The x-ray planar cavity embedded in two nuclear ensembles at node and antinode positions with fixed spacing has been used to study the electromagnetically induced transparency (EIT)-like effect previously. In this work, the same x-ray planar cavity but with a flexible spacing configuration is studied theoretically. By developing a concise transfer matrix method, the changing of spacing is reflected conveniently as the phase shift of the propagation matrices, based on which the system can be solved analytically. A periodic characteristic as a function of the spacing is observed, i.e., the first nuclear ensemble locating at any node will result in an EIT effect while the EIT effect will be completely compressed when it is at any antinode. It indicates that the phase shift between the two nuclear ensembles plays a key role for the coupling field. This kind of phase manipulation will enrich the approaches of quantum control in the x-ray regime.

中文翻译：

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X射线平面腔内具有两个核集合的与空间相关的电磁感应透明度

以前，已使用以固定间距在节点和波腹位置的两个核集成体中嵌入x射线平面空腔来研究类似电磁诱导透明（EIT）的效应。在这项工作中，理论上研究了相同的X射线平面腔，但具有灵活的间距配置。通过开发简洁的传递矩阵方法，可以将间隔的变化方便地反映为传播矩阵的相移，从而可以解析该系统。观察到作为间隔的函数的周期性特征，即，位于任何节点的第一核集合将导致EIT效应，而当它位于任何波腹时，EIT效应将被完全压缩。这表明两个核集成体之间的相移对于耦合场起关键作用。