Spectral properties of interacting cold atoms in optical lattices

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Bose Einstein Condensates of cold atomic gases provide an experimental tool for testing various predictions of condensed matter theory, quantum statistics, and quantum transport theory, with unpreceded control and accuracy. Furthermore, quantum opticians now contemplate to engineer many-particle systems of finite size - by loading a well defined number of ultracold interacting particles into confining potentials - with emerging (and addressable) characteristic properties of the condensed phase, which typically are described by quantum statistical observables. In our present proposal, we want to address the transition from few- to many-particle dynamics for cold atomic gases loaded into optical lattices, on the basis of a detailed study of the spectral structure of such finite size many-particle problems, generated by perfectly deterministic microscopic Hamiltonians. We wish to investigate the spectrum of the Bose Hubbard and of the Fermi Hubbard model, in order to identify the spectral backbone of characteristic dynamical features observed in the laboratory. Specifically, we will address (i) the resonance structure of the many-particle Wannier Stark problem realized with BEC¿s loaded into tilted optical lattices, (ii) the interaction induced decoherence of Bloch oscillations for Bose and nonpolarized Fermi atoms (and mixtures thereof), and (iii) microscopic models for the conductivity of matter waves across optical potentials.