In this paper, we demonstrate a frequency modulation technique to accurately measure the probe Stark shift of optical clocks. The effective coupling strength of the probe laser to the clock transition is precisely controlled by this frequency modulation technique, which is different from the traditional method by controlling the effective coupling strength via changing the probe light power. In an ⁸⁷Sr optical lattice clock, the probe Stark shifts are measured as a function of the square of the bare state coupling strength. The probe Stark shift coefficient of ⁸⁷Sr is experimentally determined as $-6.0(5)\times {10}^{-7}$/Hz using this frequency modulation technique. With the help of frequency modulation, the probe light power can be as large as possible without decreasing the measurement precision and the achieved measurement lever arm is improved by more than one order of magnitude compared with previous results.

中文翻译：

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87Sr光学晶格钟中调频光谱法测量探针斯塔克位移

在本文中，我们展示了一种频率调制技术来准确测量光学时钟的探针斯塔克位移。这种频率调制技术可以精确控制探测激光器对时钟跃迁的有效耦合强度，不同于传统的通过改变探测光功率来控制有效耦合强度的方法。在⁸⁷ Sr 光学晶格钟中，探针斯塔克位移作为裸态耦合强度平方的函数进行测量。⁸⁷ Sr的探针斯塔克位移系数通过实验确定为$-6.0(5)\times {10}^{-7}$/Hz 使用这种频率调制技术。借助频率调制，可以在不降低测量精度的情况下尽可能大的探测光功率，并且实现的测量杠杆臂与之前的结果相比提高了一个数量级以上。