Descriptif

This set of lectures is an introduction to the modern physics of ultracold atoms and to the notion of quantum simulators. It involves notions of quantum physics, statistical physics, condensed matter physics and atomic physics. In the first half of the course we describe a many-body ensemble of quantum particles, i.e. bosons or fermions and derive the microscopic theory of atomic Bose-Einstein condensates in the presence of interactions. In doing so we introduce several key notions: quantum statistics, atom scattering, second-quantization, superfluidity, etc. In the second half of the course, we discuss the physics of atoms in optical lattices. This leads us to introduce the concept of quantum phase transition and illustrate the idea of quantum simulation with a simple case. The last lecture is devoted to a recently emerged topic in ultracold atoms.