This book deals with the important developments that have recently occurred in two different research fields, laser manipulation of atoms on the one hand, non-Gaussian statistics and anomalous diffusion processes on the other hand. It turns out that fruitful exchanges of ideas and concepts have taken place between these two apparently disconnected fields. This has led to cross-fertilization of each of them, providing new physical insights into the most efficient laser cooling mechanisms as well as simple and mathematically soluble examples of anomalous random walks.
We thought that it would be useful to present in this book a detailed report of these developments. Our ambition is to try to improve the dialogue between different communities of scientists and, hopefully, to stimulate new, interesting developments. This book is therefore written as a case study accessible to the non-specialist.
Our aim is also to promote, within the atomic physics and quantum optics community, a way to approach and solve problems that is less based on exact solutions, but relies more on the identification of the physically relevant features, thus allowing one to construct simplified, idealized models and qualitative (and sometimes quantitative) solutions. This approach is of course common in statistical physics, where, often, details do not matter, and only robust global features determine the relevant physical properties. Laser cooling is an ideal case study, where the power of this methodology is clearly illustrated.