在本論文中，我們使用全量子模型來研究基於電磁誘發透明（EIT）的雙 Λ 四波 混頻（FWM）。在第一部分中，我們解釋了為什麼使用兩道雷射的基於 EIT 的 FWM 方案可以有效地產生關聯性光子對。基於全量子模型，我們計算了不同光學密度下 的雙光子產生率頻譜，並提供了物理的解釋。在第二部分中，我們發展了基於 Λ 四 波混頻的量子轉頻器全量子模型。在計算了光子規範算子的方差變量，我們發現如 果此四波混頻的轉換效率接近 100%，則轉換光子的量子態幾乎與輸入光子的量子態 相同。

In this thesis, we use a full quantum model to study double-Λ four-wave mixing (FWM) based on electromagnetically induced transparency (EIT). In the first part, we explained why an EIT-based FWM scheme using two lasers can efficiently generate correlated photon pairs. Based on the full quantum model, we calculated the biphoton generationratespectraatdifferentopticaldensitiesandprovidedaphysicalexplanation. In the second part, a full quantum model of a quantum frequency converter based on double-ΛFWMwasdeveloped. WecalculatedthevarianceofthephotoncanonicaloperatorandfoundthatiftheFWMconversionefficiencyapproaches100%,thequantum stateoftheconvertedphotonsarealmostthesameasthatoftheinputphotons.

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