Predictions on the transverse momentum spectra for charged particle production at LHC-energies from a two component model

Transverse momentum spectra, $d^2\sigma/(d\eta dp_T^2)$, of charged hadron production in $pp$-collisions are considered in terms of a recently introduced two component model. The shapes of the particle distributions vary as a function of c.m.s. energy in the collision and the measured pseudorapidity interval. In order to extract predictions on the double-differential cross-sections $d^2\sigma/(d\eta dp_T^2)$ of hadron production for future LHC-measurements the different sets of available experimental data have been used in this study.Comment: 5 pages, 7 plot

Real-space observation of vibrational strong coupling between propagating phonon polaritons and organic molecules

Phonon polaritons (PPs) in van der Waals (vdW) materials can strongly enhance light-matter interactions at mid-infrared frequencies, owing to their extreme infrared field confinement and long lifetimes. PPs thus bear potential for achieving vibrational strong coupling (VSC) with molecules. Although the onset of VSC has recently been observed spectroscopically with PP nanoresonators, no experiments so far have resolved VSC in real space and with propagating modes in unstructured layers. Here, we demonstrate by real-space nanoimaging that VSC can be achieved between propagating PPs in thin vdW crystals (specifically h-BN) and molecular vibrations in adjacent thin molecular layers. To that end, we performed near-field polariton interferometry, showing that VSC leads to the formation of a propagating hybrid mode with a pronounced anti-crossing region in its dispersion, in which propagation with negative group velocity is found. Numerical calculations predict VSC for nanometer-thin molecular layers and PPs in few-layer vdW materials, which could make propagating PPs a promising platform for ultra-sensitive on-chip spectroscopy and strong coupling experiments

Remote near-field spectroscopy of vibrational strong coupling between organic molecules and phononic nanoresonators

Vibrational strong coupling (VSC) promises ultrasensitive IR spectroscopy and modification of material properties. Here, nanoscale mapping of VSC between organic molecules and individual IR nanoresonators is achieved by remote near-field spectroscopy. Phonon polariton (PhP) nanoresonators can dramatically enhance the coupling of molecular vibrations and infrared light, enabling ultrasensitive spectroscopies and strong coupling with minute amounts of matter. So far, this coupling and the resulting localized hybrid polariton modes have been studied only by far-field spectroscopy, preventing access to modal near-field patterns and dark modes, which could further our fundamental understanding of nanoscale vibrational strong coupling (VSC). Here we use infrared near-field spectroscopy to study the coupling between the localized modes of PhP nanoresonators made of h-BN and molecular vibrations. For a most direct probing of the resonator-molecule coupling, we avoid the direct near-field interaction between tip and molecules by probing the molecule-free part of partially molecule-covered nanoresonators, which we refer to as remote near-field probing. We obtain spatially and spectrally resolved maps of the hybrid polariton modes, as well as the corresponding coupling strengths, demonstrating VSC on a single PhP nanoresonator level. Our work paves the way for near-field spectroscopy of VSC phenomena not accessible by conventional techniques.This work was supported by the MCIN/AEI/10.13039/501100011033 under the María de Maeztu Units of Excellence Program (CEX2020-001038-M) and the Projects RTI2018-094830-B-100, PID2021-123949OB-I00, PID2019-107432GB-I00 and PID2021-122511OB-I00, as well as by the Graphene Flagship (GrapheneCore3, No. 881603). J.L. and J.H.E. are grateful for support from the Office of Naval Research (Award No. N00014-20-1-2474), for the BN crystal growth. S.V. acknowledges financial support by the Comunidad de Madrid through the Atracción de Talento program (grant no. 2020-T1/IND-20041). C.M.-E., R.E., and J.A. received funding from grant no. IT 1526-22 from the Basque Government for consolidated groups of the Basque University

Infrared permittivity of the biaxial van der Waals semiconductor α\alpha-MoO3_3 from near- and far-field correlative studies

The biaxial van der Waals semiconductor $\alpha$-phase molybdenum trioxide ($\alpha$-MoO$_3$) has recently received significant attention due to its ability to support highly anisotropic phonon polaritons (PhPs) -infrared (IR) light coupled to lattice vibrations in polar materials-, offering an unprecedented platform for controlling the flow of energy at the nanoscale. However, to fully exploit the extraordinary IR response of this material, an accurate dielectric function is required. Here, we report the accurate IR dielectric function of $\alpha$-MoO$_3$ by modelling far-field, polarized IR reflectance spectra acquired on a single thick flake of this material. Unique to our work, the far-field model is refined by contrasting the experimental dispersion and damping of PhPs, revealed by polariton interferometry using scattering-type scanning near-field optical microscopy (s-SNOM) on thin flakes of $\alpha$-MoO$_3$, with analytical and transfer-matrix calculations, as well as full-wave simulations. Through these correlative efforts, exceptional quantitative agreement is attained to both far- and near-field properties for multiple flakes, thus providing strong verification of the accuracy of our model, while offering a novel approach to extracting dielectric functions of nanomaterials, usually too small or inhomogeneous for establishing accurate models only from standard far-field methods. In addition, by employing density functional theory (DFT), we provide insights into the various vibrational states dictating our dielectric function model and the intriguing optical properties of $\alpha$-MoO$_3$

Real-space observation of vibrational strong coupling between propagating phonon polaritons and organic molecules

Phonon polaritons in van der Waals materials can strongly enhance light–matter interactions at mid-infrared frequencies, owing to their extreme field confinement and long lifetimes1,2,3,4,5,6,7. Phonon polaritons thus bear potential for vibrational strong coupling with molecules. Although the onset of vibrational strong coupling was observed spectroscopically with phonon-polariton nanoresonators8, no experiments have resolved vibrational strong coupling in real space and with propagating modes. Here we demonstrate by nanoimaging that vibrational strong coupling can be achieved between propagating phonon polaritons in thin van der Waals crystals (hexagonal boron nitride) and molecular vibrations in adjacent thin molecular layers. We performed near-field polariton interferometry, showing that vibrational strong coupling leads to the formation of a propagating hybrid mode with a pronounced anti-crossing region in its dispersion, in which propagation with negative group velocity is found. Numerical calculations predict vibrational strong coupling for nanometre-thin molecular layers and phonon polaritons in few-layer van der Waals materials, which could make propagating phonon polaritons a promising platform for ultrasensitive on-chip spectroscopy and strong-coupling experiments.We acknowledge financial support from the Spanish Ministry of Science, Innovation and Universities (national projects MAT2017-88358-C3, RTI2018-094830-B-100, RTI2018-094861-B-100, and the project MDM-2016-0618 of the Maria de Maeztu Units of Excellence Program), the Basque Government (grant numbers IT1164-19 and PIBA-2020-1-0014) and the European Union’s Horizon 2020 research and innovation programme under the Graphene Flagship (grant agreement numbers 785219 and 881603, GrapheneCore2 and GrapheneCore3). F. Calavelle acknowledges support from the European Union H2020 under the Marie Skłodowska-Curie Actions (766025-QuESTech). J.T.-G. acknowledges support through the Severo Ochoa Program from the Government of the Principality of Asturias (number PA-18-PF-BP17-126). P.A.-G. acknowledges support from the European Research Council under starting grant number 715496, 2DNANOPTICA. Further, support from the Materials Engineering and Processing program of the National Science Foundation, award number CMMI 1538127 for h-BN crystal growth is greatly appreciated.Peer reviewe

Planar refraction and lensing of highly confined polaritons in anisotropic media

Refraction between isotropic media is characterized by light bending towards the normal to the boundary when passing from a low- to a high-refractive-index medium. However, refraction between anisotropic media is a more exotic phenomenon which remains barely investigated, particularly at the nanoscale. Here, we visualize and comprehensively study the general case of refraction of electromagnetic waves between two strongly anisotropic (hyperbolic) media, and we do it with the use of nanoscale-confined polaritons in a natural medium: α-MoO3. The refracted polaritons exhibit non-intuitive directions of propagation as they traverse planar nanoprisms, enabling to unveil an exotic optical effect: bending-free refraction. Furthermore, we develop an in-plane refractive hyperlens, yielding foci as small as λp/6, being λp the polariton wavelength (λ0/50 compared to the wavelength of free-space light). Our results set the grounds for planar nano-optics in strongly anisotropic media, with potential for effective control of the flow of energy at the nanoscale.G.Á.-P. and J.T.-G. acknowledge support through the Severo Ochoa Program from the Government of the Principality of Asturias (nos. PA-20-PF-BP19-053 and PA-18-PF-BP17-126, respectively). S.X. acknowledges the support from Independent Research Fund Denmark (Project No. 9041-00333B). B.C. acknowledges the support from VILLUM FONDEN (No. 00027987). The Center for Nanostructured Graphene is sponsored by the Danish National Research Foundation (Project No. DNRF103.) K.V.V. and V.S.V. gratefully acknowledge the financial support from the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-15-2021-606). J.M.-S. acknowledges financial support through the Ramón y Cajal Program from the Government of Spain (RYC2018-026196-I). A.Y.N. and J.I.M. acknowledge the Spanish Ministry of Science, Innovation and Universities (national projects MAT201788358-C3-3-R and PID2019-104604RB/AEI/10.13039/501100011033). R.H. acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities (national project RTI2018-094830-B-100 and the project MDM-2016-0618 of the Marie de Maeztu Units of Excellence Program) and the Basque Government (grant No. IT1164-19). A.Y.N. also acknowledges the Basque Department of Education (grant no. PIBA-2020-1-0014). P.A.-G. acknowledges support from the European Research Council under starting grant no. 715496, 2DNANOPTICA and the Spanish Ministry of Science and Innovation (State Plan for Scientific and Technical Research and Innovation grant number PID2019-111156GB-I00).Peer reviewe

Cómo manipular nanoluz en varias frecuencias

En este estudio también han participado científicos de otros centros nacionales (DIPC, CIC nanoGUNE y la Universidad del País Vasco) e internacionales (Academia de Ciencias de China, Universidad Case Western Reserve de EE UU, Instituto Tecnológico de Austria, Centro de Materiales de París y Universidad de Tokio).Científicos de la Universidad de Oviedo y el Centro de Investigación en Nanomateriales y Nanotecnología han descubierto un método para controlar la frecuencia de la luz en la nanoescala intercalando átomos de sodio en los llamados materiales de van der Waals. El avance se podría aplicar en tecnologías de la información y sensores biológicos de alta sensibilidad.Peer reviewe

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis