這些年來長距離的量子通訊已受到廣泛的關注，在這篇論文中，我們一開始會先介紹糾纏態的互換特性與量子中繼器並說明如何以DLCZ 的機制實現長距離的量子通訊。在第二章中，我們會先半古典的方式介紹量子光學的基本理論: 電磁波引發透明，而這也正是DLCZ 模型的第二步作法。在第三章中，我們會以全量子的方式結合海森堡朗之萬方程以及馬克斯威爾薛丁格方程計算出在DLCZ 機制下第一步所產生的史托克光子穩態產生率的解析解、頻譜解析解以及二階的自我關聯函數，並分析了基態去同調率以及拉曼增益對系統達到穩態所需時間與產生率的影響。在我們系統下解出史托克光的頻寬極窄，幾乎只受限於基態去同調率，其解析解為柯西-勞侖茲分布，藉由增加拉曼增益後，甚至可以得到幾乎為單頻光的頻譜。由此，史提克光子可以得到極長的同調時間。在第四章中，我們會直接從頻率域出發來解出史托克光，這個作法相較前者簡潔很多，而這個方法的結果與第一種方法幾乎一致且能揭露出史塔克效應造成的影響。

In recent years, large-scale quantum communication earns widespread attention. In the beginning, we will introduce entanglement swapping, purification, and quantum repeater to elaborate on how to realize quantum communication over long distance. In chapter two, we briefly illustrate the semi-classical theory of electromagnetically induced transparency, which denotes the second step of DLCZ scheme. In chapter three, we utilize the Heisenberg-Langevin equation and Maxwell-Schrödinger equation to derive the time-dependent Stoke photons generation by Laplace transform. In addition, we provide the analytic solution of spectrum and the second-order autocorrelation function of Stoke photons. After that, we will discuss the influence of two ground-states decoherence on generation rate and the time it takes to attain steady-state condition. The spectrum of Stoke photons is extremely narrow, which is constricted by two ground-states decoherence. The analytic solution of the spectrum is Cauchy–Lorentz distribution. (owing to the collision of particles) By increasing Raman gain, the spectrum is similar to the spectrum of single-mode photons. In consequence, Stoke photons possess a long coherent time. In chapter four, we exploit an alternative and convenient approach to resolve the spectrum, which reveals the Stark effect that is arduous to be carried out by the first method. The results of several theoretical predictions are almost consistent with the first method.

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