Nonlinear matter wave optics: Experiments on nonlinear quantum dynamics in double-well and periodic potentials

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Bose Einstein condensates are model systems for the investigation of nonlinear wave dynamics. This new experimental system allows to gain new insight into phenomena already known from nonlinear photon optics, since the precision of preparation and detection of interacting matter waves in atom optics is very advanced. Also new physics is anticipated since the interaction strength between atoms is much stronger than the Kerr nonlinearity for photons. Thus nonlinearities become already important for few atoms, which allows the generation of nonlinear quantum states. Our group has the expertise in the reliable production of small condensates with approximately 1000 atoms, which is the crucial prerequisite to investigate onedimensional nonlinear physics. In this proposal we put forward the idea to extend our BEC machine in order to prepare more stable double-well and manywell potentials in the weak link regime. Another major improvement will be the implementation of a high precision lens very close to the condensate. This will be used on the one hand to realize phaseimprinting techniques with laser beams on a scale smaller than individual wells of the designed potentials and combined with Raman-transitions to internal state preparation on a similar scale. On the other hand this opens up a new imaging resolution for condensates allowing for a direct observation of the ongoing physics in each individual well.