Electric field measurement using a three-photon double-dark-state model in Rydberg atoms

Rydberg atoms, leveraging their unique properties, have been increasingly investigated and applied in the field of electric field measurement, demonstrating significant advantages. Nevertheless, challenges persist in measuring low-frequency electric fields below kHz, including difficulties in field loading and weak field effects. To address these issues and enable the measurement of weak low-frequency electric fields below kHz, we propose a novel measurement scheme based on a Double-Dark State Three-Photon System (DDSTPS). The proposed scheme overcomes the shielding effect of the glass vapor cell by employing a built-in electrode plate sampling technique and adjusting the electric field loading method. A three-photon double-dark-state system model was established, utilizing an inverted Y-type system structure. This configuration ensures that the dark state generated during the excitation of the atomic ground state is further excited to the intermediate state through photon interactions. The increased population of atoms in the intermediate state significantly enhances the resolution of the transmission spectrum. Compared to conventional two-photon three-level systems, the proposed scheme improves the maximum slope of the electromagnetically induced transparency (EIT) spectral peak by 122.53% and reduces the full width at half maximum (FWHM) of the spectral peak by more than half. When compared to experimental data from two-photon systems, the FWHM is narrowed by a factor of eight, substantially improving the resolution of the EIT spectrum and further advancing the performance of Rydberg atom-based electric field measurements. In addition, this study investigates the response of DDSTPS under low-frequency electric fields and analyzes its optimal operational region.