标题： 马豪克斯-维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、量子点或空位中心之间的共振传播——可以直接求解，而无需应用二次量子化形式。 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矩阵可以通过Mahaux-Weidenmüller公式精确确定，这大大简化了对复杂腔QED系统的分析。 首先，该方法用于解决单个光子与光学腔内任意分布的N个两能级QEs共振相互作用的问题。 该问题的解展示了之前仅在特殊情况下已知的QEs累积作用效应。 QEs的类似累积作用是否可以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，在没有外部驱动场且腔损耗和QE耗散足够小的情况下，能够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为在腔QED中识别和描述新现象提供了一种实用的方法。 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 for 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 absence 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.