本文主要描述二能階的玻色—愛因斯坦原子系統在量子化的光學共振腔中，雙光子的吸收與放射。玻色—愛因斯坦凝結態（以下簡稱BEC）在光學共振腔中的Hamitonian—對應到整個系統的能量—可分成四部分：光子的能量、原子個別能階的能量、原子與光子之間的交互作用，以及原子間的交互作用，其中最後一項—也就是原子間的交互作用—在BEC中才需要特別考慮。
研究方法是以半古典假設來得出運動方程式，會發現此系統可等價於非剛性、非線性的單擺。系統中會有下列幾個可變參數：Excitation ratio、原子間耦合常數、失諧參數等，我們試著改變這些參數，並觀察population difference與相位之間的關係。結果發現隨著參數的不同，系統會產生不同的震盪形式：Rabi regime以及Josephson reg ime，以及一個較少見的震盪模式：two-fixed points regime。如果給予適當的參數此系統可以用來分辨雙能階BEC原子系統的自旋量。

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