Spectral properties of interacting cold atoms in optical lattices

玻色爱因斯坦冷原子气体凝聚提供了一种实验工具，用于测试凝聚态理论、量子统计和量子传输理论的各种预测，具有前所未有的可控性和准确性。此外，量子光学学者现在考虑设计有限大小的多粒子系统-通过将定义良好的数量的超冷相互作用粒子加载到禁闭势中-具有凝聚相的新的(和可寻址的)特性，这些特性通常由量子统计观测来描述。在我们目前的提议中，我们希望在详细研究由完全确定的微观哈密顿量产生的有限大小的多粒子问题的谱结构的基础上，解决加载到光学晶格中的冷原子气体的从少粒子动力学到多粒子动力学的转变。我们希望研究玻色-哈伯德模型和费米-哈伯德模型的光谱，以确定在实验室观察到的特征动力学特征的光谱主干。具体地说，我们将解决(I)在倾斜光学晶格中加载BEC-S实现的多粒子Wannier Stark问题的共振结构，(Ii)玻色和非极化费米原子(及其混合物)相互作用引起的Bloch振荡的退相干，以及(Iii)物质波通过光势的电导的微观模型。

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.