Matrix product states and numerical mode decomposition for the analysis of gauge-invariant cavity quantum electrodynamics
Matrix product states and numerical mode decomposition for the analysis of gauge-invariant cavity quantum electrodynamics
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DOI：
10.1103/physreva.107.063707
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发表时间：
2022-12
影响因子：
2.9
通讯作者：
C. Ryu;Dong-Yeop Na;W. C. Chew
中科院分区：
文献类型：
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作者：
C. Ryu;Dong-Yeop Na;W. C. Chew
拉比哈密顿量有一个规范模糊的问题，因为它可以由两个形式上不同但物理上等效的基本哈密顿量推导出来。对于单量子化电磁模式的模型，这个问题最近已经得到了解决。在这项工作中，我们对多模模型进行了数学和数值验证。在此基础上，我们结合数值方法、矩阵积态（MPS）和数值模态分解（NMD）对腔QED系统进行了分析。MPS方法用于有效地表示和时间演化量子态。但由于拉比哈密顿量的耦合结构与MPS不兼容，因此在数值上将其转化为具有链式耦合结构的等效哈密顿量，使MPS能够有效地应用。利用NMD技术提取任意环境下的数值电磁模态。作为概念验证，通过分析各种设置下的1D腔QED系统来证明这种组合方法。
There has been a problem of gauge ambiguities with the Rabi Hamiltonian due to the fact that it can be derived from two formally different but physically equivalent fundamental Hamiltonians. This problem has recently been resolved for models with single quantized electromagnetic mode. In this work, we mathematically and numerically verify this for multimode models. With this established, we combine the numerical methods, matrix product states (MPS) and numerical mode decomposition (NMD), for analyzing cavity QED systems. The MPS method is used to efficiently represent and time evolve a quantum state. However, since the coupling structure of the Rabi Hamiltonian is incompatible with MPS, it is numerically transformed into an equivalent Hamiltonian that has a chain coupling structure, which allows efficient application of MPS. The technique of NMD is used to extract the numerical electromagnetic modes of an arbitrary environment. As a proof of concept, this combined approach is demonstrated by analyzing 1D cavity QED systems in various settings.