2025/01/01 by Edgar Guardiola-Navarrete, Silvia Cardenas-Lopez, Ana Asenjo-Garcı́a +1
Computer Science · Physics and Astronomy · #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #Quantum Information and Cryptography #quant-ph
paper · pdf · doi:10.1016/bs.aamop.2025.04.003
published as Adv. At. Mol. Opt. Phys. 74, 87 (2025) · 51 pages, 12 figures
openalex publication_date 2025/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/22 · arxiv created 2026/07/31 · arxiv updated 2026/08/04
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.