Dynamik ultrakalter Quantengase

Modern quantum and atom-optical experiments allow for an unprecedented control of microscopic degrees of freedom, not just in the initialization but also in the dynamical evolution of quantum states. This talk focuses on the dynamics of ultracold bosons in optical lattice structures. As a paradigm, we report on experimental as well as theoretical results on the interband transport in a tilted lattice, i.e., a realization of the famous Wannier-Stark problem. An extended Bose-Hubbard model is presented for two coupled energy bands. For reasonable lattice sizes, this model gives access to the full quantum spectrum, which allows us a good characterization of ``horizontal'' (spatially) and ``vertical'' (energetic) quantum transport. For specific parameters, resonant tunnelling between the bands can be exploited to map the original model onto a much simpler effective spin Hamiltonian. We conclude with general perspectives on future directions of our study of strongly correlated bosons in lattice structures.