The study of open quantum systems – microscopic systems exhibiting quantum coherence that are coupled to their environment – has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physics, and it has become important to extend previous understanding of open system dynamics in single- and few-body systems to this many-body context. A key formalism that has already proven very useful in this context is the quantum trajectories technique. This method was developed in quantum optics as a numerical tool for studying dynamics in open quantum systems, and falls within a broader framework of continuous measurement theory as a way to understand the dynamics of large classes of open quantum systems. In this article, we review the progress that has been made in studying open many-body systems in the AMO context, focussing on the application of ideas from quantum optics, and on the implementation and applications of quantum trajectories methods in these systems. Control over dissipative processes promises many further tools to prepare interesting and important states in strongly interacting systems, including the realisation of parameter regimes in quantum simulators that are inaccessible via current techniques.

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量子轨迹和开放的多体量子系统

开放量子系统（表现出与其环境耦合的量子相干性的微观系统）的研究在过去几年变得越来越重要，因为在各种物理系统中已经开发出在单个粒子水平上控制量子相干性的能力. 在量子光学中，对开放系统的研究远远超出了理解量子相干性的破坏。在那里，与环境的耦合被充分理解，它可以被操纵以将系统驱动到所需的量子状态，或通过量子测量中的反馈将系统投影到已知状态。已经开发了许多数学框架来描述这样的系统，其中包括原子的、分子的、和光学 (AMO) 系统通常在微观层面上提供对开放量子系统的非常准确的描述。近年来，包括冷原子和分子气体以及俘获离子在内的 AMO 系统已大量应用于多体物理的研究，将先前对单体和少体系统中开放系统动力学的理解扩展到这种多体上下文。在这方面已经证明非常有用的一个关键形式是量子轨迹技术。这种方法是在量子光学中发展起来的，作为研究开放量子系统动力学的数值工具，属于更广泛的连续测量理论框架，是理解大型开放量子系统动力学的一种方式。在本文中，我们回顾了在 AMO 背景下研究开放多体系统取得的进展，重点是量子光学思想的应用，以及量子轨迹方法在这些系统中的实现和应用。对耗散过程的控制有望为在强相互作用系统中准备有趣且重要的状态提供许多进一步的工具，包括在量子模拟器中实现当前技术无法访问的参数机制。