We propose a scheme to study the topic of manipulating the Goos-Hänchen (GH) shift of the reflected beam in an optomechanical cavity (OMC). Our system consists of two mirrors where one is fixed and the other is movable and a two-level atom is trapped inside the OMC. The fixed mirror is partially reflecting, whereas the movable mirror is perfectly reflecting. We theoretically investigated the behavior of the GH shift in the reflected beam when a Gaussian beam is an incident on the OMC. We find that GH shifts can be greatly enhanced in positive or negative directions via manipulating the quantum parameters such as optomechanical strength $g_{\text{mc}}$ and atom-cavity strength $g_{\text{ac}}$ under the influence of beam width of a Gaussian beam. Besides, we study the GH shift in the case of the partially coherent light beam as an incident probe field. Giant negative GH shift is achieved for an incident partially coherent beam in the presence of $g_{\text{mc}}, g_{\text{ac}}$, a measure of global coherence and beam width of a partially coherent beam. The proposed model provides feasibility in practical experiments for studying the behavior of the GH shift.

中文翻译：

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通过量子控制研究光机械腔中的Goos-Hänchen位移

我们提出了一个方案来研究在光机械腔（OMC）中操纵反射光束的Goos-Hänchen（GH）位移的主题。我们的系统由两个反射镜组成，其中一个是固定的，另一个是可移动的，并且两层原子被困在OMC内部。固定镜可部分反射，而可移动镜可完美反射。我们从理论上研究了高斯光束入射到OMC时反射光束中GH偏移的行为。我们发现，通过操纵量子参数（例如光机械强度），可以在正向或负向大大增强GH位移$G_{\text{mc}}$ 和原子腔强度 $G_{\text{交流电}}$受高斯光束宽度的影响。此外，我们研究了部分相干光束作为入射探测场的情况下的GH偏移。对于存在部分相干光束的情况，在存在$G_{\text{mc}}， G_{\text{交流电}}$，是部分相干光束的整体相干性和光束宽度的度量。所提出的模型为研究GH转变的行为提供了在实际实验中的可行性。