Directed transport within Hamiltonian dynamics: From theory to cold atoms experiments

这个项目的目的是详细研究消失耗散(哈密顿输运)极限附近的产生条件、机制和定向输运的控制。这项任务将在经典和量子体制下进行。光学晶格中超冷原子的实验操作的现代进展构成了主题研究的一个令人兴奋的领域，因为这些系统在量子和经典哈密顿动力学之间建立了直接的联系。因此，我们计划的项目是解决哈密顿混沌、非平衡(量子)热力学和量子光学之间的交叉学科。在项目的第一部分，我们计划阐明经典相空间结构在量子演化中的作用。我们要解决的具体问题是，由于潜在的哈密顿混合相空间，量子动力学的新输运模式如何出现，以及这些模式如何建设性地用于新的冷原子操纵方案。项目的第二部分致力于研究棘轮系统在热浴和/或不同单棘轮之间的协同作用形式的退相环境下的定向输运机制。这里的目标是研究退相干在当前的纠偏过程中的作用，在半经典区域和量子区域(耦合量子棘轮，带有玻色-爱因斯坦凝聚体的棘轮)。

This project is aimed at a detailed study of the conditions of emergence, the mechanisms and the control of directed transport at/near the limit of vanishing dissipation (Hamiltonian transport). This task will be undertaken, both in the classical and quantum regimes. Modern progress in the experimental manipulation of ultra-cold atoms in optical lattices constitute an exciting field of topical research, inasmuch as these systems create a direct link between quantum and classical Hamiltonian dynamics. Thus, our planned project is interdisciplinary being settled at the borderline of Hamiltonian chaos, non.equilibrium (quantum)-thermodynamics and quantum optics.In a first part of the project, we plan to elucidate the role of the classical phase space structure in quantum evolution. The specific problem we want to address, is how new transport modes of quantum dynamics may arise due to underlying Hamiltonian mixed phase space, and how these modes can constructively put to use for new schemes of cold-atom manipulations.The second part of the project is devoted to the study of directed transport mechanisms in the case when a ratchet system is subjected to a dephasing environment in the form of heat bath and/or cooperative interactions among different single ratchets. The goal here is to study the role of decoherence in the current rectification processes both, in the semi-classical regime and the quantum regime (coupled quantum ratchets, ratchet with Bose-Einstein condensates).