Bose-Einstein condensation and the physics of cold atom collisions

In the second lesson, we presented an introduction to the physics of ultra-cold atoms. The properties of radiative forces (resonant and dispersive) were recalled, as well as the principles of optical manipulation of cold atoms. A qualitative description of evaporative cooling and Bose Einstein condensation was presented. The second part of the lesson was devoted to low-energy atomic collisions in degenerate quantum gases. After recalling the essential ideas of collision theory and the properties of scattering partial-wave development, we characterized low-energy atomic collisions by the scattering length in the S-wave. We physically interpreted this length and quantitatively studied its dependence on the shape of the inter-atomic potential. The notion of effective contact potential was introduced and the concept of mean field for the description of condensates was presented. The limiting cases of small and large condensates were discussed. The phenomenon of Feshbach resonance, which enables the diffusion length to be varied continuously and in a controlled way, and even to change its sign, was briefly presented.