[论文解读] Many-Body Open Quantum Systems

Rosario Fazio, Jonathan Keeling+2 more|St Andrews Research Repository (St Andrews Research Repository)|Sep 16, 2024

Advanced Thermodynamics and Statistical Mechanics被引用 7

一句话总结

这些讲义笔记概述了在开放量子多体系统中理论进展，其中耗散和相干动力学都是可调的，涵盖框架、耗散态工程、耗散相变、向稳态的动力学，以及被监测的量子轨迹。

ABSTRACT

These Lecture Notes discuss the recent theoretical advances in the understanding of open quantum many-body physics in platforms where both dissipative and coherent processes can be tuned and controlled to a high degree. We start by reviewing the theoretical frameworks and methods used to describe and tackle open quantum many-body systems. We then discuss the use of dissipative processes to engineer many-body stationary states with desired properties and the emergence of dissipative phase transitions arising out of the competition between coherent evolution and dissipation. We review the dynamics of open quantum many body systems in the presence of correlated many-body dissipative processes, such as heating and many-body losses. Finally we provide a different perspective on open quantum many-body systems by looking at stochastic quantum trajectories, relevant for the case in which the environment represents a monitoring device, and the associated measurement-induced phase transitions.

研究动机与目标

• 介绍开放量子多体系统的理论框架（Lindblad、Schwinger–Keldysh、量子轨迹）。
• 解释如何通过定制化耗散来创建所需的多体稳态。
• 讨论由相干动力学与耗散的竞争引发的耗散性相变。
• 在加热和多体损耗下，考察向稳态的动力学。
• 呈现被监测的动力学及测量诱发现象在开放量子系统中的作用。

提出的方法

• 给出 Lindblad 主方程形式，并讨论对称性与稳态。
• 描述用于驱动-耗散动力学的 Schwinger–Keldysh 路径积分形式。
• 概述量子轨迹作为 Lindblad 方程的解卷。
• 综述其他框架：相空间方法、海森堡-朗之万方程、第三量子化、有效非厄米哈密顿量。
• 总结数值与解析方法：MF、DMFT、簇方法、MPS、神经网络猜想、角空间重正化、累积展开、MCTDH，以及 Schwinger–Keldysh 技术。

Figure 1: (a-b) Experimental measurement of a dissipative phase transition in a Josephson junction arrays, from [ 44 ] . (a) The Josephson array (on the top of the device) is in electrostatic contact with a two-dimensional electron gas (2DEG) that is responsible for a voltage noise on the supercondu

实验结果

研究问题

• RQ1 如何通过耗散的工程化来稳定特定的多体稳态？
• RQ2 开放量子多体系统中的耗散性相变的特征与分类是什么？
• RQ3 相关的多体耗散过程（如加热和损耗）如何影响动力学与稳态？
• RQ4 量子轨迹与测量诱导转变在平均密度矩阵动力学之外提供了哪些见解？
• RQ5 各种实验平台如何实现并探测驱动-耗散开放系统物理？

主要发现

• 可以通过工程化的耗散来稳定非平凡多体状态，并通过耗散实现量子计算。
• 耗散性相变源于相干演化与耗散的竞争，其分类与谱理论和 Schwinger–Keldysh 场论相关。
• 驱动、耗散与对称性破缺之间的相关性导致边界时间晶体和吸收态转变等现象。
• 被监测的量子系统揭示了在平均密度矩阵中看不到的测量诱导相变。
• 多种特定平台的方法（例如用于驱动-耗散晶格的 DMFT、MPS、神经网络）使开放多体动力学的可处理分析成为可能。

Figure 2: (Left) Energy levels of 9 Be + ions in a magnetic field $B$ employed in the experiment on the quantum Zeno effect [ 62 ] . The two hyperfine levels, $1$ and $2$ , are coupled by a radio-frequency field; a strong laser pulse couples the level $1$ with the excited level $3$ , which undergoes