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Communications Physics

Machine learning enhanced microwave electrometry in many-body Rydberg atoms

Bin-Bin Wang, Dong Yan, Jin‐Hui Wu

Published Aug 15, 2026• 0 citations
Publisher

Abstract

Precision microwave electrometry using Rydberg atoms is limited by many-body interactions at moderate or not too low excitation densities, which may result in distorted probe spectra of electromagnetically induced transparency (EIT) as predicted by mean-field superatom simulations. This nonlinearity fundamentally restricts measurement accuracy and renders the linear response formula of Autler-Townes splitting to microwave (MW) amplitude inapplicable. Here we present a machine learning (ML) framework assisted by principal component analysis (PCA) that can well overcome this difficulty by mapping distorted noisy EIT spectra directly to MW electric fields. Numerical results show that a basic PCA-assisted regression model reduces the minimal detectable MW field by a few folds as compared to both linear response formula and nonlinear least squares fitting in the interaction-dominant regime. It is of more interest that we can employ a four-class ensemble ML scheme to further reduce the minimal detectable MW field by two orders of magnitude to approach its noise-dependent physical limit and hence largely improve the measurement sensitivity. Our work transforms detrimental Rydberg interactions into beneficial spectral features, providing a practical route toward optimal sensitivity for MW quantum sensing in the nonlinear regime. Rydberg atom-based microwave electrometry is hindered by many-body interactions, distorting probe spectra and limiting measurement accuracy. Here, the authors employ a machine learning framework with principal component analysis to map distorted spectra to microwave fields, significantly enhancing sensitivity and transforming interaction challenges into advantageous spectral features for quantum sensing.

DOI
10.1038/s42005-026-02826-x

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Precision microwave electrometry using Rydberg atoms is limited by many-body interactions at moderate or not too low excitation densities, which may result in distorted probe spectra of electromagnetically induced transparency (EIT) as predicted by mean-field superatom simulations. This nonlinearity fundamentally restricts measurement accuracy and renders the linear response formula of Autler-Townes splitting to microwave (MW) amplitude inapplicable. Here we present a machine learning (ML) framework assisted by principal component analysis (PCA) that can well overcome this difficulty by mapping distorted noisy EIT spectra directly to MW electric fields. Numerical results show that a basic PCA-assisted regression model reduces the minimal detectable MW field by a few folds as compared to both linear response formula and nonlinear least squares fitting in the interaction-dominant regime. It is of more interest that we can employ a four-class ensemble ML scheme to further reduce the minimal detectable MW field by two orders of magnitude to approach its noise-dependent physical limit and hence largely improve the measurement sensitivity. Our work transforms detrimental Rydberg interactions into beneficial spectral features, providing a practical route toward optimal sensitivity for MW quantum sensing in the nonlinear regime. Rydberg atom-based microwave electrometry is hindered by many-body interactions, distorting probe spectra and limiting measurement accuracy. Here, the authors employ a machine learning framework with principal component analysis to map distorted spectra to microwave fields, significantly enhancing sensitivity and transforming interaction challenges into advantageous spectral features for quantum sensing.
We demonstrate the use of an auxiliary microwave field to extend the bandwidth sensitivity of Rydberg-atom-based microwave electrometry. Electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg atom microwave electrometry provide advantageous sensitivity for the resonant detection of microwave (MW) fields because the Stark shift of the target Rydberg state takes the linear form of AT splitting. However, the sensitivity is reduced by several orders of magnitude for detuned MW fields because the Stark shift of the target Rydberg state depends on a weak nonlinear effect. We show that the auxiliary microwave field with appropriate Rabi frequency or detuning could shift the atomic energy levels to bring a particular Rydberg-Rydberg transition of interest for microwave sensing into resonance with the target microwave field. Using the atomic superheterodyne method, we verified the general method that regulates Rydberg energy levels using an auxiliary microwave field. The experimental results of this study confirm that this technique works efficiently for detecting microwave fields detuned by up to 100 MHz from resonance with the field-free Rydberg-Rydberg transition used for sensing. The measurement sensitivity of the detuned target field is increased by a factor of 10 compared with that achieved without the application of the auxiliary dressing field.
The Rydberg-based microwave detection is an all-optical technology that uses the strong coherent interaction between Rydberg atoms and microwave field. Different from the traditional microwave meter, the Rydberg atomic sensing is a new-type microwave detector that transforms the microwave spectrum into a coherent optical spectrum, and arouses increasingly the interests due to its high sensibility. For this kind of sensor, the coherence effect induced by coupling atoms with microwave plays a key role, and the decoherence may reduce the sensitivity. A multi-level Rydberg atomic scheme with optimized quantum coherence, which enhances both the bandwidth and the sensitivity for 4 GHz microwave sensing, is demonstrated experimentally in this work. The enhanced quantum coherence of Rydberg electromagnetically induced transparency (EIT) and microwave induced Autler-Townes (AT) splitting in EIT windows are shown using optical pumping at D1 line. The enhanced sensitivity at 3.4 GHz with 0.3 GHz bandwidth can be realized, based on the enhanced EIT-AT spectrum. The experimental results show that in the stepped Rydberg EIT system, the spectral width of EIT and microwave field EIT-AT can be narrowed by optical pumping (OP), so the sensitivity of microwave electric field measurement can be improved. After optimizing the EIT amplitude and adding single-frequency microwaves, the sensitivity of the microwave electric field measurement observed by the AT splitting interval is improved by 1.3 times. This work provides a reference for utilizing atomic microwave detection.
This study addresses the restrictions imposed by nonlocal van der Waals (vdW) and dipole-dipole (DD) interactions on the microwave electrometry in cold Rydberg atoms driven into the four-level cascade configuration with relatively high excitation densities. Utilizing the mean-field superatom model, we examine, in particular, the effects of vdW and DD interactions on microwave-controlled transmission spectra of a probe field in the regime of electromagnetically induced transparency (EIT). In response to spectral shifts depending on such Rydberg interactions, we propose a modified formula for correctly describing the nonlinear relationship between the microwave electric field and the splitting of two EIT peaks, which could enhance the measurement accuracy. This formula also extends the lower limit set by a certain measurement accuracy into the nonlinear response region by approximately five times, effectively mitigating the restrictions imposed by vdW and DD interactions. Our findings suggest that an accurate measurement of weak microwave electric fields could be achieved under both high and low-density conditions through data correction, yet without altering the experimental method. This research provides an alternative solution for microwave electrometry in weakly interacting atomic gases and highlights its potential applications in integrated quantum devices.
The microwave (MW) field can be measured by the Autler–Townes (AT) splitting of the electromagnetically induced transparency (EIT) spectrum in the Rydberg atomic system; however, the EIT-AT splitting method fails in weak MW fields. We used the amplitude modulation of the MW field to resolve the EIT-AT splitting in weak MW fields. The EIT-AT splitting interval can be directly obtained, and the minimum detectable MW strength is improved by six times compared with the traditional EIT-AT splitting method. The proposed method is more intuitive and convenient for measuring the strength of weak MW fields in practical applications.
The Rydberg-based microwave detection is an all-optical technology that uses the strong coherent interaction between Rydberg atoms and microwave field. Different from the traditional microwave meter, the Rydberg atomic sensing is a new-type microwave detector that transforms the microwave spectrum into a coherent optical spectrum, and arouses increasingly the interests due to its high sensibility. For this kind of sensor, the coherence effect induced by coupling atoms with microwave plays a key role, and the decoherence may reduce the sensitivity. A multi-level Rydberg atomic scheme with optimized quantum coherence, which enhances both the bandwidth and the sensitivity for 4 GHz microwave sensing, is demonstrated experimentally in this work. The enhanced quantum coherence of Rydberg electromagnetically induced transparency (EIT) and microwave induced Autler-Townes (AT) splitting in EIT windows are shown using optical pumping at D1 line. The enhanced sensitivity at 3.4 GHz with 0.3 GHz bandwidth can be realized, based on the enhanced EIT-AT spectrum. The experimental results show that in the stepped Rydberg EIT system, the spectral width of EIT and microwave field EIT-AT can be narrowed by optical pumping (OP), so the sensitivity of microwave electric field measurement can be improved. After optimizing the EIT amplitude and adding single-frequency microwaves, the sensitivity of the microwave electric field measurement observed by the AT splitting interval is improved by 1.3 times. This work provides a reference for utilizing atomic microwave detection.
Abstract We theoretically and experimentally studied quantum microwave electrometry in a cold atomic system using Rydberg electromagnetic induction transparency (EIT) and Autler–Townes splitting (EIT-AT splitting). In cold atoms, a spectral linewidth of ∼500 kHz for EIT was achieved owing to a significant reduction in residual Doppler width, i.e. by at least an order of magnitude, compared to that in vapor cells at room temperature. Therefore, the minimum microwave electric field intensity (E MW) that can be measured is 430 µV cm−1, which is one order higher sensitivity in the EIT-AT regime than that in vapor cells at room temperature. Unlike microwave electrometry in atomic vapor cells, EIT-AT splitting cannot be observed if E MW is so large that the EIT-AT splitting interval Δ f m exceeds the absorption peak width of the cold atom while scanning the frequency of the probe laser (ω p ). Moreover, EIT-AT splitting can be observed if Δ f m exceeds the natural linewidth Γ eg of the intermediate states while scanning the coupling laser (ω c ) and maintains a high spectral resolution with a high signal-to-noise ratio. While scanning ω c , the upper microwave electric field intensity is limited by the scanning range of our setup. Using our system, we measure the maximum field to be 21.6 mV cm−1, nearly three times higher than that of 6.8 mV cm−1 while scanning ω p . The results indicate that the linear range of E MW measured using EIT-AT splitting considerably improves in cold Rydberg atoms.