Phase Transitions and Non-equilibrium Dynamics in Homogeneous Quantum Gases

原子气体冷却到绝对零度以上不到百万分之一度，为量子力学效应的基础研究提供了灵活的实验系统。特别是，它们为多体现象的理论提供了极好的试验平台，例如玻色-爱因斯坦凝聚和超流性，这些现象是由许多相互作用粒子的集体行为引起的。在过去的二十年里，超冷原子气体的多体物理研究非常成功。由此产生的对量子力学基本原理的更好理解也有望导致许多实际应用，包括开发新材料，导航仪器和量子信息处理平台。对多体物理学的完整理解是这种发展所必需的，必须包括平衡和非平衡现象，在后一方面，超冷原子气体提供了一些重要的实验优势。传统上，“传统”多体系统（如液氦和固态物质）与超冷气体之间的一个重要区别是，前者通常是空间均匀的，而后者是在碗状谐波阱中产生的。这种差异有时可以使用所谓的局部密度近似（LDA）来解决，该近似假设气体密度在空间中缓慢变化。然而，对于一些非常重要的问题的研究，这是一个严重的障碍。特别是，LDA在接近不同物质状态之间的相变时发生分解，其中粒子在非常大的距离上变得相关，并且还出现了一些最有趣的非平衡效应。最近，我们的小组在超冷原子领域取得了重大突破，在一个基本上均匀的光箱阱的捕获势中产生了第一个量子气体。这使得与其他多体系统和理论计算的联系更加紧密，并开辟了全新的研究可能性。它已经导致了非平衡多体物理学研究的一个重要进展，即迄今为止对连续相变动力学的Kibble-Zurek理论的最直接确认，其影响深远，可以理解早期宇宙中大型结构的形成。在本奖学金下，我们将专注于充分利用这些令人兴奋的新发展。我们将在具有动态可调相互作用的均匀玻色气体中对非平衡现象进行全面研究，并将与法国学院和麻省理工学院的其他两个国际领先小组合作，将这些研究扩展到低维系统和费米气体。这将巩固英国在均匀量子气体新兴领域的领导地位，并更普遍地提高英国在竞争激烈的超冷原子领域的地位。

Atomic gases cooled to less than a millionth of a degree above absolute zero temperature offer flexible experimental systems for fundamental studies of quantum mechanical effects. In particular they offer excellent test-beds for theories of many-body phenomena, such as Bose-Einstein condensation and superfluidity, which arise from the collective behaviour of many interacting particles. Over the past two decades, studies of many-body physics with ultracold atomic gases have been very successful. The resulting improved understanding of the fundamental principles of quantum mechanics is promising to also lead to many practical applications, including the development of novel materials, navigation instruments, and platforms for quantum information processing. A complete understanding of many-body physics, necessary for such developments, must include both equilibrium and non-equilibrium phenomena, and in the latter respect ultracold atomic gases offer some significant experimental advantages. Specifically they feature relatively long characteristic timescales (milliseconds to seconds), which allow for time-resolved studies of non-equilibrium processes.Traditionally, an important difference between "conventional" many-body systems, such as liquid helium and solid-state materials, and ultracold gases has been that the former are usually spatially uniform, while the latter were produced in bowl-like harmonic traps. This difference can sometimes be addressed using the so-called local density approximation (LDA), which assumes that the gas density varies slowly in space. However, for studies of some very important problems this is a serious hindrance. In particular, LDA breaks down close to phase transitions between different states of matter, where the particles become correlated over very large distances, and where some of the most interesting non-equilibrium effects also emerge. Recently, our group has made a major breakthrough in the field of ultracold atoms by creating first quantum gases in an essentially uniform trapping potential of an optical-box trap. This allows for closer connections with both other many-body systems and the theoretical calculations, and has opened up completely new research possibilities. It has already led to an important advance in the studies of non-equilibrium many-body physics, namely the most direct confirmation so far of the Kibble-Zurek theory of the dynamics of continuous phase transitions, which has implications as far reaching as understanding the formation of large structures in the early universe.Under this Fellowship we will focus on fully capitalising on these exciting new developments. We will perform a comprehensive study of non-equilibrium phenomena in a homogeneous Bose gas with dynamically tuneable interactions, and will also collaborate with two other internationally leading groups, at College de France and MIT, to extend these studies to low-dimensional systems and Fermi gases. This will cement the UK's leadership in the emerging field of homogeneous quantum gases and more generally enhance the UK's position in the highly competitive field of ultracold atoms.