Nonlinear interferometry in Bose Einstein condensates : the effect of atom-atom interactions

The seventh lesson was devoted to the study of nonlinearities in Bose Einstein condensates, due to interactions between atoms. These interactions, linked to elastic collisions in the sample, have the effect of introducing a non-linear term into the equation describing the evolution of matter waves quite analogous to the non-linearity produced in photon propagation by an intensity-dependent refractive index (Kerr effect). But whereas the Kerr effect requires the introduction of a material medium external to the system along the photon path, condensate non-linearities are intrinsic. Atomic optics, unlike photonic optics, is therefore spontaneously non-linear. This affects the phase of matter waves. The phenomena of spreading and resurgence that we have described are present. Recent experiments have demonstrated these non-linear effects intrinsic to condensates. The possibility of using these effects to prepare and study atomic "Schrödinger cat" states was mentioned.