标题： 马豪克斯-魏登穆勒方法在腔量子电动力学中的应用以及单光子频率的完全共振下转换 显示英文标题

标题： Mahaux-Weidenmüller approach to cavity quantum electrodynamics and complete resonant down-conversion of the single photon frequency

摘要： 研究表明，一类广泛的腔量子电动力学（QED）问题，这些问题是考虑单个光子与量子发射器（QEs），如原子、量子点或空位中心，共振传播的情况，可以直接求解而不使用二次量子化形式。 在所开发的方法中，哈密顿量通过集体（光子+腔+QEs）状态的态矢量积来表示。 因此，输入输出问题的S矩阵由Mahaux-Weidenmüller公式精确确定，这大大简化了复杂腔QED系统的分析。 首先，该方法通过一个光子与光学腔内任意分布的N个双能级QEs共振相互作用的问题进行说明。 该问题的解展示了之前在特殊情况下已知的QEs累积作用效应。 QEs的类似累积作用能否增强单个光子的非弹性共振传输？ 我们解决了光学腔与N个三能级QEs的电子跃迁共振耦合的情况。 结果表明，所描述的结构是最简单的现实结构，它能够在没有外部驱动场的情况下，且腔损耗和QE耗散足够小的情况下，实现单个光子频率的下转换，其振幅接近于1。 总体而言，所开发方法的简洁性和普遍性暗示了一种实用的方法来识别和描述腔QED中的新现象。 显示英文摘要

摘要： It is shown that a broad class of cavity quantum electrodynamics (QED) problems, which consider the resonant propagation of a single photon interacting with quantum emitters (QEs), such as atoms, quantum dots, or vacancy centers, can be solved directly without application of the second quantization formalism. In the developed approach, the Hamiltonian is expressed through the ket-bra products of collective (photon + cavities + QEs) states. Consequently, the S-matrix of input-output problems is determined exactly by the Mahaux-Weidenm\"uller formula, which dramatically simplifies the analysis of complex cavity QED systems. First, this approach is illustrated on the problem of propagation of a photon resonantly interacting with N two-level QEs arbitrary distributed inside the optical cavity. Solution of this problem manifests the effect of cumulative action of QEs previously known for special cases. Can a similar cumulative action of QEs enhance the inelastic resonant transmission of a single photon? We solve this problem for the case of an optical cavity having two modes resonantly coupled to electronic transitions of N three-level QEs. It is shown that the described structure is the simplest realistic structure which enables the down-conversion of the single photon frequency with the amplitude approaching unity in the absent of the external driving field and for sufficiently small cavity losses and QE dissipation. Overall, the simplicity and generality of the developed approach suggest a practical way to identify and describe new phenomena in cavity QED.