在冷原子系統中，利用87Rb 的D2 譜線，我們將驅動光和耦合光反向打入系統產生了雙Λ 型自發四波混頻。理論分析上運用海森堡-朗之萬方程結合微擾理論，對原子與光場的交互作用進行了理論分析，推導出斯托克斯和反斯托克斯光子的理論產生率，同時利用格勞勃二階關聯性函數分析時間關聯性函數。我們進一步對包含環境漏光的實驗數據進行了詳細分析，並與理論值進行了擬合，結果顯示實驗數據與理論分析良好吻合。
在實驗中，首先在低雙光子產生率的條件下，觀察到峰值訊號-背景比為123，這違反了柯西-史瓦茲不等式，達到了3844 倍，表示在此時間區間光子間的量子關聯性非常大。為增加產生率，並保持光學密度一致性，我們調整了驅動光光強，這導致了背景產生率的增加，而峰值訊號保持不變，因此降低了峰值訊號-背景比。接著，我們進一步提升雙光子產生率，將驅動光調變縮小至5Γ，此時產生率達每秒
1.3 × 10^7，為已知最高雙光子產生率。然而，在此超亮雙光子條件下，光學密度為20 時，雙光子配對比為0.57，仍有相當部分光子無關聯性。隨後，我們在光學密度為40、60、80、100 和120 條件下，調整驅動光調變和耦合光光強以保持相同產生率和雙光子頻寬，得到雙光子配對比與光學密度呈正相關。在光學密度為120 條件下，雙光子配對比為0.87，提升了雙光子的配對比。此外，在雙Λ 型自發四波混頻過程中，由於存在Λ 型的電磁誘發透明結構，可以控制關聯性時間，進而決定系統的雙光子頻寬。主導延遲時間主要受兩個因素影響：一是由電磁誘發透明引起的慢光效應，二是由耦合光引起的拉比振盪。最終的延遲時間由這兩項因素之間的競爭所決定。我們在這兩個區域進行了實驗調整耦合光調變。耦合光調變越大，合理的延遲時間也越大，而產生率變化較小，因產生率主要受驅動光和光學密度影響。隨著耦合光調變增加，雙光子配對比變差，我們認為這是兩個基態間去同調率造成的資訊耗損。在耦合光較強的拉比振盪區域，雙光子配對比的耗損較少。
綜上所述，我們成功地在冷原子系統中產生了雙Λ 型自發四波混頻，並調整實驗參數研究其光子配對比和關聯性時間。這些結果有助於更深入了解光場與原子系統的交互作用，並為量子光學和量子信息處理領域的應用提供了有價值的參考。

In our study, we employed a double-Λ configuration to generate biphotons through spontaneous four-wave mixing (SFWM). The resulting photon pairs exhibited temporal correlation, where the appearance of the second photon, anti-Stokes photon, was conditional on detecting the first photon, Stokes photon, within the correlated time window. The temporal correlation profile could be adjusted by manipulating the intrinsic electromagnetically induced transparency (EIT), which was predicted using the Heisenberg-Langevin operator approach in our theoretical analysis. Remarkably, we achieved an impressive biphoton generation rate of up to 1.3*10^7 pairs per second at a relatively low optical depth of 20. However, under these conditions, we observed that only 60% of the Stokes photons were successfully paired. To overcome this limitation, we conducted further experiments and demonstrated that by increasing the optical depth to 120, the pairing efficiency could be significantly improved to 89%. This outcome highlights the tremendous potential of the double-Λ SFWM scheme as a robust source of biphotons, capable of achieving high generation rates while enhancing the efficiency of biphoton pairing through increased optical depth. Furthermore, under different experimental conditions, we observed a signal-to-background ratio of 123, which violated the Cauchy-Schwarz criterion by a factor of more than 3800. This remarkable result indicates the exceptional quality of the generated biphotons and opens up exciting possibilities for their applications in various fields, particularly in advancing the efficiency of photonic quantum communication and information processing.

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