Non-equilibrium Dynamics of Quantum Open Systems: From Fundamental Theory to Applications in Cold Atoms, Superconducting Circuits and Quantum Glasses

在过去的20年里，量子系统的实验实现发生了一场革命。超冷原子气体通常在实验室中产生，用于研究复杂的多体现象。实验的进步也允许在单量子自由度的水平上进行前所未有的控制，例如在捕获离子、量子点和纳米机电系统中。这些发展不仅具有根本的重要性，而且还承诺了令人兴奋的技术应用，如量子计算和精确测量设备。真实的量子系统是开放的，这意味着它们与周围的环境相互作用。这导致相干性或量子性的不可逆损失。今天量子力学中的大多数实际和概念问题都直接或间接地与保持量子相干性的问题有关。此外，开放量子系统本质上是不平衡的系统。但是，尽管我们对经典（即非量子）系统的理解最近取得了很大进展，但对类似的量子问题的理解却少得多。这项研究将使我们对开放量子系统的非平衡动力学的理解发生重大变化。第一个目标是通过将统计非平衡物理学中最新颖的方法、概念和技术应用于开放量子系统，弥合经典和量子非平衡系统之间存在的理解上的差距。经典非平衡态科学的许多最新进展都起源于对复杂的“软”凝聚态系统（如玻璃）的研究。由此产生的一系列新的想法和技术尚未在量子领域得到充分利用。这项建议将弥合这一差距。结果将是双重的：一个新的一般方法和一套概念，用于研究远离平衡的复杂量子系统;以及对当前感兴趣的特定系统的新预测和见解，如冷原子和量子超导电路，包括新的实验建议。第二个总的目标是设计和执行创新的实验，发现意想不到的动态相变和其他动态波动行为的超冷原子系统，采用新的高灵敏度和时间分辨率探测器。实验将基于原子芯片附近不同维度的高度受控动态微工程环境中的超冷热和量子简并气体（玻色-爱因斯坦凝聚）。这个提议是关于一个多管齐下的方法来解决当前的量子非平衡问题。它的目的是建立一个新的概念框架，在理论和实验层面，以解决这个问题。它将为开放量子系统的表征提供一系列新的理论，计算和实验方法和技术。更雄心勃勃的目标是发现量子非平衡物质的动力学相变，这有可能改变我们对非平衡现象的看法。

The last twenty years have seen a revolution in the experimental realisation of quantum systems. Ultra-cold atomic gases are routinely created in the laboratory and used for the study of complex many body phenomena. Experimental advances have also allowed an unprecedented degree of control at the level of single quantum degrees of freedom, such as in trapped ions, quantum dots, and nano-electromechanical systems. These developments are not only of fundamental importance, but also promise exciting technological applications as varied as quantum computing and precise measurement devices.Real quantum systems are open which means that they interact with their surrounding environment. This leads to an irreversible loss of coherence or quantumness . Most of the practical and conceptual questions in quantum dynamics today are related directly or indirectly to the problem of maintaining quantum coherence. Furthermore, open quantum systems are intrinsically systems not in equilibrium. But while there has been much recent progress in our understanding of classical (i.e. non-quantum) systems out-of-equilibrium, much less is understood about the analogous quantum problem. The proposed research will produce a step-change in our understanding of the non-equilibrium dynamics of open quantum systems.Our proposal has two general aims. The first one is to bridge the gap in understanding that exists between classical and quantum non-equilibrium systems, by applying and adapting the most novel methods, concepts and techniques from statistical non-equilibrium physics to open quantum systems. Many of the recent advances in classical non-equilibrium science have originated from the study of complex ``soft'' condensed-matter systems such as glasses. The new set of ideas and techniques that this has spawned has not yet been fully exploited in the quantum realm. This proposal will bridge this gap. The outcomes will be two-fold: a new general methodology and set of concepts for studying complex quantum systems far from equilibrium; and new predictions and insights for specific systems of current interest, such as cold atoms and quantum superconducting circuits, including novel experimental proposals. The second general aim is to design and perform innovative experiments on ultracold atomic systems that uncover unexpected dynamical phase transitions and other dynamical fluctuation behaviour by employing novel high sensitivity and temporal resolution detectors. The experiments will be based on ultracold thermal and quantum degenerate gases (Bose-Einstein condensates) in highly controlled dynamic microengineered environments of varying dimensionality near atom chips. This proposal is about a multi-pronged approach to the current issue of quantum non-equilibrium. It aims to establish a novel conceptual framework, both at the theoretical and experimental level, to address this problem. It will deliver a range of new theoretical, computational and experimental methodologies and techniques for the characterisation of open quantum systems. The more ambitious goal is the discovery of dynamical phase transitions in quantum non-equilibrium matter, with the potential to change the way we think about non-equilibrium phenomena.