Semiclassical limit Bose-Einstein condensate dynamics

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Ultracold Bose gases have proven to be an ideal experimental test bed for many different aspects of physics. Furthermore the theoretical description of weakly interacting Bose gases in designed time-spatial dependent potentials is very challenging. In this proposal we want to follow both routes in close collaboration between theory and experiment. In the experimental part we will utilize ultracold gases for the exploration of new effective ħ regimes where especially the semiclassical limit seems for the first time accessible. As one of the first examples we will explore the possibilities of the realization of a single particle classical Hamiltonian ratchet, employing the flexible design of temporal and spatial potentials and the strong localization in phase space due to the very low temperature. In contrast to the experiments performed so far the new systems allows the realization of driven periodic potentials with long wavelengths leading to small effective ħ values. The quantum gas system also allows the exploration of the semiclassical limit in a different way, by identifying the meanfield treatment as the classical counterpart to the full quantum mechanical many body description. In this context the effective ħ scales inversely with the particle number which can be changed experimentally over few orders of magnitude offering a unique system. Specifically we will explore driven dynamics of Bose-Einstein condensates in double and many well systems, where meanfield as well as certain many particle aspects are accessible experimentally. Theoretically we will develop different effective descriptions which will be tested against experimental results but also to exact solutions of the corresponding few particle problem.