本篇論文研究的是分析雙階梯躍遷四波混頻系統將波長為 795 奈米之遠紅外光
子轉至波長為 1367 奈米或 1529 奈米之通訊光子轉頻。而我們所使用的介質為銣原
子，銣原子的激發態能階分別為 6S1/2 以及 4D1/2。根據我們的研究，當分析出各項
最佳參數後，在此系統中波長 1367 奈米通訊光子的轉換效率可達百分之九十，而波
長 1529 奈米通訊光子轉換效率可達百分之八十。在此論文中我們寫下如何利用光學
布拉赫方程式以及馬克士威薛丁格方程式建構此系統進行數值分析，且研究其相位
不匹配是否對其轉換效率造成影響。最後，我們考量各項參數對其進行分析，進而
了解其背後的物理機制。

We study on the conversion of a far-infrared photon with a wavelength of 795 nm to a telecom photon with a wavelength of either 1367 nm or 1529 nm through the four-wave mixing process in a medium with a double-cascade transition configuration. We numerical simulate the system with Optical-Bloch equations and Maxwell-Schrodinger equations to analyze the affections from various conditions, including the phase-mismatch effect. In simulation, we use the transition of the Rubidium 87 between energy levels of |6S1/2⟩ and |4D1/2⟩ . Under the optimal parameters, the results show that the conversion efficiencies are up to 90% and 80% for photons with 1367 nm and 1529 nm.

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