A case study is a lecture on three hours only aiming is to tell the complete “story” of a quantum device or a quantum effect from the discovery or realisation to today’s impact on the scientific community and even to society. The challenge is to be exhaustive within the time limit, i.e. to give the theoretical basis, describe the quantum nature of the effect and explain how it is possible to measure it.

A few examples to give you an idea of what it is about are: Superconducting Quantum Interference Device (SQUID), single-photon detection, a concrete example of light trapping (atoms, dielectric spheres, etc.), the Aharonov-Bohm effect, quantum cascade lasers, ...

The aim is to illustrate a concrete case that demonstrates the quantum effect and makes it visible, bearing in mind that the lecture has to be adapted for the knowledge of M2 students.

Alexandru Petrescu, Pierre Rouchon

Can the whole not merely be the sum of its parts? How do collective patterns appear?
Could three molecules of water form ice?
Could higher-level abilities be created from interacting AI agents?

The notion of complexity pertains to systems in which somewhat unexpected properties emerge from the interplay of a sufficiently large number of  entities — be they particles, living cells, artificial neurons, organisms, people, abtract agents... or even a mixture of some (or all!) of these.

Statistical physics has been the first branch of science to try and model in a mathematical manner such systems, focusing especially on the subtle and often elusive passage from the micro/individual level to the macro/collective level. This lecture course explores further how the mindset of statistical physics can provide fertile ground for the analysis and modelling of complexity — including across disciplinary boundaries.

The main goal of the course is to study the light-matter interaction at the fundamental level where one two-level system interacts with a single mode of the electromagnetic field. 

The lecture will first present the fundamental concept of cavity quantum electrodynamics (Jaynes–Cummings model, resonant and dispersive interaction, Schrödinger cat states of light) and then moves to the more recent developments of circuit QED.