Quantum dynamics of ultracold atomic gases far from equilibrium

原子物理学在过去的几十年里发生了革命性的变化，特别是通过现代冷却和捕获技术的出现。这一演变的亮点是制备量子简并的超冷原子气体，即玻色-爱因斯坦凝聚体或简并费米气体。原子陷阱的几何形状几乎可以随意改变，并且可以在非常快的时间尺度上改变。有了这一点，以及通过外部电磁场诱导的强大的原子间作用力，原子气体可以远远脱离平衡。虽然超冷原子气体中的许多现象允许对固态物理学中的对应现象进行补充研究，但与固体中的电子气体相比，研究短时间和中时间尺度上的远离平衡的动力学是可能的。关于这一动态的理论仍处于起步阶段。本申请中概述的项目旨在超越标准动态量子场理论近似，后者通常需要较弱的原子间作用力。基于作用功能技术的最新、最先进的量子场理论程序将扩展到捕获的超冷原子气体。其目的是使这些方法能够进行实验验证，这在物理学的任何其他领域都是不可能的。这种精确的实验验证对重离子碰撞或宇宙学等其他领域具有重要的潜在影响，这些领域需要非平衡方法，但实验验证要困难得多。这些项目的重点是一维陷阱和光学晶格中的动力学，超冷气体中量子简并相的形成，以及费米气体中从分子凝聚到库珀对超流体的动力学。这些关键现象具有重要的潜在应用，例如在量子信息技术、新时间标准的定义以及原子和分子物理中的精确测量方面。

Atomic physics has been revolutionized during the past decades, especially through the advent of modern cooling an trapping technologies. Highlights of this evolution are the preparation of quantum-degenerate ultracold atomic gases, i.e., of Bose-Einstein condensates or degenerate Fermi gases. The geometry of the atom traps can be varied almost at will and on very fast time scales. With this, as well as through strong interatomic forces induced by external electromagnetic fields, the atom gases can be brought far out of equilibrium. While many phenomena in ultracold atomic gases allow for complementary studies of their counterpart in solid state physics, with this, as compared to electron gases in solids, studies of the far-from-equilibrium dynamics over short and intermediate time scales are possible. The theory of this dynamics remains still in its beginnings. The projects outlined in this application aim at progressing beyond standard dynamical quantum field theoretical approximations, which in general require weak interatomic forces. Novel, most advanced quantum-field theoretical procedures on the basis of action-functional techniques will be extended for trapped ultracold atomic gases. The aim is to make these methods accessible to experimental verification, which has not been possible in any other field in physics. Such a precise experimental verification has important potential impact on other areas like heavy ion collisions or cosmology, where non-equilibrium methods are needed and much more difficult to check experimentally. The projects focus on the dynamics in one-dimensional traps and optical lattices, the formation of quantum-degenerate phases in ultracold gases, as well as the dynamics of the transition from a molecular condensate to a superfluid of Cooper pairs in a Fermi gas. These key phenomena have important potential applications, e.g., in quantum information technology, for the definition of new time standards, and for precision measurements in atomic and molecular physics.