在我的工作中，我首先通過求解光學Bloch方程來得到密度矩陣分量的解，呈現了在兩能階系統中光和原子的交互作用。接著，我們用數值模擬來描述原子在基態和激發態的機率以及在不同的Rabi frequencies下不同的雷射光頻率下對原子吸收的影響。更進一步，將光學Bloch方程應用於具有兩個外場（弱探測場和強耦合場）的梯形三能階系統，並且通過數值計算求出密度矩陣分量在穩定狀態下的解。
此篇論文的目地在於呈現133Cs系統中(6^2 S_(1/2)-6^2 P_(3/2)-〖11〗^2 S_(1/2)) 梯形狀的電磁誘發透明的數值模擬結果。在EIT中的Doppler effect以及耦合光的Rabi frequency也有被考慮在本論文中。最後，我們在有雙光子干涉的梯形三能階系統中再加上一道雷射光。在改變不同Rabi frequency的雷射光後，我們得到四波混頻（FWM）的信號和三光子的電磁誘發吸收信號。我們也針對電磁誘發透明和三光子電磁誘發吸收的不同進行了討論。

In this research, we firstly present the interaction of light and atoms in the simplest way that is the two-level system by solving the optical Bloch equation to get the solution of density matrix components. We subsequently use numerical simulation to describe the probability of atom being in the ground state and the excited state, as well as the influence of absorption of light with changing the frequency of laser field for various Rabi frequencies. Furthermore, the optical Bloch equation is applied into the ladder-type three-level system with two external fields (a weak probe field and a strong coupling field), and the solution of density matrix is presented after solving numerical method in steady state condition.
The purpose of this research is to present numerical simulation results of Electromagnetically Induced Transparency (EIT) in ladder-type three-level system for the 6^2 S_(1/2)-6^2 P_(3/2)-〖11〗^2 S_(1/2) transition of 133Cs atom. Moreover, influences of the Rabi frequency of coupling field and Doppler effect in EIT are also presented. Finally, an additional driving field is introduced into ladder-type three-level system to form a modified three-level system which involves two-photon coherence. We obtain the four-wave mixing (FWM) signal with various Rabi frequencies of driving field and the three-photon electromagnetically induced absorption (TPEIA) signal. A comparison between EIT and TPEIA with the change of Rabi frequency of the driving field is also illustrated in this research.

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