INTERACTIVE DYNAMICS OF MANY-BODY QUANTUM SYSTEMS

在我们的日常生活中，我们很少考虑量子力学的影响，但它们却一直围绕在我们身边，决定着我们世界上每一个物质物体的性质。量子物理定律定义了物质的每一个属性，从单个原子的行为，到原子如何结合在一起形成材料，再到这些合成材料的特征。它们还决定了由许多相互作用的粒子组成的系统是否以及如何在少数统计定律的控制下建立平衡或稳定状态。物理学家现在能够在量子计算设备、超冷原子气体和固态材料中设计大量可调的相互作用量子粒子集合。通常，这样的系统不能用标准技术来描述，因为标准技术关注的是具有简单结构的量子态。在许多情况下，这些系统达到平衡的路径涉及量子力学的微妙和令人惊讶的特征，需要全新的思维方式，或者需要对旧方法（如流体力学）进行实质性的扩展。最近出现的另一个引人注目的新想法是，即使在多体系统远离其最低能量状态时，量子力学相干性也可以保持。这里的“相干性”一词意味着许多微观物体协同作用。当这种行为发生时，量子物理的效应会大大增强，但当系统达到平衡时，它通常会被淘汰，这通常可以用经典物理学来描述。寻找避开这种平衡的路径允许新的和不寻常的物理现象，对量子技术具有重要的潜在效用。然而，第三组新概念是由当今“嘈杂、中等规模量子”（NISQ）设备的能力所激发的。与传统平台相比，这些平台提供了通过测量来打断多体系统时间演化的可能性，并利用结果来塑造未来的演化——这是一种新形式的“量子交互动力学”，科学家是积极的参与者，而不是被动的旁观者。了解在此设置中启用的物质的新状态以及在NISQ处理器上实现它们所需的协议是一个令人兴奋的新领域。我们将我们的研究分为三个主题：(1)量子系统接近平衡状态的机制是什么？我们将对量子多体系统中平衡态的普遍方面有更好的理解。我们还将设法理解某些实验系统，如冷原子气体或固态材料，这些系统可以用流体力学原理及其推广来研究。(2)量子多体系统如何逃避热化而进入新的非平衡态？我们将试图了解冻结的随机性和特殊对称性如何阻止平衡的方法，并允许量子相干性即使在高激发态下也能持续存在。(3)“量子相互作用动力学”带来了哪些新的可能性？我们将阐明如何通过测量和反馈来塑造量子系统向平衡或远离平衡的演变。这些问题的答案可能是利用量子力学的全部力量来完成复杂任务的核心。理解量子多粒子系统的非平衡和相互作用动力学，可能在未来量子计算设备的发展中发挥类似的作用，就像固体量子理论在上个世纪的技术革命中所起的作用一样。因此，虽然我们的研究主要是学术性质的，但我们希望我们的发现将使解决下个世纪挑战所需的技术成为可能。

In our everyday life we rarely think about the effects of quantum mechanics, and yet they are constantly around us, determining the properties of every material object in our world. The laws of quantum physics define every property of matter, from the behaviour of individual atoms, to how the atoms bind together to form materials, to the characteristics of these resultant materials. They also determine if and how systems of many interacting particles establish an equilibrium or steady state governed by a handful of statistical laws.Physicists are now able to engineer large, tunable collections of interacting quantum particles, both in quantum computing devices and in ultracold atomic gases and solid-state materials. Often, such systems cannot be described by standard techniques that focus on quantum states that have simple structures. In many cases, the routes by which such systems come to equilibrium involve subtle and surprising features of quantum mechanics, necessitating entirely new ways of thinking, or require substantial extensions of older approaches such as hydrodynamics. Another striking new idea that has emerged recently is that quantum mechanical coherence can be preserved even when many-body systems are far from their lowest-energy state. The word "coherence" here implies that many microscopic objects are acting together in concert. Such behaviour, when it occurs, allows for the effects of quantum physics to be greatly enhanced, but it is usually washed out as systems achieve equilibrium, which can often be described well using classical physics. Finding routes to evade this equilibrium allows for new and unusual physical phenomena with significant potential utility for quantum technology.Yet a third set of new concepts is motivated by the capabilities of the present-day "noisy, intermediate-scale quantum" (NISQ) devices. In contrast to conventional platforms, these offer the possibility of punctuating the time evolution of a many-body system by measurements, and using the results to shape future evolution - a new form of "quantum interactive dynamics", where the scientist is an active participant rather than a passive spectator. Understanding the new states of matter enabled in this setting and the protocols needed to implement them on NISQ processors is an exciting new frontier.We have organised our research into three themes:(1) What are the mechanisms by which quantum systems approach an equilibrium state?We will develop a better understanding of universal aspects of the equilibrium state in quantum many-body systems. We will also seek to understand certain experimental systems, such as cold atomic gases or solid-state materials, that can be studied using hydrodynamic principles and their generalizations.(2) How can quantum many-body systems evade thermalization to access novel non-equilibrium regimes?We will seek to understand how frozen-in randomness and special symmetries can arrest the approach to equilibrium and allow quantum coherence to persist even in highly excited states.(3) What new possibilities are enabled by "quantum interactive dynamics"?We will clarify how the evolution of quantum systems towards or away from equilibrium can be shaped by measurement and feedback.The answers to these questions are likely to be central in harnessing the full power of quantum mechanics to accomplish complex tasks. Understanding the far-from-equilibrium and interactive dynamics of quantum many-particle systems is likely to play a similar role in the development of future quantum computing devices as the quantum theory of solids did in the technological revolutions of the past century. Thus, while our research is mainly academic in nature, we hope that our discoveries will enable technologies needed to address the challenges of the next century.