Investigation of universal non-equilibrium dynamics using coupled 2-D quantum systems

不平衡的系统是普遍存在的，但描述起来可能很复杂。平衡态的系统被统计力学描述得非常成功，但是对于封闭的多体量子系统如何进化到这种热态，还没有通用的理论框架。例子从一杯咖啡的冷却到早期宇宙中结构的出现。非平衡（NEQ）过程对于包括量子计算机（诸如基于超导量子比特的那些）的量子系统也是重要的。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化。我们将用来更好地理解NEQ物理的系统是一个温度为数十纳凯的二维（2D）原子气体。2D系统的性质在物理学中具有核心重要性，2016年诺贝尔物理学奖的一部分授予了Kosterlitz和Kosterlitz，以表彰他们在2D系统中的相变方面的工作，该相变以他们的名字命名，Berezinskiii-Kosterlitz-Kosterlitz-Kosterless（BKT）转变。这种转变发生在二维量子气体冷却时，在一定的温度下，它变成了一种超流体，除了其他迷人的特性外，这种超流体的流动没有摩擦。超冷原子被困在非常良好的控制条件下，从而使我们能够与理论预期进行明确的定量比较。局限于2D的量子系统对于研究NEQ过程特别有趣，因为作为量子力学固有部分的涨落在阻止真正的长程有序方面发挥了很大作用。这种方法将为其他二维系统（如薄膜超导体和液晶）中类似的相变提供见解，量子气体通常充当二维量子物理的量子模拟器。实现所提出的研究的一个关键因素是我们通过创新地使用组合射频（RF）和静态磁场来创建超冷铷原子的双阱势。通过这种技术，我们已经实现了一个二维量子气体的双层，其中层间距离被控制在数十纳米的精度，这是不可能的替代（光学）方法被广泛使用。这使得两层之间的量子耦合被设置为精确的值，我们使用现代RF电子的可编程性来实现纳秒分辨率的双阱势的动态控制。双层结构的另一个优点是，我们可以利用超冷原子的物质波干涉来探测二维量子气体中固有的系统的微观相位波动，这使我们能够探测局部涡旋密度和一阶关联函数，这是理解BKT物理的关键。进一步的技术改进将允许检测更高阶的相关性，以及波动观测量的全概率分布函数，这代表了量子观测量的本质。使用这种冷原子装置作为2D系统中多体相位的“量子模拟器”将提供新的见解。这些实验技术已经发展和完善到两个威尔斯阱之间的量子隧穿是可控的水平，这种最先进的设备使长期存在的研究问题的实验调查。

Systems that are not in equilibrium are ubiquitous but can be complex to describe. Systems at equilibrium are described with great success by statistical mechanics but there are no general theoretical framework for how closed many-body quantum systems evolve to reach such thermalised states. Examples range from the cooling of a cup of coffee to the emergence of structures in the early universe. Non-equilibrium (NEQ) processes are also important for quantum systems including quantum computers such as those based on superconducting qubits. 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 systems that is named after them, the Berezinskii-Kosterlitz-Thouless (BKT) transition. This transition occurs as the 2D quantum gas is cooled and, at a certain temperature, it changes into a superfluid that 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 approach 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 of 2D quantum physics in general.A key factor that enables the proposed investigation is the double-well potential for ultracold rubidium atoms that we have created by an innovative use of combined radiofrequency (RF) and static magnetic fields. With this technique we have realised a bilayer of 2D quantum gases where the inter-layer distance is controlled with a precision of tens of nanometres, which is impossible with alternative (optical) methods that are widely used. This allows the quantum coupling between two layers to be set to precise values, and we use the programmability of modern RF electronics to implement dynamical control of the double-well potential with nanosecond resolution. A further advantage of having two layers, is that we can use matter-wave interference of the ultracold atoms to probe the microscopic phase fluctuations of the system that are intrinsic in 2D quantum gases.This allows us to probe the local vortex density and first-order correlation functions which are the key to understanding BKT physics. Further technical improvement will allow the detection of higher-order correlations, as well as the full probability distribution function of the fluctuating observables, which represent the essence of quantum observables. Using this cold-atom apparatus as a 'quantum simulator' of many-body phases in 2D systems will provide fresh insights. These experimental techniques have been developed and refined to the level at which the quantum tunnelling between the two wells is controllable and this state-of-the-art apparatus enables the experimental investigation of long-standing research questions.