Investigating non-equilibrium physics and universality using two-dimensional quantum gases

不处于平衡状态的系统无处不在，但描述起来可能很复杂。尽管量子力学成功地描述了处于平衡状态的系统，但迄今为止，还没有一个通用的理论框架来解释一个封闭的多体量子系统是如何进化到这样的热化状态的。该项目研究了非平衡（NEQ）系统放松到热平衡的过程，我们称之为热化。宏观的例子包括从一杯咖啡的冷却到早期宇宙结构的出现。NEQ过程对于包括量子计算机和量子热机在内的量子系统也很重要。我们的实验技术允许在精确定义的NEQ情况下制备多体量子系统，然后以前所未有的细节水平跟踪它们向平衡的演变。我们将用来更好地理解NEQ物理的系统是一种温度为几十纳米开尔文的二维（2D）原子气体。二维系统的性质在物理学中至关重要，2016年诺贝尔物理学奖的一部分授予了Kosterlitz和Thouless，以表彰他们在二维量子系统中以他们的名字命名的相变方面的工作。当量子气体被冷却并在一定温度下变成超流体时，这种转变就会发生，这种超流体在没有摩擦的情况下流动，具有其他迷人的特性。超冷原子被困在极好控制的条件下，从而使我们能够与理论期望进行明确的定量比较。限于二维的量子系统对于研究NEQ过程特别有趣，因为涨落是量子力学的固有部分，在阻止真正的远程秩序方面起着重要作用。这种新方法将为其他二维系统（如薄膜超导体和液晶）的类似相变提供见解，量子气体通常充当二维量子物理的量子模拟器。这项提议的基石是我们最近通过联合射频（RF）和静态磁场的创新使用创造出的超冷铷原子的双阱潜力。这种技术非常适合于二维量子气体的相干分裂，因为势的形状和高度直接由应用的射频场控制，从而利用射频电子的极高精度。分裂的速率决定了沉积到系统中以产生选定的初始状态的能量。在分裂后的预定时间，两个云从双阱势中释放出来，使它们膨胀并重叠。这样就可以对物质波的相对相位进行干涉测量。通过重复测量，每个初始状态都以相同的方式准备，我们将能够确定二维平面中所有位置的量子气体相对相位对应的概率分布函数（PDF）。pdf代表了量子力学的本质，与通常监测某些观测值的期望值的时间演变相比，它允许与理论模型进行更全面的比较。这种冷原子装置作为二维系统中多体相的“量子模拟器”，从而为长期存在的研究问题提供了新的见解。

Systems that are not in equilibrium are ubiquitous but can be complex to describe. Although systems at equilibrium are described with great success by quantum mechanics there is, as yet, no general theoretical framework for how a closed many-body quantum system evolves to such thermalised states. This project investigates the process by which non-equilibrium (NEQ) systems relax towards thermal equilibrium, which we call thermalisation. Macroscopic examples range from the cooling of a cup of coffee to the emergence of structures in the early universe. NEQ processes are also important for quantum systems including quantum computers and quantum heat engines. Our experimental techniques allow many-body quantum systems to be prepared in precisely defined NEQ situations and then track their evolution towards equilibrium in unprecedented level of detail.The system that we will use to gain a better understanding of NEQ physics is a two-dimensional (2D) gas of atoms at temperatures of tens of nanokelvin. The properties of 2D systems are of central importance in physics and part of the Nobel prize for Physics (2016) was awarded to Kosterlitz and Thouless for their work on a phase transition in 2D quantum systems that is named after them. This transition occurs as the quantum gas is cooled and at a certain temperature changes into a superfluid, which flows without friction amongst other fascinating properties. The ultracold atoms are trapped in extremely well-controlled conditions thus enabling us to make definitive quantitative comparisons with theoretical expectations. Quantum systems confined to 2D are especially interesting for studying NEQ processes because the fluctuations, that are an inherent part of quantum mechanics, play a large role in preventing true long-range order. This new method will provide insights into similar phase transitions in other 2D systems such as thin-film superconductors and liquid crystals, and the quantum gas acts as a quantum simulator for 2D quantum physics in general.A cornerstone of this proposal is the double-well potential for ultracold rubidium atoms that we have created recently by an innovative use of combined radio-frequency (RF) and static magnetic fields. This technique is ideally suited for coherent splitting of a 2D quantum gas because the shape and height of the potential are controlled directly by the applied RF fields, thus exploiting the extremely high precision of RF electronics. The rate of splitting determines the energy deposited into the system to produce a chosen initial state. At a predefined time after the splitting, the two clouds are released from the double-well potential so that they expand and overlap. This permits interferometric measurements of the relative phase of the matter waves. From repeated measurements, each with the initial state prepared in the same way, we will be able to determine the probability distribution function (PDF) corresponding to the relative phase of the quantum gas for all positions in the 2D plane. PDFs represent the essence of quantum mechanics and allow a more comprehensive comparison with theoretical models than monitoring the time evolution of the expectation values of certain observables as is commonly done. This cold-atom apparatus acts as a 'quantum simulator' of many-body phases in 2D systems thus providing fresh insights relevant to long-standing research questions.