\hbar\to0$. We prove local uniform convergence of the rescaled integral kernel of this projector towards a universal model, inside the classically allowed region as well as on its boundary. This implies universality of microscopic fluctuations for the corresponding free fermions (determinantal) point processes, both in the bulk and around regular boundary points. Our results apply for a general class of smooth potentials in arbitrary dimension $n\ge 1$. These results are complemented by studying both macroscopic and mesoscopic fluctuations of the point process. We obtain tail bounds for macroscopic linear statistics and, provided $n\geq 2$, a central limit theorem for both macroscopic and mesoscopic linear statistics in the bulk., Comment: Journal of the European Mathematical Society, in press

We develop a direct approach to the semiclassical asymptotics for Bergman projections in exponentially weighted spaces of holomorphic functions, with real analytic strictly plurisubharmonic weights. In particular, the approach does not rely upon the Kuranishi trick and it allows us to shorten and simplify proofs of a result due to Rouby-Sj\"ostrand-V\~u Ngoc and Deleporte, stating that in the analytic case, the amplitude of the asymptotic Bergman projection is a realization of a classical analytic symbol.

We consider semiclassical self-adjoint operators whose symbol, defined on a two-dimensional symplectic manifold, reaches a non-degenerate minimum $b_0$ on a closed curve. We derive a classical and quantum normal form which allows us, in addition to the complete integrability of the system, to obtain eigenvalue asymptotics in a window $(-\infty,b_0+\epsilon]$ for $\epsilon > 0$ independent on the semiclassical parameter. These asymptotics are obtained in two complementary settings: either a symmetry of the system under translation along the curve, or a Morse hypothesis reminiscent of Helffer-Sj\"ostrand's "miniwell" situation.

Random lasing is an intriguing phenomenon occurring in disordered structures with optical gain. In such lasers, the scattering of light provides the necessary feedback for lasing action. Because of the light scattering, the random lasing systems emit in all the directions in contrast with the directional emission of the conventional lasers. While this property can be desired in some cases, the control of the emission directionality remains required for most of the applications. Besides, it is well known that the excitation of cavity exciton-polaritons is intrinsically directional. Each wavelength (energy) of the cavity polariton, which is a superposition of an excitonic state and a cavity mode, corresponds to a well-defined propagation direction. We demonstrate in this article that coupling the emission of a 2D random laser with a cavity polaritonic resonance permits to control the direction of emission of the random laser. This results in a directional random lasing whose emission angle with respect to the microcavity axis can be tuned in a large range of angles by varying the cavity detuning. The emission angles reached experimentally in this work are 15.8$^\circ$ and 22.4$^\circ$., Comment: Article : 10 pages, 5 figures Supplementary : 11 pages, 14 figures

We prove several results of concentration for eigenfunctions in Toeplitz quantization. With mild assumptions on the regularity, we prove that eigenfunctions are $O(exp(-cN^{\delta}))$ away from the corresponding level set of the symbol, where N is the inverse semiclassical parameter and $0 < \delta < 1$ depends on the regularity. As an application, we prove a precise bound for the free energy of spin systems at high temperatures, sharpening a result of Lieb.

Exciton-polaritons, elementary excitations arising from the strong coupling regime between photons and excitons in insulators or semiconductors, represent a promising platform for studying quantum fluids of light and realizing prospective all-optical devices. Among different materials for room temperature polaritonic devices, two-dimensional (2D) layered perovskites have recently emerged as one of the promising candidates thanks to their prominent excitonic features at room temperature. Here we report on the experimental demonstration of exciton-polaritons at room temperature in resonant metasurfaces made from a subwavelength 2D lattice of perovskite pillars. These metasurfaces are obtained via spincoating, followed by crystallization of the perovskite solution in a pre-patterned glass backbone. The strong coupling regime is revealed by both angular-resolved reflectivity and photoluminescence measurements, showing anticrossing between photonic modes and the exciton resonance with a Rabi splitting in the 200 meV range. Moreover, we show that the polaritonic dispersion can be engineered by tailoring the photonic Bloch mode to which perovskite excitons are coupled. Linear, parabolic, and multi-valley polaritonic dispersions are experimentally demonstrated. All of our results are perfectly reproduced by both numerical simulations based on a rigorous coupled wave analysis and an elementary model based on a quantum theory of radiation-matter interaction. Our results suggest a new approach to study exciton-polaritons and pave the way towards large-scale and low-cost integrated polaritonic devices operating at room temperature.

We provide almost eigenfunctions for Toeplitz operators with real-analytic symbols, at the bottom of non-degenerate wells. These almost eigenfunctions follow the WKB ansatz; the error is O(exp(--cN)), where c > 0 and N $\rightarrow$ +$\infty$ is the inverse semiclassical parameter.

We provide asymptotic formulas for the Bergman projector and Berezin-Toeplitz operators on a compact K{\"a}hler manifold. These objects depend on an integer N and we study, in the limit N $\rightarrow$ +$\infty$, situations in which one can control them up to an error O(e^{-cN}) for some c > 0. We develop a calculus of Toeplitz operators with real-analytic symbols, which applies to K{\"a}hler man-ifolds with real-analytic metrics. In particular, we prove that the Bergman kernel is controlled up to O(e^{-cN}) on any real-analytic K{\"a}hler manifold as N $\rightarrow$ +$\infty$. We also prove that Toeplitz operators with analytic symbols can be composed and inverted up to O(e^{-cN}). As an application, we study eigenfunction concentration for Toeplitz operators if both the manifold and the symbol are real-analytic. In this case we prove exponential decay in the classically forbidden region.

We present an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, and products of them. The error term is exponentially small with respect to the inverse semiclassical parameter.

Hybrid halide perovskites are now considered as low-cost materials for contemporary research in photovoltaics and nanophotonics. In particular, because these materials can be solution processed, they represent a great hope for obtaining low-cost devices. While the potential of 2D layered hybrid perovskites for polaritonic devices operating at room temperature has been demonstrated in the past, the potential of the 3D perovskites has been much less explored for this particular application. Here, we report the strong exciton-photon coupling with 3D bromide hybrid perovskite. Cavity polaritons are experimentallly demonstrated from both reflectivity and photoluminescence experiments, at room temperature, in a 3$\lambda$/2 planar microcavity containing a large surface spin-coated $CH_3NH_3PbBr_3$ thin film. A microcavity quality factor of 92 was found and a large Rabi splitting of 70 meV was measured. This result paves the way to low-cost polaritonic devices operating at room temperature, potentially electrically injectable as 3D hybrid perovskites present good transport properties., Comment: 7 pages, 4 figures

We report mathematical results on the process by which quantum order by disorder takes place for spin systems. The selection rules follow the influence of several competing contributions. Moreover there is no link between quantum selection and thermal selection. We present work in the general setting as well as toy models and examples for which quantum selection has an interesting behaviour.

We measure the surface of CH$_3$NH$_3$PbI$_3$ single crystals by making use of two photon photoemission spectroscopy. Our method monitors the electronic distribution of photoexcited electrons, explicitly discriminating the initial thermalization from slower dynamical processes. The reported results disclose the fast dissipation channels of hot carriers (0.25 ps), set a upper bound to the surface induced recombination velocity ($<4000$ cm/s) and reveal the dramatic effect of shallow traps on the electrons dynamics. The picosecond localization of excited electrons in degraded CH$_3$NH$_3$PbI$_3$ samples is consistent with the progressive reduction of photoconversion efficiency in operating devices. Minimizing the density of shallow traps and solving the aging problem may boost the macroscopic efficiency of solar cells to the theoretical limit., Comment: 7 pages, 8 figures

In the semiclassical limit, it is well-known that the first eigenvector of a Toeplitz operator concentrates on the minimal set of the symbol. In this paper, we give a more precise criterion for concentration in the case where the minimal set of the symbol is a submanifold, in the spirit of the "miniwell condition" of Helffer-Sj{\"o}strand.

In the 1980s, Helffer and Sj\"ostrand examined in a series of articles the concentration of the ground state of a Schr\"odinger operator in the semiclassical limit. In a similar spirit, and using the asymptotics for the Szeg\"o kernel, we show a theorem about the localization properties of the ground state of a Toeplitz operator, when the minimal set of the symbol is a finite set of non-degenerate critical points. Under the same condition on the symbol, for any integer K we describe the first K eigenvalues of the operator.

Hybrid perovskite thin films have demonstrated impressive performance for solar energy conversion and optoelectronic applications. However, further progress will benefit from a better knowledge of the intrinsic photophysics of materials. Here, the low temperature emission properties of CH3NH3PbI3 single crystals are investigated and compared to those of thin polycrystalline films by means of steady-state and time-resolved photoluminescence spectroscopy. While the emission properties of thin films and crystals appear relatively similar at room temperature, low temperature photoluminescence spectroscopy reveals striking differences between the two materials. Single crystals photoluminescence exhibits a sharp excitonic emission at high energy, with Full Width at Half Maximum of only 5 meV, assigned to free excitonic recombination and a broad band at low energy. We analyzed the thermal evolution of the free excitonic intensity and linewidth. An excitonic binding energy of 28 meV is extracted from the quenching of the photoluminescence. We highlight a strong broadening of the emission due to LO phonon coupling. The free excitonic emission turned to be very short-lived with a sub-nanosecond dynamics, mainly induced by the fast trapping of the excitons. The free excitonic emission is completely absent of the thin films spectra, which are dominated by trap states band. The trap states energies, width and recombination dynamics present important similarities between films and crystals. These results suggest that the trap states are formed at the surface and grain interface of perovskites., Comment: 29 pages, 10 figures

Due to their high potentiality for photovoltaic applications or coherent light sources, a renewed interest in hybrid organic perovskites has emerged for few years. When they are arranged in two dimensions, these materials can be considered as hybrids quantum wells. One consequence of the unique structure of 2D hybrid organic perovskites is a huge exciton binding energy that can be tailored through chemical engineering. We present experimental investigations of the exciton nonlinearities by means of femtosecond pump-probe spectroscopy. The exciton dynamics is fitted with a bi-exponential decay with a free exciton life-time of ~100 ps. Moreover, an ultrafast intraband relaxation (< 150 fs) is also reported. Finally, the transient modification of the excitonic line is analysed through the momenta analysis and described in terms of reduction of the oscillator strength and linewidth broadening. We show that excitonic non-linearities in 2D hybrid organic perovskites share some behaviours of inorganic semiconductors despite their huge exciton binding energy.

Carbon nanotubes are quantum sources whose emission can be tuned at telecommunication wavelengths by choosing the diameter appropriately. Most applications require the smallest possible linewidth. Therefore, the study of the underlying dephasing mechanisms is of utmost interest. Here, we report on the low-temperature photoluminescence of high crystalline quality individual single-wall carbon nanotubes synthesized by laser ablation (L-SWNTs) and emitting at telecommunication wavelengths. A thorough statistical analysis of their emission spectra reveals a typical linewidth one order of magnitude narrower than that of most samples reported in the literature. The narrowing of the PL line of L-SWNTs is due to a weaker effective exciton-phonon coupling subsequent to a weaker localization of the exciton. These results suggest that exciton localization in SWNTs not only arises from interfacial effects, but that the intrinsic crystalline quality of the SWNT plays an important role., Comment: To be published in Physical Review B: Rapid Communications

Photoluminescence excitation measurements in semi-conducting carbon nanotubes show a systematic non-resonant contribution between the well known excitonic resonances. Using a global analysis method, we were able to delineate the contribution of each chiral species including its tiny non-resonant component. By comparison with the recently reported excitonic absorption cross-section on the $S_{22}$ resonance, we found a universal non-resonant absorbance which turns out to be of the order of one half of that of an equivalent graphene sheet. This value as well as the absorption line-shape in the non-resonant window is in excellent agreement with microscopic calculations based on the density matrix formalism. This non-resonant absorption of semi-conducting nanotubes is essentially frequency independent over 0.5~eV wide windows and reaches approximately the same value betweeen the $S_{11}$ and $S_{22}$ resonances or between the $S_{22}$ and $S_{33}$ resonances. In addition, the non-resonant absorption cross- section turns out to be the same for all the chiral species we measured in this study. From a practical point of view, this study puts firm basis on the sample content analysis based on photoluminescence studies by targeting specific excitation wavelengths that lead to almost uniform excitation of all the chiral species of a sample within a given diameter range.

We report on the quantum confinement of zero-dimensional polaritons in perovskite-based microcavity at room temperature. Photoluminescence of discrete polaritonic states are observed for polariton localized in symmetric sphere-like defects which are spontaneously nucleated on the top dielectric Bragg mirror. The linewidth of these confined states are found much sharper (almost one order of magnitude) than that of photonic modes in the perovskite planar microcavity. Our results show the possibility to study organic-inorganic cavity polariton in confined microstructure and suggest a fabrication method to realize integrated polaritonic devices operating at room temperature.

The variation of the optical absorption of carbon nanotubes with their geometry has been a long standing question at the heart of both metrological and applicative issues, in particular because optical spectroscopy is one of the primary tools for the assessment of the chiral species abundance of samples. Here, we tackle the chirality dependence of the optical absorption with an original method involving ultra-efficient energy transfer in porphyrin/nanotube compounds that allows uniform photo-excitation of all chiral species. We measure the absolute absorption cross-section of a wide range of semiconducting nanotubes at their S22 transition and show that it varies by up to a factor of 2.2 with the chiral angle, with type I nanotubes showing a larger absorption. In contrast, the luminescence quantum yield remains almost constant.

We report on a new, orginal and efficient method for "pi-stacking" functionalization of single wall carbon nanotubes. This method is applied to the synthesis of a high-yield light-harvesting system combining single wall carbon nanotubes and porphyrin molecules. We developed a micelle swelling technique that leads to controlled and stable complexes presenting an efficient energy transfer. We demonstrate the key role of the organic solvent in the functionalization mechanism. By swelling the micelles, the solvent helps the non water soluble porphyrins to reach the micelle core and allows a strong enhancement of the interaction between porphyrins and nanotubes. This technique opens new avenues for the functionalization of carbon nanostructures., Comment: 6 pages, 5 figures

We report on optical spectroscopy (photoluminescence and photoluminescence excitation) on two-dimensional self-organized layers of $(C_{6}H_{5}C_{2}H_{4}-NH_{3})_{2}PbI_{4}$ perovskite. Temperature and excitation power dependance of the optical spectra gives a new insight into the excitonic and phononic properties of this hybrid organic/inorganic semiconductor. In particular, exciton-phonon interaction is found to be more than one order of magnitude higher than in GaAs QWs. As a result, photoluminescence emission lines have to be interpreted in the framework of a polaron model.

Functionalization of carbon nanotubes with hydrosoluble porphyrins (TPPS) is achieved by "$\pi$-stacking". The porphyrin/nanotube interaction is studied by means of optical absorption, photoluminescence and photoluminescence excitation spectroscopies. The main absorption line of the porphyrins adsorbed on nanotubes exhibits a 120 meV red shift, which we ascribe to a flattening of the molecule in order to optimize $\pi-\pi$ interactions. The porphyrin-nanotube complex shows a strong quenching of the TPPS emission while the photoluminescence intensity of the nanotubes is enhanced when the excitation laser is in resonance with the porphyrin absorption band. This reveals an efficient excitation transfer from the TPPS to the carbon nanotube.