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。尽管量子力学在描述处于平衡状态的系统方面取得了巨大的成功，但对于封闭的多体量子系统如何演化到这样的热化态，目前还没有一个通用的理论框架。这个项目研究非平衡(NEQ)系统向热平衡松弛的过程，我们称之为热化。宏观的例子从一杯咖啡的冷却到早期宇宙中结构的出现。NEQ过程对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，然后以前所未有的详细程度跟踪它们向平衡的演化。我们将使用的系统是在数十纳米开尔文的温度下更好地理解NEQ物理的二维(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被授予Kosterlitz和Thouless，以表彰他们在2D量子系统相变方面的工作，该相变是以他们的名字命名的。这种转变发生在量子气体冷却并在一定温度下转变为超流体时，这种超流体流动时没有摩擦和其他令人着迷的特性。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预期进行明确的定量比较。受限于2D的量子系统对于研究NEQ过程特别感兴趣，因为涨落是量子力学固有的一部分，在阻止真正的长程有序方面发挥了很大作用。这一新方法将为薄膜超导体和液晶等其他2D系统中类似的相变提供见解，量子气体通常充当2D量子物理的量子模拟器。这一提议的基石是我们最近通过创新地使用射频(RF)和静态磁场创建的超冷Rb原子的双势垒。这项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所施加的射频场控制，从而利用了射频电子学的极高精度。分裂的速率决定了储存在系统中以产生所选择的初始状态的能量。在分裂后的预定时间，两个云从双势垒势中释放出来，以便它们扩展和重叠。这允许对物质波的相对相位进行干涉测量。通过重复测量，每次以相同的方式制备初始态，我们将能够确定对应于2D平面中所有位置的量子气体的相对相位的概率分布函数(PDF)。PDF代表了量子力学的本质，允许与理论模型进行更全面的比较，而不是像通常所做的那样，监测某些可观测到的期望值的时间演变。这种冷原子装置充当了2D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.