Abstract: Frequency calibration is a key step in analyzing the spectral frequency shift of electromagnetically induced transparency (EIT) in precision electric field measurements with Rydberg atoms. It is well known that minor frequency shift error (MHz magnitude) in the measurement can lead to significant changes of the field strength inversion results, and if the calibration accuracy is insufficient, the electric field inversion error will be nonlinearly amplified. In this paper, a frequency calibration method based on the saturated absorption spectrum of cesium atom D2 line is proposed, in which six characteristic absorption spectral peaks of cesium atom 6S1/2→6P3/2 transition are captured by designing a back propagation pump-probe optical path, and a time-frequency conversion model is constructed based on the inherent transition frequency of cesium atoms. The experimental results show that the frequency measurement error obtained by this method is kept within 1%, and the frequency calibration coefficient is obtained by multi-peak collaborative calibration. The method is further applied to the electric field measurement of EIT-Stark effect of Rydberg atoms, and it is shown that the fitting accuracy of the quadratic relationship between the frequency shift caused by the external electric field and the field strength is 0.997, with a measurement error less than 0.74%. Compared with the traditional single-peak calibration scheme, the method proposed in this work can greatly improve the anti-interference ability and calibration efficiency in complex noise environment by using the multi-peak collaborative calibration strategy.

Key words: quantum optics, frequency calibration, saturated absorption spectrum, Rydberg atom, cesium atom D2 line