Motivés par les expériences de pensée au coeur de la mécanique quantique puis sous la pression croissante du domaine de l’information quantique, les progrès des méthodes de fabrication, d’observation et de manipulation d’objets individuels ont fortement élargi la variété d'émetteurs de photons uniques. On sait ainsi aujourd'hui fabriquer des émetteurs individuels de taille nanométrique, suffisamment petits pour que la transition entre leurs états électroniques corresponde au rayonnement d’un dipôle unique. Les boîtes quantiques en semiconducteurs et les centres colorés du diamant en font partie.

En tant qu'objet individuel, les boîtes quantiques forment des émetteurs uniques pouvant produire des photons un par un ou en cascade. Ces photons peuvent même être rendus indiscernables, en isolant les boîtes dans des microrésonateurs optiques de volume ultime limité par la diffraction. En tant qu'ensemble, les boîtes forment un milieu à gain; et en les isolant à nouveau dans un microrésonateur optique, on réalise des lasers de dimensions submicroniques. Cette réduction des dimensions change cependant radicalement la physique qui gouverne la source laser ainsi que son rayonnement, marqué par le caractère corpusculaire de la lumière.

Les centres colorés du diamant, et en particulier les centres NV (formés par une impureté d'azote associée à une lacune électronique), sont aussi des sources de photons uniques. Outre émettre des états quantiques de la lumière, les centres NV présentent des propriétés de spin électronique qui en font un système quantique modèle à l’état solide. Depuis quelques années, il a été démontré que le spin du centre NV peut également servir de magnétomètre ultrasensible et plus récemment de thermomètre, permettant la réalisation de microscopes de champ magnétique et de gradient de température à forte résolution spatiale et grande sensibilité. Les premières réalisations montrent qu'un tel dispositif d'imagerie thermique devrait permettre d’atteindre des sensibilités autour du mK avec des résolutions spatiales de quelques dizaines à centaines de nanomètres, et ce entre 200 K et 600 K. Cette approche pourrait de fait s’avérer extrêmement intéressante pour un grand nombre d’applications. Un premier domaine potentiel d'intérêt porte sur les origines physiques des changements de lois dans le comportement thermique d'objets de taille inférieure à ou de l’ordre du micron. On peut ici mentionner à titre d'exemple la modification et le contrôle de la conductivité thermique de nanomatériaux tels que nanotubes ou graphène; ou bien la place du rayonnement de champ proche dans l’examen global des transferts thermiques. Un autre domaine d'intérêt provient de la miniaturisation des composants optoélectroniques et microélectroniques, dans lesquels la dissipation et la non-uniformité thermiques sont devenues un véritable défi. L'imagerie de points chauds ou de distribution de chaleur, pourrait contribuer aux stratégies de contrôle thermique dans de tels composants. Enfin, un dernier domaine d'intérêt tire partie de la biocompatibilité du diamant, ouvrant ainsi la voie à des études de biologie thermique à l'échelle de la cellule unique, telles que l'influence de la température sur le métabolisme des cellules.

The random packing of spherical objects has fascinated researchers for centuries. When hard or soft spheres are quenched above a sphere volume fraction of about sixty per cent, a supercooled fluid of spheres enters an amorphous solid phase. The state of matter of this phase is peculiar since it has both fluid- and solid-like attributes: it has a liquid-like structure, yet mechanically responds to an applied stress as a solid. This called "jamming” phenomenon is not only of fundamental interest but also of prime importance in materials science since it governs the elasticity and flow of many soft materials such as emulsions, particle dispersions, polymeric thickeners as well as granular materials (sand, powders, etc.). After a general introduction I will discuss experiments and concepts derived from jammed assemblies of microscale hard and soft spheres. In the first set of studies we investigate deformable particles suspended in water either consisting of oil droplets or microgel-particles that are driven into a glassy and jammed state. We probe both translational and rotational motion using confocal microscopy, spatially resolved light scattering and optical birefringence. Our results show clear evidence of spatial and temporal heterogeneities, both thermally activated and driven by applying external fields. In a second set of experiments we used jammed assemblies of spheres as templates for photonic structures. We follow a protocol based on mapping the hyperuniform point coordinates of the spheres into tessellations for disordered photonic materials design. Using direct laser writing in a polymer photoresist we succeeded in fabricating such structures with features on the submicron scale.

In this seminar I will give an introduction to integrability and the $q$KZ equation, with a focus on the integrable Temperly--Lieb loop model. The associated Temperley-Lieb algebra can be represented in graphical form, which in turn allows a graphical construction of the solutions of the $q$KZ equation.

Using this graphical construction, we derive a factorised form for a generalised sum over components of the $q$KZ solution. Specialising this sum gives the normalisation of the ground state vector of the Temperley--Lieb loop model. But in its general form there are connections to certain Razumov--Stroganov conjectures and Macdonald and Koornwinder polynomials.

The geometry of supersymmetric gauge theories hides interesting algebraic structures responsible for the integrability of the theory. In this talk I will review how quantum algebraic structures such as affine Kac-Moody algebras, quantum affine groups, W-algebras and their relatives appear in the context of the supersymmetric gauge theories.

Horaire Exceptionnel - 10h

Surface-enhanced Raman scattering (SERS) describes the giant enhancement of the Raman cross section close to a metal surface. SERS can detect single molecules by optical spectroscopy. Its variant, tip-enhanced scattering (TERS) increases the resolution of Raman imaging down to the molecular limit. Despite the wide-spread use of plasmon-enhanced Raman spectroscopy in imaging and materials characterization its fundamental principles remain debated. The dominant mechanism for SERS is thought to be plasmonic enhancement; the large Raman cross section is explained as an enhancement by the localized surface plasmons of metal nanoparticles.
Here we present our results on plasmon-enhanced Raman scattering in graphene and carbon nanotubes. The enhancement is induced by the plasmons of well-controlled lithographically prepared gold nanodimers. Mechanically exfoliated graphene is deposited in a dry transfer process, whereas carbon nanotubes are placed by dieelectrophoresis. This setup allows to study the fundamental of SERS. We present results of the polarization and wavelength-dependence of plasmonic enhancement. The enhancement is extremely strongly localized in space (10 nm) and frequency (15 meV). We propose a new theory of SERS, where the plasmon forms an integral part of a higher-order Raman process and discuss its consequences for SERS in molecules and artificial nanostructures.

Quantum mechanics is the theory that describes the behavior of matter at the nano scale.
Though routinely applied to the electrons in a molecular system, quantum theory is generally not applied to the atomic nuclei (except for very simple molecules), because such “exact quantum dynamics” (EQD) calculations are regarded to be too difficult. This is due to the “curse of dimensionality”: the computational (CPU) cost scales exponentially with system dimensionality. Nevertheless, quantum dynamical effects are known to be important in a wide range of molecular applications, and must therefore be accounted for at least approximately, if sensible numerical simulations are to be performed.

In this presentation, we will discuss powerful new EQD methods developed in recent years, as well as applications. The methods are mostly based on so-called “quantum trajectories”—similar to those used in Bohmian mechanics, but arising from a completely new formulation of quantum mechanics for which the wavefunction Ψ(t, x) plays no role. Instead, quantum states are represented solely as ensembles of real-valued probabilistic trajectories, x(t, C), where C is a trajectory label. The applications discussed span a broad range, from models to highly accurate treatments of real molecules, and will be drawn from the following: (1) wavepacket barrier scattering; (2) extremely deep tunneling; (3) coupled 2D model chemical reaction system; (4) collinear H+H2 reaction; (5) hydrogen adsorbate dynamics on carbon nanotubes; (6) Fluxional H atom scrambling dynamics in Fe(H)2(H2)(PEtPh2)3 coordination complex.

In a point pattern, let the variance associated with the number of points contained in a spherical window of radius $R$ be denoted by $\sigma^2(R)$. Hyperuniform point patterns in $d$ dimensions do not possess infinite-wavelength fluctuations or, equivalently, possess a number variance $\sigma^2(R)$ that grows more slowly than the window volume, i.e., $R^d$, and thus the corresponding static structure factor $S(k)$ vanishes as $k \to 0$. Hyperuniform systems include all infinite periodic structures, aperiodic quasicrystals, and some special disordered systems. Previous investigations showed that the characteristic small-wavelength scaling of the structure factor and the number variance for large $R$ in hyperuniform systems can be thought of as a useful tool to rank order systems according to the degree to which large-scale density fluctuations are suppressed. In this talk, we investigate the hyperuniformity in one- and two-dimensional quasicrystals with a variety of different scaling factors and rotational symmetries. First, we deliver a proof of the hyperuniformity of quasicrystals. We further study how the small-wavelength scaling and the number variance depends on the intrinsic properties of the quasicrystal such as incommensurate length scales. We find that, unlike crystals, quasicrystals' small-wavelength scattering behavior crucially depends on the dimension. We compare these results to a number of different periodic systems as well as disordered hyperuniform systems.