Dynamics of Entanglement in Dissipative Many-Body Systems

量子纠缠是一种量子力学现象，它量化了系统中空间分离部分之间的相互依赖关系，已经成为物理学中的一个基本概念，有着广泛的应用，从量子信息到量子计量学，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研究纠缠动力学的新方法，即在长程相互作用系统的理论工作和实验实现之间建立密切联系，特别强调自组装晶体中的俘获离子阵列。在这些系统中，可以通过调整照射离子并给予自旋相关力的激光的频率来设计依赖于离子(自旋)内部状态的远程相互作用。研究工作的范围可以放在“量子模拟”的背景下：将进行实验，以模拟那些通过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。这项工作将使人们对复杂量子系统中的自旋动力学和纠缠有一个更基本的了解，并将有助于实现新的量子材料和技术。此外，它还将为一名研究生和博士后提供培训和研究经验。他们将有机会与NIST/Boulder实验离子陷阱小组合作，此外还有JILA和科罗拉多大学博尔德分校的理论小组，因此将暴露在高度合作的气氛中。这个项目的总体目标是开发新的方法来描述由多个具有两个内部自由度(Spin)的粒子组成的系统中的纠缠动力学，这些粒子相互作用和长距离串扰。研究人员将允许自旋系统也与外部储存库(开放系统)交换能量和信息的可能性。这项研究的学术重点将分为三个主要方面：(I)哈密顿动力学，(Ii)单粒子退相干的耗散动力学和(Iii)更复杂的多体退相干的驱动耗散动力学。推力(I)计划研究具有任意耦合常数的自旋1/2XXZ模型在失超后纠缠和关联的发展，从容易制备和高保真的产品态开始。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)将研究在存在外部驱动源的情况下，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--拥有跨越量子光学、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，而这些问题对于单个研究人员项目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.