A simple fourth order propagator based on the Magnus expansion in the Liouville space: Application to a $Λ$-system and assessment of the rotating wave approximation
Queens College, City University of New York（纽约市立大学皇后学院）；Graduate Center of the City University of New York（纽约市立大学研究生中心）；Korea Institute for Advanced Study（韩国高等研究院）
一种基于Magnus展开的简单四阶传播算子[郭尔和姜，J. Phys. Chem. A. 128, 2871 (2024)]被扩展到李群空间，用于闭合系统和Lindblad开放系统量子动力学。对于这两种动力学，提供了无交换子的四阶传播算子。这些传播算子随后应用于驱动Λ系统的动力学，其中Lindblad项代表光子浴的影响。对于这两种动力学，评估了旋转波近似(RWA)在物质-辐射相互作用中的准确性。我们确认了RWA在弱场和共振场中的合理性能。然而，中等强度场中会出现小误差，强场中则会出现显著误差，即使相干人口陷阱仍可预期。我们还发现，开放系统量子动力学中光子浴的存在一致地降低了RWA的误差。这些结果提供了关于RWA在非弱场或非共振情况下的失效程度的定量信息。主要结果与我们基于六阶Magnus展开的传播算子的结果进行了对比。我们还提供了针对Λ系统的其他四阶算法的数值比较。这些结果确认了我们简单传播算子的合理性能以及通过无交换子表达式获得的改进。
英文摘要：
A simple 4th order propagator [Ture and Jang, {\it J. Phys. Chem. A.} {\bf 128}, 2871 (2024)] based on the Magnus expansion (ME) is extended to the Liouville space for both closed-system and Lindbladian open-system quantum dynamics. For both dynamics, commutator free versions of 4th order propagators are provided as well. These propagators are then applied to the dynamics of a driven $Λ$-system, where Lindblad terms represent the effect of a photonic bath. For both dynamics, the accuracy of the rotating wave approximation (RWA) for the matter-radiation interaction is assessed. We confirmed reasonable performance of RWA for weak and resonant fields. However, small errors appear for moderate fields and substantial errors can be found for strong fields where coherent population trapping can still be expected. We also found that the presence of bath for open system quantum dynamics consistently reduces the errors of the RWA. These results provide a quantitative information on how the RWA breaks down beyond weak field or for non-resonant cases. Major results are benchmarked against results of our 6th order ME-based propagator. We also provide numerical comparison of our algorithms with other 4th order algorithms for the $Λ$-system. These confirm reasonable performance of our simple propagators and the improvement gained through commutator-free expressions.
The Floquet-Magnus expansion of unbounded operators
Institute of Theoretical Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学理论物理研究所）；School of Mathematical Sciences, Lancaster University（兰卡斯特大学数学科学学院）
TECNALIA, Basque Research and Technology Alliance (BRTA)（泰克纳利亚，巴斯克研究与技术联盟）；University of the Basque Country UPV/EHU（巴斯克大学）；Forschungszentrum Jülich（于利希研究中心）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；CSIC（西班牙国家研究委员会）；Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所）
A Lie-algebraic approach to non-Markovian quantum dynamics
The University of Hong Kong（香港大学）；Tsinghua University（清华大学）；Materials Innovation Institute for Life Sciences and Energy (MILES)（生命科学与能源材料创新研究所）；HKU-SIRI, Shenzhen（香港大学深圳研究院）
Liouvillian Geometry of Multidimensional Spectra: Pathway Transport and Observational Holonomy in Open Quantum Systems
University of Houston（休斯顿大学）；Université de Montréal（蒙特利尔大学）；Georgia Institute of Technology（佐治亚理工学院）；Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV)（墨西哥国立理工大学高级研究中心）
