We present a simple method to measure the degrees of circular polarization (DoCP) of laser light inside a vacuum chamber and the birefringence of a vacuum window by detecting the fluorescence emitted by Doppler cooled ions in an ion trap. Imperfect laser polarization will cause ions to be pumped to the dark state which will decrease the fluorescence rates of the ions. With a simulation based on the rate equations of the relevant energy levels of 25Mg+ ions, we find that the fluorescence rate is sensitive to the DoCP of the laser. Based on the simulation result, we present a new method to optimize the DoCP of the laser inside the vacuum chamber by adjusting fast axis azimuthal angles of a half-wave plate and a quarter-wave plate outside the vacuum chamber. The laser light is optimized to be circularly polarized with an uncertainty of the DoCP of 7.8 × 10-5. With the obtained polarization information on both sides of the vacuum window and treating the vacuum window as an unknown wave plate, the phase delay and the fast axis azimuthal angle of the vacuum window can be determined in the form of Mueller matrix. The phase delay is determined to be 197.60(39)°, and the fast axis azimuthal angle is determined to be 104.00(5)°.

中文翻译：

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一种简单的真空窗口双折射原位测量方法

我们提出了一种简单的方法，通过检测离子阱中多普勒冷却离子发射的荧光，测量真空室内激光的圆偏振度 (DoCP) 和真空窗口的双折射。不完美的激光偏振会导致离子被泵送到暗态，从而降低离子的荧光率。通过基于 25Mg+ 离子相关能级的速率方程的模拟，我们发现荧光速率对激光的 DoCP 很敏感。基于仿真结果，我们提出了一种通过调整真空腔外的半波片和四分之一波片的快轴方位角来优化真空腔内激光DoCP的新方法。激光被优化为圆偏振，DoCP 的不确定性为 7。8 × 10-5。利用获得的真空窗两侧的偏振信息，将真空窗视为未知波片，可以用穆勒矩阵的形式确定真空窗的相位延迟和快轴方位角。相位延迟确定为197.60(39)°，快轴方位角确定为104.00(5)°。