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%.
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 demonstrate the measurement of super low-frequency electric field using Rydberg atoms in an atomic vapor cell with inside parallel electrodes, thus overcoming the low-frequency electric-field-screening effect at frequencies below a few kHz. Rydberg electromagnetically induced transparency (EIT) spectra involving 52 D 5/2 state is employed to measure the signal electric field. An auxiliary DC field is applied to improve the sensitivity. A DC Stark map is demonstrated, where the utilized 52 D 5/2 exhibits m j = 1/2, 3/2, 5/2 Stark shifts and splittings. The m j = 1/2 state is employed to detect the signal field because of its larger polarizability than that of m j = 3/2, 5/2. Also, we show that the strength of the spectrum is dependent on the angle between the laser polarizations and the electric field. With optimization of the applied DC field to shift the m j = 1/2 Rydberg energy level to a high sensitivity region and the laser polarizations to obtain the maximum m j = 1/2 signal, we achieve the detection of the signal electric field with a frequency of 100 Hz down to 214.8 µ V/cm with a sensitivity of 67.9 µ V cm −1 Hz −1/2 , and the linear dynamic range is over 37 dB. Our work extends the measurement frequency of Rydberg sensors to super low frequency with high sensitivity, which has the advantages of high sensitivity and miniaturization for receiving super low frequency.
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%.
We demonstrate a continuously tunable electric field measurement based on the far off-resonant AC stark effect in a Rydberg atomic vapor cell. In this configuration, a strong far off-resonant field, denoted as a local oscillator (LO) field, acts as a gain to shift the Rydberg level to a high sensitivity region. An incident weak signal field with a few hundreds of kHz difference from the LO field is mixed with the LO field in the Rydberg system to generate an intermediate frequency signal, which is read out by Rydberg electromagnetically induced transparency (Rydberg-EIT) spectroscopy. Not like resonant EIT-Autler–Townes spectra, we realize the electric field measurement of the signal frequency from 2 to 5 GHz using a single Rydberg state. The detectable field strength is down to 2.25 μV/cm with sensitivity of the electrometry 712 nV cm−1 Hz−1/2, and a linear dynamic range is over 65 dB. The detectable field strength is comparable with a resonant microwave-dressed Rydberg heterodyne receiver using the same system, which is 0.96 μV/cm with sensitivity of 304 nV cm–1 Hz−1/2. We also show the system has an inherent polarization selectivity feature. Our method can provide high sensitivity of electric field measurement and be extended to arbitrary frequency measurements.
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 high polarizability of Rydberg atoms enables the multi-parameters measurement of electromagnetic fields. In this paper, we report on an atomic antenna based on Rydberg atoms in a room temperature vapor cell. The EIT is a destructive interference spectroscopy with a narrow linewidth and can be used to detect small electric fields through Autler-Townes splitting or Stark shifts. In our experiments, we employ cascade-type two-photon excitation electromagnetically induced transparency (EIT) spectroscopy to measure the shift of the Rydberg energy level. We introduce a low-frequency electric field (~kHz frequency) using a built-in electrode technique in the cesium cell. The interaction between the Rydberg atom and electric field induces the Stark shifts, where the amplitude of the electric field is converted into corresponding two-photon detuning by the EIT effect. Furthermore, the amplitude of the low-frequency electric field is converted into an intensity signal of EIT probe beam. Under weak field conditions, it is an approximate linear relationship between EIT transmission signal and input electric field amplitude, enabling measurement of waveform, amplitude, and frequency. We have demonstrated optical measurements of low-frequency electric field using Rydberg atoms. By increasing the power of probe beam and coupling beam, the EIT can increase the response bandwidth from ~MHz to hundreds of MHz. This provides a scalable approach for measuring high-frequency electric fields.
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.