Rydberg atom electric field based quantum measurement method and polarization influence analysis

The interaction between an electric field and the energy levels of Rydberg states results in the Stark effect, which can be used for quantum detection by measuring the frequency shift in electromagnetically induced transparency (EIT) spectra. By using the functional relationship between the frequency shift and the electric field, it is possible to measure the electric field in question. However, the mismatch between the probe laser and the polarization direction of the coupled laser leads to errors in the measurement of the frequency shift, affecting the accurate measurement of the electric field. In this work, the Schrödinger equation is solved by perturbation method to derive the functional relationship between the energy offset and the electric field strength. Then, the functional relationship between the energy offset and the electric field strength is brought into the solution of the density matrix equation, and the influences of the polarization direction of the detected light and coupled light on the EIT-Stark mathematical model are analyzed. Then an internal electrode method is used to prevent shielding effects caused by alkali metal atoms adhering to the surface of the atomic vapor cell, thereby enabling the application of the electric field. The calibration of the Rydberg state polarisation rate is achieved by using a standard source and measuring the frequency shift of the EIT spectrum. Finally, the effects of polarisation mismatch on the measurement results of EIT spectrum and the electric field are verified by modulating the laser polarization direction. The experimental data show that when the polarization directions of the probe laser and coupled laser are parallel to each other, it is the most matched polarization direction for the lasers, the peak value of the EIT spectrum is the largest, and the maximum relative error of the electric field measurement is 1.67%. When the angle between the polarisation directions of the probe light and the coupled light laser is 45°, the laser polarisation mismatch is the most severe, the EIT spectral peak is the lowest and the maximum relative error of the electric field measurement is 10.24%.