Matter-wave interference in Bose Einstein condensates

The sixth lesson dealt with the study of matter waves (atomic optics). For some years now, we've been able to produce ultra-cold samples of atoms forming Bose Einstein condensates, in which a large number of atoms are all in the same wave function, with an almost macroscopic extent. These giant matter waves share many similarities with laser waves. They have very similar coherence properties. Atom optics, which is developing very actively, enables experiments in which atoms replace light-wave photons, with fascinating potential applications. The lesson recalled how these condensates were made and studied, and showed some analogies between photonic optics and "atomic optics". For this, it is convenient to place ourselves in the formalism of the second quantization, which introduces the operators of atom creation and annihilation playing in atomic optics the role that the usual operators of photon creation and annihilation play in quantum optics. We have described the atomic equivalent of quantum-optical splitters, made possible by exploiting a Josephson effect between two modes of condensed bosons. We have described the coherence of two-mode boson systems and analyzed recent condensate interference experiments.