Construction d'une nouvelle expérience pour l'étude de gaz quantiques dégénérés des réseaux optiques, et étude d'un système d'imagerie super-résolution

摘要

For some time now, theoretical physicists in condensed matter face a majorproblem: the computing power needed to numerically simulate and study some interactingmany-body systems is insufficient. As the control and use of ultracold atomic systems hasexperimented a significant development in recent years, an alternative to this problem is to usecold atoms trapped in optical lattices as a quantum simulator. Indeed, the physics of electronsmoving on a crystalline structure of a solid, and the one of trapped atoms in optical lattices areboth described by the same model, the Fermi-Hubbard model, which is a simplifiedrepresentation of fermions moving on a periodic lattice. The quantum simulators can thusreproduce the electrical properties of materials such as conductivity or insulating behavior, andpotentially also the magnetic ones such as antiferromagnetism.The AUFRONS experiment, in which I worked during my PhD, aims at building a quantumsimulator based on cooled atoms of 87Rb and 40K trapped in near field nanostructured opticalpotentials. In order to detect the atom distribution at such small distances, we have developedan innovative imaging technique for getting around the diffraction limit. This imaging systemcould potentially allow us to detect single-site trapped atoms in a sub-wavelength lattice.In this thesis, I introduce the work I have done for building the AUFRONS experiment, as wellas the feasability study that I did for the super-resolution imaging technique.