本論文研究量子干涉效應下的非線性光學理論，包括三能階 Λ 型式的電磁波引發透明以及四能階N形式的光學開關、交錯相位調變和四波混頻。另外，我們提出一基於電磁波引發透明雙 Λ 形式的交錯相位調變。根據我們的理論分析，此機制可突破N形式交錯相位調變的極限，達到單光子脈衝 π 的相位操控。

We theoretically study the nonlinear optics by quantum interference, including three-level Λ-type electromagnetically-induced transparency as well as four-level N-type photon switching, cross-phase modulation, and four-wave mixing. In addition, we propose a novel cross-phase modulation using double-Λ electromagnetically-induced transparency. According to our theoretical analysis, the phase shift in the double-Λ scheme can overcome the limitation in the N-type scheme and achieve π phase shift at the single-photon level.

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