Abstract The electric field sensor based on the electromagnetically induced transparency (EIT) effect and the Stark effect of Rydberg atom (Rydberg sensor) has overcome the limitations of traditional sensors that require standard calibration fields and complex traceability chains. It directly traces the electric field value to fundamental physical constants using the inherent energy level structure and spectral features of atoms. Quantum sensing inherently includes calibration capabilities, making it possible to achieve non-invasive, non-destructive, and precise electric field measurements. Firstly, this article elaborates on the quantum coherent effects of Rydberg atoms interacting with external fields, including the EIT effect and the Stark effect. The EIT effect is a nonlinear quantum coherent optical effect that arises from the interaction of lasers with atoms, resulting in quantum interference between two laser beams and atoms, leading to the formation of a narrow transparent window near the resonant frequency of the detection light field, i.e., the EIT spectral peak. Furthermore, under the influence of low frequency external field, Rydberg atom experience fine-level splitting, causing a frequency shift in the EIT spectrum, known as the Stark frequency shift. By constructing a mathematical model between electric field strength and Stark frequency shift, Rydberg atoms enable all-optical and non-destructive electric field measurements. Secondly, the Rydberg atom sensing measurement system is constructed in the experiment, using two tunable semiconductor lasers to generate weak probe laser at 852 nm, 500 μW, and strong coupling laser at 509 nm, 50 mW. These lasers propagate in opposite directions into a glass cell to excite atoms to Rydberg states. Based on the EIT effect of Rydberg atoms, the change in the atomic spectra under the influence of the external field is observed. The main peak and sub-peaks form a frequency scale with a strict frequency interval, converting the oscilloscope's horizontal axis into a frequency axis, thus transforming electric field values into optical frequency responses. Upon establishing the Rydberg sensor measurement system, error sources are analyzed, and various uncertainty components of the sensor are defined and calculated. These mainly include uncertainties introduced by Rydberg atomic polarization, EIT spectral frequency shift, field inhomogeneity, and other factors. By combining the uncertainties of several factors, the combined relative standard uncertainty is 3.885%, and conservatively, the extended uncertainty is 7.77% when the inclusion probability is greater than 95.45%, in this process, the main influencing factors of uncertainty are identified and recommendations for reducing their impact are proposed. In principle, polarizability and EIT spectral frequency shift uncertainties can be reduced through more advanced computational methods and more precise lasers and photodetectors in the future. Additionally, reducing the field inhomogeneity between plates and optimizing the external optical path design can significantly reduce the overall system uncertainty. Finally, the linearity of the Rydberg sensor is being validated. A series of electric field values is set in the experiment, and a corresponding series of spectral frequency shifts is measured. The least squares method is employed for curve fitting, and the results indicate that the sensor's fitted curve aligns with the theoretical analysis, following a relationship of Δ∝E2. Further consideration of experimental environmental noise yields the fitted relationship: Δnoise=80.414E2-2.72, the constant term represents that Δnoise encompasses a background noise spectrum of 2.72 MHz at zero field, and the coefficient of determination reaches 0.996 9.
Xiao Dongping,Shi Zhuxin,Yan Sheng等. Self-Calibration Analysis and Measuring Uncertainty Assessment of Electric Field Sensors Based on Rydberg Atom[J]. Transactions of China Electrotechnical Society, 2024, 39(17): 5321-5330.
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