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EPJ Quantum Technology

Optical spectral features and electric field inversion method for Rydberg atoms under ultra-low frequency electric field

Dongping Xiao, Sheng Yan, Ling Chen, Huaiqing Zhang

Published Jul 8, 2025• 4 citations
Publisher

Abstract

The quantum measurement of the microwave electric field based on Rydberg atoms developed in recent years has shown promise for enhancing accuracy, sensitivity and stability. However, the study of ultra-low frequency electric field measurements in power systems is still in its early stages, presenting new challenges for Rydberg-based measurement techniques. In this work, a ladder-type two-photon three-level structure of Cs atoms is selected, and the corresponding experimental system is constructed. Two kinds of laser control schemes, which are referred to as mismatch and match measurement schemes, are then proposed, and the quantum effect’s optical spectrum is obtained by using the two measurement schemes. After these measured spectral properties are compared, the match measurement scheme is chosen for real-time measurement of ultra-low frequency electric fields. Additionally, dynamic models of the interactions among the laser field, ultra-low frequency electric field and atoms are derived, on the basis of which theoretical simulations are being conducted to study the effects of the input parameters of the electric field and laser power on the optical spectrum. On the basis of the optical spectral features, an inversion method for the excitation electric field in real time is proposed, and its effectiveness is demonstrated.

DOI
10.1140/epjqt/s40507-025-00389-4

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Journal of Physics D Applied Physics•Sep 9, 2025•1 citation
The quantum measurement of the microwave electric field based on Rydberg atoms developed in recent years has shown promise for enhancing accuracy, sensitivity and stability. However, the study of ultra-low frequency electric field measurements in power systems is still in its early stages, presenting new challenges for Rydberg-based measurement techniques. In this work, a ladder-type two-photon three-level structure of Cs atoms is selected, and the corresponding experimental system is constructed. Two kinds of laser control schemes, which are referred to as mismatch and match measurement schemes, are then proposed, and the quantum effect’s optical spectrum is obtained by using the two measurement schemes. After these measured spectral properties are compared, the match measurement scheme is chosen for real-time measurement of ultra-low frequency electric fields. Additionally, dynamic models of the interactions among the laser field, ultra-low frequency electric field and atoms are derived, on the basis of which theoretical simulations are being conducted to study the effects of the input parameters of the electric field and laser power on the optical spectrum. On the basis of the optical spectral features, an inversion method for the excitation electric field in real time is proposed, and its effectiveness is demonstrated.
Introduction: Rydberg atoms are ideal for measuring electric fields due to their unique physical properties. However, low-frequency electric fields below MHz can be challenging due to the accumulation of ionized free electrons on the atomic vapor cell’s surface, acting as a shield. Method: This paper proposes a Cavity-enhanced three-photon system (CETPS) measurement scheme, which uses a long-wavelength laser to excite the Rydberg state, reducing atomic ionization and enhancing detection spectrum resolution. A theoretical model is proposed to explain the quantum coherence effect of the light field, measured electric field, and the atomic system. Result: The results show that the proposed scheme significantly increases the electromagnetically induced transparency (EIT) spectral peak and narrows the spectral width, resulting in the maximum slope increasing by more than an order of magnitude. Discussion: The paper also discusses the impact of the Rabi frequency of the two laser fields and the coupling coefficient of the optical cavity on the transmission spectrum amplitude and linewidth, along with the optimal configuration of these parameters in the CEPTS scheme.
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.
Atom in Rydberg state has large polarizability, large electric dipole and low ionization threshold field. It is very sensitive to electric field, therefore it can be used to measure the amplitude of electric field, especially the microwave electric field. The new developed scheme is based on quantum interference effects (electromagnetically induced transparency and Autler-Townes splitting) in Rydberg atoms. Instead of the direct amplitude measurement, this method tests the Rabi frequency value of the transmission spectrum which is determined by the microwave electric field strength and the corresponding atom nature. The minimum measured strengths of microwave electric fields are far below the standard values obtained by traditional antenna methods. Compared with the traditional methods, this new scheme has several advantages, such as self-calibration, non-perturbation to the measured field and independence of the probe length. Besides, this scheme can also be used to measure the polarization direction of microwave electric field and realize sub-wavelength imaging. Through adjusting the wavelength of coupling laser, a broadband 1-500 GHz microwave electric field measurement can be achieved. This new scheme is benefitial to conducting the continue electric field measurement and the miniaturization of the test equipment. In this paper, the researches about using Rydberg atom to measure electric field with high precision are reviewed. The basic theory and experimental techniques are introduced. Finally, we discuss a promising method of using Rydberg atom interferometer to detect the accumulated phase in the process of interaction between electric field and Rydberg atoms. This method converts amplitude measurement into phase test, which may improve the precision and sensitivity.
High-precision Rydberg atom EIT spectroscopy has significant application value in studying the interactions between Rydberg atoms, the energy level structure of Rydberg atoms, and the precise measurement of electric fields. Therefore, it is of great importance to study the parameters influencing atomic EIT spectroscopy. In this paper, a theoretical model for the generation of a two-photon three-level EIT spectrum is established, and the influence of the coupling light's Rabi frequency and corresponding power on the EIT spectrum is theoretically explored. The changes in the EIT spectrum's amplitude and FWHM caused by variations in the coupling light power are experimentally verified. Furthermore, the effect of the overlap between the probe light and the coupling light in the atomic vapor cell on the EIT spectrum is investigated. The results show that as the laser power increases, the amplitude of the EIT spectrum first increases and then decreases, while the FWHM increases. The optimal coupling light laser power of 35 mW is determined using the quality factor. A decrease in the overlap of the two lasers leads to a reduction in the EIT spectrum's amplitude. This study provides a reference for selecting coupling light parameters and improving the accuracy of electric field measurements using Rydberg atoms.
Quantum measurement based on Rydberg atoms enables self-calibrated, high-precision, and high-dynamic-range electric field sensing, meeting the stringent demands of modern power systems. However, low-frequency AC voltage measurement using Rydberg atoms is still in its early stage, with key techniques yet to mature. This paper proposes a dual-photon, three-level excitation scheme with both probe and coupling lasers frequencylocked to atomic transitions. Then the light intensity of transmitted probe varies periodically with the applied AC field, allowing extraction of amplitude, frequency, and phase for electric field reconstruction. The mathematical models of light intensity after dual-laser locking and applied electric field are established in this paper. To suppress the influence of signal distortion and noise on measurement accuracy, an improved least mean square (LMS) adaptive algorithm is developed, dynamically adjusting the step size to mitigate non-stationary noise. Integrating the conversion relationships and processing technologies into the voltage measurement system based on Rydberg atoms, the experimental measurement for35/3kV35/\sqrt{} 3 \text{kV}35/​3kVpower-frequency voltage shows the measurement accuracy can reach class 0.2.
Abstract Rydberg atoms will produce the Stark effect under the action of non-resonant electric fields. Due to Rydberg atoms’ inherent energy level characteristics, they show sensitivity to electric fields and excellent self-calibration, which makes them promising in electric field measurement. In this paper, an experimental platform is established by fixing the probe and coupling laser frequencies. The ‘amplitude attenuation’ phenomenon of resonance point laser intensity oscillation caused by the change of electric field frequency is observed and analyzed, and its evolution trend is clarified; then, in different frequency bands (Hz band and kHz band), the density matrix equations are constructed and solved respectively in combination with the atomic energy level excitation structure, through which the dynamic response characteristics between atoms and AC electric fields are revealed. Finally, this paper proposes the Hz band electric field measurement method and the kHz band electric field measurement method: (1) in the steady-state solution of the electromagnetically induced transparency (EIT)-Stark mathematical model, the laser intensity curve at the resonance point laser intensity is inverted into an electric field waveform in real time to achieve Hz electric field measurement based on Rydberg atoms; (2) in the non-steady-state solution of the EIT-Stark mathematical model, the electric field amplitude is predicted by identifying the laser intensity amplitude and frequency at the laser intensity curve with the help of a neural network, thus achieving kHz electric field measurement based on Rydberg atoms. Experimental results show that the accuracy of the Hz band electric field measurement method proposed in this paper is greater than 99%, and the accuracy of the kHz band electric field measurement method is greater than 96%.