中文摘要：

研究了冷原子与法布里-珀罗腔内拉盖尔-高斯横模强耦合相互作用体系的透射光谱，分析了透射光谱与原子在腔中运动轨迹的关系．结果表明，与厄米特-高斯横模相比，拉盖尔-高斯横模的腔场与原子的最大耦合系数几乎不随阶数的增加而变化，使得探测光谱的对比度受模式阶数的影响较小．在拉盖尔-高斯横模场分布的圆环边缘附近，原子运动轨迹的微小偏移会引起透射光谱的很大变化，因此在这些位置可以实现原子运动轨迹的高精度探测．

英文摘要：

A coupled quantum system composed of cavity field and atoms is one of the main research contents of cavity quantum electrodynamics. It can be used to realize single atom manipulation and measurement, and has important significance for studying the interaction between light and the atom, preparing quantum states and quantum entanglement. Current research work mainly focuses on two aspects. One is to achieve the atom trapping via the feedback control of the trapping laser intensity. The other is to measure the single atomic motion in a Fabry-Perot cavity by using Hermite-Gaussian transverse modes. The detection of the atomic trajectories has been realized via the observation of transmission spectra of the strong coupling system composed of cold atoms and Hermite-Gaussian transverse modes in a Fabry-Perot cavity. In order to observe the atomic motion trajectories in the cavity, we theoretically study the transmission spectrum of a strong coupling system composed of cold atoms and Laguerre-Gaussian transverse modes in a Fabry-Perot cavity in this paper. We calculate the relationship between the coupling coefficient and the mode number of Laguerre-Gaussian transverse modes. The result shows that with the increase of Laguerre-Gaussian transverse mode number, the maximum coupling coefficient between the atoms and cavity fields is almost unchanged, so the contrast of the detected spectrum is nearly independent of the mode number. Analysis shows that Laguerre-Gaussian transverse mode provides more abundant information about atomic motion trajectory than Hermite-Gaussian transverse mode. The field distribution of Laguerre-Gaussian transverse mode is ring-shaped. Owing to the ring shape, the atoms dropped at different positions experience different electric field intensities, and the detected transmission spectra are changed. Therefore, we can implement the high precision distinguishment of the atomic trajectories by observing the features of the transmission spectra such as the number of the transmission peaks and their po