标题： 用于包含改进的朗之万噪声形式的多模Jaynes-和Tavis-Cummings模型的数值框架：耗散电磁环境中原子-场相互作用的非马尔可夫分析 显示英文标题

标题： Numerical Framework for Multimode Jaynes- and Tavis-Cummings Models Incorporating the Modified Langevin Noise Formalism: Non-Markovian Analysis of Atom-Field Interactions in Dissipative Electromagnetic Environments

摘要： 我们提出了一种新颖的数值框架，将修改后的朗之万噪声形式整合到多模Jaynes-和Tavis-Cummings模型中，从而能够在考虑辐射损耗和有损介质中的吸收耗散（或满足具有色散和吸收效应的一般非均匀因果介质）的耗散电磁（EM）环境中，对原子-场相互作用进行第一性原理的非马尔可夫分析。 在修改后的朗之万噪声形式中，边界和介质辅助（BA和MA）场，这些在耗散EM环境中构成连续EM模式集，使用有限元方法（FEM）进行数值求解。 具体而言，BA场模式通过求解平面波散射问题提取，而MA场模式则通过点源辐射问题确定。然后将这些数值获得的BA和MA场模式纳入多模Jaynes-和Tavis-Cummings模型中，以便计算原子与BA-MA场模式之间的耦合强度，从而研究耗散EM环境中的原子-场相互作用。 所提出的方法能够捕捉传统量子主方程在马尔可夫近似下无法描述的非马尔可夫原子动力学。 为了验证所提出数值框架的准确性，我们给出了四个数值例子：(i) 完美电导体（PEC）半空间中的两能级系统（TLS）；(ii) 两种极限情况下的耗散腔量子电动力学，分别接近自由空间中的自发发射和理想Rabi振荡；(iii) TLS阵列中的超辐射；以及 (iv) 耗散腔内两个TLS的纠缠突然死亡。 所提出的方法可以作为研究一般耗散EM环境中原子-场相互作用的基准数值模拟器。 显示英文摘要

摘要： We present a novel numerical framework that integrates the modified Langevin noise formalism into the multimode Jaynes- and Tavis-Cummings models, enabling a first-principles, non-Markovian analysis of atom-field interactions in dissipative electromagnetic (EM) environments that account for both radiative losses and absorptive dissipation in lossy dielectric media (or satisfying general inhomogeneous causal media exhibiting both dispersion and absorption effects). In the modified Langevin noise formalism, the boundary- and medium-assisted (BA and MA) fields, which constitute a continuum set of EM modes in dissipative EM environments, are numerically obtained using the finite-element method (FEM). Specifically, BA field modes are extracted by solving plane-wave scattering problems, while MA field modes are determined through point-source radiation problems. These numerically obtained BA and MA field modes are then incorporated into the multimode Jaynes- and Tavis-Cummings models such that the coupling strength between atoms and BA-MA field modes can be calculated for the study of atom-field interactions in dissipative EM environments. The proposed methodology captures non-Markovian atomic dynamics that cannot be described by traditional quantum master equations under the Markovian approximation. To validate the accuracy of the proposed numerical framework, we present four numerical examples: (i) a two-level system (TLS) in a perfect electric conductor (PEC) half-space; (ii) dissipative cavity electrodynamics with two limiting cases approaching spontaneous emission in free space and ideal Rabi oscillations; (iii) super-radiance in TLS arrays; and (iv) entanglement sudden death of two TLSs inside dissipative cavities. The proposed methodology can serve as a ground-truth numerical simulator for studying atom-field interactions in general dissipative EM environments.