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

不处于平衡状态的系统无处不在，但描述起来可能很复杂。统计力学成功地描述了处于平衡状态的系统，但对于封闭的多体量子系统是如何进化到这种热化状态的，还没有一个通用的理论框架。例子包括从一杯咖啡的冷却到早期宇宙结构的出现。非平衡（NEQ）过程对量子系统也很重要，包括基于超导量子比特的量子计算机。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，以表彰他们在二维系统中以他们的名字命名的相变，即berezinski -Kosterlitz-Thouless （BKT）相变方面的工作。这种转变发生在二维量子气体冷却的时候，在一定的温度下，它变成了一种超流体，在其他迷人的特性中没有摩擦。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。这种方法将为其他二维系统（如薄膜超导体和液晶）中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。实现这项研究的一个关键因素是我们通过联合射频（RF）和静态磁场的创新使用创造了超冷铷原子的双阱潜力。通过这种技术，我们已经实现了二维量子气体的双层，其中层间距离的控制精度为数十纳米，这是广泛使用的替代（光学）方法所不可能的。这使得两层之间的量子耦合可以设置为精确的值，并且我们使用现代射频电子的可编程性来实现具有纳秒分辨率的双阱势的动态控制。双层结构的另一个好处是，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相关函数，这是理解BKT物理的关键。进一步的技术改进将允许检测高阶相关性，以及波动性可观测值的全概率分布函数，这代表了量子可观测值的本质。使用这种冷原子装置作为二维系统中多体相的“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井之间的量子隧穿是可控的水平，这一最先进的设备使实验研究长期存在的研究问题成为可能。

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.