Since Witten and Kontsevich’s work, regarding the description of two-dimensional topological gravity in terms of the $\tau$-function of a solution to the KdV hierarchy, the connection between Integrable Systems and 2D Topological Field Theory is known to be a deep one.
We will introduce the fundamentals of Symplectic Field Theory (SFT), a branch of symplectic topology that studies holomorphic curves with boundaries in symplectic manifolds. The potential counting these curves is interpreted as an Hamiltonian corresponding to a Quantum Integrable System. In particular, we will consider the commuting Hamiltonians obtained from the quantisation of the dispersionless KdV hierarchy, that arise naturally in the context of SFT. A complete set of common eigenvectors of these operators is found in terms of Schur polynomials and used to compute the SFT-potential of a disk.
We will finish by providing some remarks on some more recent developments in this area, namely the case of the Quantised Toda Lattice and Double Ramification Hierarchy.

L'optomécanique s'intéresse à l’interaction entre un résonateur
mécanique et un résonateur optique. Le couplage de ces deux types de résonateurs, flexible tant dans le choix de la plateforme mécanique qu'optique, permet d'accéder à des effets physiques et des propriétés remarquables. Le champ d'étude de l'optomécanique va d'aspects aussi fondamentaux que la récente observation d'ondes gravitationnelles, aux applications en détection ultra-précise, en passant par les systèmes de conversion de fréquence et les cristaux phononiques intégrés sur silicium. Un des intérêt principal du domaine est l'obtention de résonateurs mécaniques dans leur état fondamental de vibration.

Dans ce contexte, je présenterai mes travaux sur les membranes de graphène couplées à des cavités GHz. J'introduirai le système retenu pour sonder le mouvement Brownien de la membrane de graphène, à savoir le couple graphène multi-feuillets/cavité RF. En travaillant en environnement cryogénique, nous verrons qu'il est possible de sonder les propriétés mécaniques intrinsèques de la membrane, grâce à la technique du Ring-Down. Cette technique permet de démontrer des facteurs de qualité record supérieurs à 10^6 dans ces membranes.
Je présenterai les travaux conduits parallèlement dans le but de
refroidir les membranes de graphène dans leur état fondamental de vibration (ou ground-state). Ces travaux s'appuient d'une part sur des expériences de refroidissement par pompage de la cavité hors-résonance et d'autre part sur les possibilités offertes par le squeezing du mode mécanique. Nous verrons qu'il est possible de s'approcher de l'état fondamental grâce à ces techniques, atteignant une population résiduelle de 7 phonons dans le résonateur. Par ailleurs, être proche de l'état fondamental permet la réalisation de capteurs ultra-sensibles basés sur les membranes de graphène, ce qui sera détaillé à travers les mesures de sensibilité de force et de masse.

I will give an outline of the different projects I was involved in during my previous postdoc, working with Rob Jack at the University of Bath. At first glance they may not appear to have much in common, but I hope to convince you of the common threads that connect them.
I will begin by talking about measuring amorphous order in stable glasses (produced using transition path sampling) using point-to-set correlations. This makes some interesting links between structure and dynamics in glassy states. Then I will talk about optimizing the nucleation and growth of clusters in a system of sticky spheres as a model of self assembly - how can one make the biggest crystals in the shortest time possible? I will also talk about simulating the formation of gels under the influence of gravity in the same system, with the eventual aim of comparing simulated and experimental results. Finally I will discuss some early work I have been doing to cook up a model of the kind of material that could be used to produce phase-change memory, where stable ordered and amorphous states are in competition with each other allowing lots of data to be stored in a very small physical volume.

A brief introduction is given to various kinds of topological insulators. In particular, recently discovered topological crystalline insulators PbSnSe are discussed which experience a change of trivial to nontrivial band ordering as the energy gap goes through zero as a function of temperature. Experimental evidence of their topological insulator band structure on the surface is presented.
Experimental data on the bulk electron transport near the vanishing energy gap in PbSnSe are shown. In particular, it is demonstrated that the Nernst-Ettingshausen thermoelectric effect goes through a maximum when the energy gap goes through zero. A situation is reached in which both the surface states and the bulk states are massless Dirac fermions. A theoretical description of electron transport at the vanishing energy gap encounters serious difficulties when the energy gap goes through zero and it is demonstrated how to overcome them by introducing damping. It is indicated that the presented experiments and their description have quite general applications

andau quantization has provided fascinating magnetotransport and magneto-optical phenomena in low-dimensional semiconductors. Due to progress in Terahertz (THz) techniques, high quality data on the magneto-optical effects have become available. Compared with cyclotron absorption experiments or THz photoresponse in resistivity, however, studies of the current-induced Landau-level (LL) emission are still difficult because of the requirement of ultrahigh sensitive detectors. In this talk, we briefly review THz photon counting techniques based on quantum dot (QD) detectors and show experimental results on the inter-LL radiative transition in quantum electron transport at strong magnetic fields.

Our approach for studies of LL emission is an on-chip THz photon detection scheme in which an emitter (an object: LL emitter), a photon counter (a QD) and a metal structure (that functions as a transmission or a resonator) are embedded in a single chip. We utilize a split-ring resonator for resolving photon energies of the LL emission. The energy-resolved photon-counting results indicate that, in violation of selection rules, the spin-flip LL radiative transition takes place in the spin-polarized edge channels. We will also discuss the exchange interaction and the spin-orbit interaction in the spin-polarized edge channels.

I will review the state of the art about Bethe ansatz for models without U(1) symmetry and explain my contribution in the case of models with “hidden symmetry” of rank 1. Then I will present some results related to the higher rank case by considering the toy model : the sl(3) XXX chain with a twist.

The group "Nanophotonics and quantum optics" at INSP studies the coupling between a fluorescent emitter (generally a colloidal CdSe/CdS nanocrystal) and its optical environment : metallic surface, photonic crystal, optical nano-antenna, nanocavity... I will first briefly present the group's activities and a few recent results on the coupling of nanocrystals to a "patch" nano-antenna and to optical Tamm-modes cavities. I will then detail how, by taking into account its optical environment (nature of the substrate etc), the polarization analysis of a nano-emitter can give access to its orientation or to its emission fine structure (a single linear dipole or two degenerate dipoles). We applied this method to spherical nanocrystals and to CdSe/CdS nanorods, as well as to nanoplatelets (colloidal 20x20 nm quantum wells of a few monolayers thickness). For the latter type of nanostructure, a combined measure of the radiation pattern (Fourier plane) and polarization provides especially precise information about a single emitter.