Since the first observation of a Bose Einstein Condensate (BEC) with neutral atoms in 1995, the field of trapping and cooling atoms has developed dramatically. The Nobel Prize of 2001 has awarded the pioneering works on realisation of BEC, consisting of a sudden macroscopic occupation of a single quantum state. Nowadays many properties of degenerate atomic gases have been investigated with success. The recent production of vortices in BEC is one of the spectacular examples of the coherence properties in this new state of matter. Dark and bright solutions, representing another type of spectacular topological defects has also been experimentally observed. The recent formation of a Fermi sea opens a way towards the observation of the BCS transition in atomic gases.
This is far from what can be reached with this new state off matter. Indeed, as the invention of LASER has induced a revolution in optics, the production of coherent matter waves is the milestone for a revolution in atom optics. Several prospective applications are under study, while others are already within reach. Among them are: atomic waves guiding, "integrated" atom optics, "atom LASER", Quantum Information Processing, and many others. Furthermore, from a fundamental point of view the recent observation of the Mott-insulator transition in an optical lattice opens the door fruitful links between this field and condensed matter. In this respect, cold-trapped atoms play a role of a model system for condensed matter physics (the expected observation of the Kosterlitz-Thouless transition and of 1/2-anyons in a two-dimensional Bose gas also finely illustrate this idea). The prominent common feature of all these challenging tasks is their tight link to the field of degenerate trapped Atoms In Low Dimensions.
Thus training of a generation of young scientists in low dimensional atomic physics and intense scientific exchanges are vitally important and quite urgent. The school "Atoms In low Dimensions" is designed to fulfil this demand. It composed of pedagogical theoretical lectures, including an overview of the state-of-the-art and forthcoming challenges in 1D and 2D, new theoretical approaches, the case of optical lattices and links with condensed matter physics. These lectures will be completed by research seminars.