AI 中文总结
本文全面介绍相空间方法在多体量子光学中的应用，推导多体耗散演化的精确偏微分方程，扩展形式体系以计算多时间关联函数，为相关多体现象研究提供工具。
AI 中文摘要
多体量子光学系统中，一组发射体通过共同的电磁库相互作用，展现出丰富的非平衡行为，在量子技术应用中具有潜力。然而，其动力学的精确数值模拟因希尔伯特空间随系统大小指数增长而迅速变得不可行。半经典相空间方法（如截断维格纳近似（Truncated Wigner approximation, TWA））通过捕捉主导阶量子涨落提供了计算高效的替代方案。本文全面概述了如何利用相空间方法解决多体量子光学问题，推导了任意相空间表示下支配多体耗散演化的精确偏微分方程，并讨论了近似方法，得到了Mink和Fleischhauer提出的耗散TWA（SciPost Phys. 15, 233 (2023)）。研究发现，P分布和Q分布对于多体量子光学通常不是最优的。此外，本文扩展了形式体系以计算多时间关联函数，从而将开放自旋系统的相空间模拟范围拓宽，涵盖集体辐射发射体的相干性、光谱特性以及方向关联。这些进展为研究由集体耗散驱动的奇异光源、驱动耗散相变以及最先进实验平台中出现的大量多体现象提供了有价值的工具。
英文摘要
Many-body quantum-optical systems, where a collection of emitters interacts through a common electromagnetic reservoir, exhibit rich out-of-equilibrium behavior and hold promise for applications in quantum technologies. However, exact numerical simulations of their dynamics quickly become unfeasible due to the exponential growth of the Hilbert space with system size. Semiclassical, phase-space approaches -- such as the Truncated Wigner approximation (TWA) -- provide computationally efficient alternatives by capturing leading-order quantum fluctuations. In this paper, we present a comprehensive overview of how to tackle problems in many-body quantum optics using phase-space methods. We derive the exact partial differential equation governing many-body dissipative evolution in any phase-space representation and discuss the approximations that yield the dissipative TWA proposed by Mink and Fleischhauer [SciPost Phys. 15, 233 (2023)]. We find that $P$ and $Q$ distributions are generally suboptimal for many-body quantum optics. Additionally, we extend the formalism to calculate multi-time correlation functions, thereby broadening the scope of phase-space simulations of open spin systems to include coherence and spectral properties, as well as directional correlations of collectively radiating emitters. These developments provide valuable tools for investigating exotic light sources driven by collective dissipation, driven-dissipative phase transitions, and a wealth of many-body phenomena arising in state-of-the-art experimental platforms.
Comments51 pages, 12 figures
Journal refAdv. At. Mol. Opt. Phys. 74, 87 (2025)
DOI：10.1016/bs.aamop.2025.04.003
