Quantum electric field measurement based on the Stark effect of Rydberg atoms has the advantages of high precision, traceability, and self-calibration. However, the current perturbation-based modeling method for the relationship between field strength and energy level shift only applies to weak fields. In applications such as power systems, electric fields can reach the kV/m level. Under such electric fields, the Rydberg state cannot ignore the strong coupling effect between adjacent highlstates, and the relationship model established by perturbation approximation is no longer accurate. This paper introduces the Landau–Zener (L-Z) tunneling model to address this limitation and describes the coupling between energy levels. It is used to construct the Rydberg atomic Hamiltonian, which includes highlstate coupling. We calculate the eigenenergies of Rydberg atoms at various electric-field strengths via matrix diagonalization, thereby obtaining a discrete mapping between field strength and energy-level shift in the strong-field regime. Subsequently, the hybrid Levenberg–Marquardt (LM) and Bayesian polynomial regression (BPR) neural network (LM-BPR) was constructed to train the discrete mapping into a continuous prediction model. In addition, the dynamic programming (DP) algorithm performs global ridge tracking on the electromagnetically induced transparency (EIT) spectrum and extracts frequency shift information from the complex EIT spectrum. Combining the above methods, strong electric field inversion based on Rydberg atoms was achieved. Experiments using the 28D5/2 Rydberg state demonstrate electric-field measurements up to 7 kV/m, with a relative error of 2.9%.
Quantum electric field measurement based on the Stark effect of Rydberg atoms has the advantages of high precision, traceability, and self-calibration. However, the current perturbation-based modeling method for the relationship between field strength and energy level shift only applies to weak fields. In applications such as power systems, electric fields can reach the kV/m level. Under such electric fields, the Rydberg state cannot ignore the strong coupling effect between adjacent highlstates, and the relationship model established by perturbation approximation is no longer accurate. This paper introduces the Landau–Zener (L-Z) tunneling model to address this limitation and describes the coupling between energy levels. It is used to construct the Rydberg atomic Hamiltonian, which includes highlstate coupling. We calculate the eigenenergies of Rydberg atoms at various electric-field strengths via matrix diagonalization, thereby obtaining a discrete mapping between field strength and energy-level shift in the strong-field regime. Subsequently, the hybrid Levenberg–Marquardt (LM) and Bayesian polynomial regression (BPR) neural network (LM-BPR) was constructed to train the discrete mapping into a continuous prediction model. In addition, the dynamic programming (DP) algorithm performs global ridge tracking on the electromagnetically induced transparency (EIT) spectrum and extracts frequency shift information from the complex EIT spectrum. Combining the above methods, strong electric field inversion based on Rydberg atoms was achieved. Experiments using the 28D5/2 Rydberg state demonstrate electric-field measurements up to 7 kV/m, with a relative error of 2.9%.
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%.
Rydberg-assisted atomic electrometry with thermal vapors offers a promising approach for detecting external electric fields. However, this technique presents significant challenges for measuring low frequencies due to the effects of metal-alkali atoms adsorbed on the interior surface of the vacuum chamber. In this work, we apply high-contrast Rydberg electromagnetically induced transparency (EIT) spectroscopy to systematically investigate these effects, including the influence of laser power and electric field strength. We demonstrate the ability to measure electric field frequencies ranging from 10 Hz to 1 MHz. Additionally, this study identifies a fundamental limit for data capacity in such measurements. Furthermore, we propose a method for precise Stark shift measurements by locking the coupling laser to Zeeman-split Rydberg EIT peaks. Using the Zeeman shift in a reference cell as a stable frequency reference, we are able to track Stark-induced shifts in a science cell and confirm excellent agreement with theoretical predictions. These results provide valuable insights for future precision measurement techniques and field sensing applications based on Rydberg atom systems.
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%.
We report on the measurement of Stark shifted energy levels of 87 Rb Rydberg atoms in static electric fields by means of electromagnetically induced transparency (EIT). Electric field strengths of up to 500 V cm −1 , ranging beyond the classical ionization threshold, were applied using electrodes inside a glass cell with rubidium vapour. Stark maps for principal quantum numbers n = 35 and n = 70 have been obtained with high signal-to-noise ratio for comparison with results from ab initio calculations following the method described in (Zimmerman et al 1979 Phys. Rev. A 20 2251 ), which was originally only verified for states around n = 15. We also calculate the dipole matrix elements between low-lying states and Stark shifted Rydberg states to give a theoretical estimate of the relative strength of the EIT signal. The present work significantly extends the experimental verification of this numerical method in the range of both high principal quantum numbers and high electric fields with an accuracy of up to 2 MHz.
Significant progress has been made in atom-based measurements of length, time, gravity and electromagnetic fields in recently years. Rydberg atom-based microwave electric field measurement, using electromagnetically induced transparency (EIT) in room temperature alkali-metal vapors, has been extensively investigated and aroused the broad interest. This approach may establish a new standard for the measurements of microwave (MW) and radio frequency (RF) electric fields.In this review, we describe the work on a new method of measuring electric fields based on quantum interference by using either cesium or rubidium atoms contained in a dielectric vapor cell. Rydberg atoms with principal quantum number n >>1 have large direct current (DC) polarizabilities and microwave transition dipole moments, thereby making them extremely sensitive to external electric fields. Using the Rydberg three-level EIT to detect the level splitting and shift that is induced by the external field, we can realize a rapid and robust self-calibration method of measuring the electric field in a frequency range from 0.01 GHz to 1000 GHz. For the MW electric field (frequency range > 1 GHz), the MW field causes the Rydberg states to split, known as an Autler-Townes splitting (A-T) effect when the applied microwave can resonate with adjacent Rydberg states. The MW coupled A-T splitting is proportional to the applied electric field strength, from which the field strength is measured. Using the EIT window, a high sensitivity of 3 μV·cm-1·Hz-1/2 and small electric field of 1 μV/cm are expected to be achieved with a modest setup, and the limitations of the sensitivity are also addressed in the review. For the RF field at frequency mj EIT lines, and avoided crossings formed with the fine-structure levels of equal mj and different J's, which is used to calibrate and measure the RF field amplitude. On the other hand, the dependence of the EIT-line strength on the RF field polarization provides a fast and robust polarization measurement of RF fields based on matching experimental data with a theoretical simulation. The measurements of minimum strengths and sensitivity of RF fields based on Rydberg atoms are one order magnitude below the values obtained by traditional antenna methods. The atom-based field measurement paves the way for determining fields through calibration-free, invariable atomic properties and miniaturization. We also propose its various potential applications in the future.
Electric field measurement based on Rydberg atom is an emerging development direction, which has attracted attention because of its excellent characteristics such as high precision, high stability, and self-calibration, and also has a large application space in power system. When a non-resonant frequency electric field acts on a Rydberg atom, the frequency shift of the transmission spectrum peak and the electric field strength satisfy a specific mathematical relationship. However, the electric field causes the Rydberg atomic degenerate energy level to split to form an EIT-Stark spectrum containing multiple fine energy level information, which has many difficulties in accurate and online feature extraction of this spectral peak, and affects the accurate inversion of the electric field. In order to solve the above problems, this paper proposes a feature extraction method based on multi-scale wavelet transform to solve the spectral peak feature recognition in the case of transmission peak overlap and transmission peak serious depression. In addition, the scope of feature extraction is limited based on the principle of maximizing variance between classes, and the redundancy of the algorithm is reduced to meet the needs of engineering applications. Compared with the Gaussian fitting method and the multi-scale wavelet transform peak finding method based on mass spectrometry, the feature extraction method proposed in this paper has the advantage in two indicators: the peak false detection rate and the true positive rate. In addition, the method proposed in this paper is integrated into the quantum measurement of electric field, and the error of the measured results is less than 1% after simple parameter compensation for the non-parallel metal plates and the interference of the environmental electric field, which is superior to the existing traditional electric field measurement methods and the conventional EIT-Stark spectral processing method, and also effectively controls the measurement error of the small electric field without significant energy level splitting.