Dynamics of Entanglement in Dissipative Many-Body Systems

量子纠缠是一种量化系统中空间分离部分相互依存关系的量子力学现象，已成为物理学中的一个基本概念，具有广泛的应用，从量子信息到量子计量，再到凝聚态系统的分类和理解。这个项目的一个重要部分，是开发新的方法来研究纠缠动力学，是建立一个密切的理论努力和远程相互作用系统的实验实现之间的联系，特别强调自组装晶体中的捕获离子阵列。在这些系统中，可以通过调整照射离子并施加自旋相关力的激光束的频率，来设计依赖于离子内部状态（自旋）的远程相互作用。研究工作的范围可以放在“量子模拟”的背景下：将进行实验来模拟现有数值方法难以获得动力学的模型，然后将开发能够再现观察到的动力学的近似方法。这项工作将导致对复杂量子系统中自旋动力学和纠缠的更基本的理解，并将有助于实现新型量子材料和技术。此外，它还将为研究生和博士后提供培训和研究经验。除了JILA和科罗拉多大学博尔德分校的理论小组外，他们还将有机会与NIST/Boulder实验离子阱小组合作，从而将暴露在高度协作的氛围中。该项目的总体目标是开发新的方法，能够描述由具有两个内部自由度（自旋）的许多粒子组成的系统中的纠缠动力学，这些系统在远距离上相互作用和串扰。研究人员将允许自旋系统也与外部储层（开放系统）交换能量和信息的可能性。研究的智力焦点将分为三个主要方向：(i)哈密顿动力学；（ii）单粒子退相干耗散动力学；（iii）更复杂的多体退相干驱动耗散动力学。Thrust (i)计划从易于制备和高保真的产品状态开始，研究具有任意耦合常数的自旋1/2 XXZ模型在淬火后的纠缠和相关性的发展。推力（ii）将深入研究这些系统中局部马尔可夫退相干和多体相互作用之间的相互作用。推力（iii）将研究在外部驱动源存在的情况下，弹性相互作用和集体耗散耦合之间的相互作用。这些都是具有挑战性的目标，但研究人员的兴趣和能力的协同作用-跨越量子光学，凝聚态物质，理论和实验原子物理等不同但互补的领域的专业知识-将使该小组能够深入研究广泛的问题，这对于单个研究人员计划来说是困难或不可行的。

Quantum entanglement, a quantum mechanical phenomenon that quantifies the interdependence of spatially separated parts of a system, has become a fundamental concept in physics with broad applications, ranging from quantum information, to quantum metrology, to the classification and understanding of condensed matter systems. A vital part of this project, which is to develop new methods to investigate the dynamics of entanglement, is to establish a close connection between the theoretical effort and experimental realizations of long-range interacting systems with a particular emphasis on arrays of trapped ions in self-assembled crystals. In these systems it is possible to engineer long-range interactions that depend on the internal states of the ions (spin) by adjusting the frequency of laser beams that illuminate the ions and impart a spin dependent force. The scope of the research effort can be placed in the context of "quantum simulation": experiments will be conducted to simulate models whose dynamics is difficult to access by existing numerical methods, and approximate methods capable of reproducing the observed dynamics will then be developed. This work will lead to a more fundamental understanding of spin dynamics and entanglement in complex quantum systems, and will contribute towards the realization of new classes of quantum materials and technologies. Moreover, it will train and provide research experience to a graduate student and a postdoc. They will have the opportunity to work with the NIST/Boulder experimental ion trap group, in addition to the theory groups at JILA and the University of Colorado at Boulder and thus will be exposed to a highly collaborative atmosphere. The overall goal of this project is to develop new methods capable to describe the dynamics of entanglement in systems made of many particles with two internal degrees of freedom (spin), that interact and crosstalk at long distances. The investigators will allow the possibility that the spin system also exchanges energy and information with an external reservoir (open system). The intellectual focus of the research will be divided in three main thrusts: (i) Hamiltonian dynamics, (ii) Dissipative dynamics with single particle decoherence and (iii) Driven-dissipative dynamics with more complex many-body decoherence. Thrust (i) plans to investigate the development of entanglement and correlations in spin 1/2 XXZ models with arbitrary coupling constants after a quench, starting with easily preparable and high fidelity product states. Thrust (ii) will delve on the interplay between local Markovian decoherence and many-body interactions in these systems. Thrust (iii) will study the interplay between elastic interactions and collective dissipative couplings, in the presence of external driving sources. These are challenging goals but the synergy of interests and abilities of the investigators -- with expertise that spans the different but complementary areas of quantum optics, condensed matter, and theoretical and experimental atomic physics-- will allow the group to delve into a broad range of problems, which would be difficult or unfeasible for a single investigator program.