Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Express

Enhanced microwave electrometry in weakly interacting Rydberg atoms using a modified formula

binbin wang, Dong Yan, Jin‐Hui Wu

Published Mar 27, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oe.554472

Related papers

Restrictions of microwave electrometry due to nonlocal interactions in Rydberg atoms

Binbin Wang, Xiao-Jun Zhang, Jin‐Hui Wu

Large dipole moments between high Rydberg states have been utilized to measure microwave electric fields based on electromagnetically induced transparency, while nonlocal Rydberg interactions are not suitably addressed yet in most relevant works. Here we adopt a mean-field superatom model to investigate the main restrictions of Rydberg microwave electrometry due to nonlocal interactions in atomic samples of appropriate densities. It is found that accurate microwave measurements can be attained in the linear regime only for dilute enough atomic samples and not too strong probe fields, which jointly determine whether Rydberg excitations are insignificant. This then leads to the critical lines of atomic density and probe intensity, below which the discrepancy between measured and real values is negligible due to vanishing Rydberg interactions, for a fixed microwave or coupling field. Our findings are instructive to identify the optimal conditions for Rydberg microwave electrometry by reaching a compromise between high precisions and high accuracies, requiring, respectively, large and small numbers of Rydberg excitations, when measuring weaker microwave fields.

Physical Review Applied•Aug 12, 2024•3 citations

Electromagnetically induced transparency with cold Rydberg atoms: Superatom model beyond the weak-probe approximation

Yi-Mou Liu, Dong Yan, Xue-Dong Tian +2 more

We present an improved superatom model for examining nonlinear optical responses of cold Rydberg atoms in the regime of electromagnetically induced transparency (EIT). By going beyond the weak-probe approximation, we find that several higher-order collective states should be included to correctly describe the coherent Rydberg excitation of superatoms. Otherwise, numerical results based on the simple ladder system of superatoms will contribute wrong predictions on light intensity and photon correlation of the transmitted probe field. In particular, a great photon-bunching effect will be improperly expected somewhere out of the EIT window in one dilute atomic sample. The essence of this improved superatom model lies in that it can provide reliable predictions on the nonlinear Rydberg-EIT phenomena even in dense atomic samples and may be extended to realize lossless conditional light interactions in appropriate multilevel systems exhibiting dipole blockade.

Physical Review A•Mar 24, 2014•49 citations

Microwave electrometry with bichromatic electromagnetically induced transparency in Rydberg atoms

Mingzhi Han, He Hao, Xiaoyun Song +4 more

Abstract A scheme for measuring microwave (MW) electric (E) fields is proposed based on bichromatic electromagnetically induced transparency (EIT) in Rydberg atoms. A bichromatic control field drives the excited state transition, whose absorption shows three EIT windows. When a MW field drives the Rydberg transition, the EIT windows split and six transmission peaks appear. It is interesting to find that the peak-to-peak distance of transmission spectrum is sensitive to the MW field strength, which can be used to measure MW E-field. Simulation results show that the measurement accuracy could be increased by about 4 times, and the minimum detectable strength of the MW E-field may be improved by about 3 times compared with the common EIT scheme. After the Doppler averaging, the minimum detectable MW E-field strength is about 5 times larger than that without Doppler effect. Also, we investigate other effects on the sensitivity of the system.

EPJ Quantum Technology•Jul 14, 2023•6 citations

Influence of intra-cavity photons and Rydberg interactions on microwave electric field sensing in an atom–cavity coupled system

Aparajita Das, Md. Mabud Hossain, Jayanta K. Saha

The effects of Rydberg interactions, such as van der Waals and dipole–dipole interactions, on the probe absorption, cavity transmission, and reflection in a microwave (MW)-mediated pump–probe laser-driven atom–cavity system are theoretically investigated. The results demonstrate that the nonlinear probe absorption is enhanced by increasing intra-cavity photon numbers and is significantly influenced by the external MW field. Notably, the presence of the MW field alters the characteristics of Autler–Townes (AT) peaks in the absorption spectra and modifies the transmission windows in the cavity-transmitted or reflected intensity profiles. These alterations may facilitate the optimization of Rydberg atom-based MW sensing in atomic environments. Furthermore, we show that the variations in cavity length can considerably affect the smallest detectable MW electric field. The resolution of transmitted and reflected signals is improved under the strong pump field condition. Finally, an MW electric field measurement technique based on the phases of cavity-transmitted and reflected light is proposed, considering the influence of Rydberg interactions.

Journal of the Optical Society of America B•Jan 21, 2025•0 citations

Machine learning enhanced microwave electrometry in many-body Rydberg atoms

Bin-Bin Wang, Dong Yan, Jin‐Hui Wu

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.

Communications Physics•Aug 15, 2026•0 citations

Electromagnetically induced transparency and photon-photon interactions with Rydberg atoms

David Petrosyan, Michael Fleischhauer

We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.

Journal of Physics Conference Series•Mar 14, 2012•3 citations
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.
Large dipole moments between high Rydberg states have been utilized to measure microwave electric fields based on electromagnetically induced transparency, while nonlocal Rydberg interactions are not suitably addressed yet in most relevant works. Here we adopt a mean-field superatom model to investigate the main restrictions of Rydberg microwave electrometry due to nonlocal interactions in atomic samples of appropriate densities. It is found that accurate microwave measurements can be attained in the linear regime only for dilute enough atomic samples and not too strong probe fields, which jointly determine whether Rydberg excitations are insignificant. This then leads to the critical lines of atomic density and probe intensity, below which the discrepancy between measured and real values is negligible due to vanishing Rydberg interactions, for a fixed microwave or coupling field. Our findings are instructive to identify the optimal conditions for Rydberg microwave electrometry by reaching a compromise between high precisions and high accuracies, requiring, respectively, large and small numbers of Rydberg excitations, when measuring weaker microwave fields.
We present an improved superatom model for examining nonlinear optical responses of cold Rydberg atoms in the regime of electromagnetically induced transparency (EIT). By going beyond the weak-probe approximation, we find that several higher-order collective states should be included to correctly describe the coherent Rydberg excitation of superatoms. Otherwise, numerical results based on the simple ladder system of superatoms will contribute wrong predictions on light intensity and photon correlation of the transmitted probe field. In particular, a great photon-bunching effect will be improperly expected somewhere out of the EIT window in one dilute atomic sample. The essence of this improved superatom model lies in that it can provide reliable predictions on the nonlinear Rydberg-EIT phenomena even in dense atomic samples and may be extended to realize lossless conditional light interactions in appropriate multilevel systems exhibiting dipole blockade.
Abstract A scheme for measuring microwave (MW) electric (E) fields is proposed based on bichromatic electromagnetically induced transparency (EIT) in Rydberg atoms. A bichromatic control field drives the excited state transition, whose absorption shows three EIT windows. When a MW field drives the Rydberg transition, the EIT windows split and six transmission peaks appear. It is interesting to find that the peak-to-peak distance of transmission spectrum is sensitive to the MW field strength, which can be used to measure MW E-field. Simulation results show that the measurement accuracy could be increased by about 4 times, and the minimum detectable strength of the MW E-field may be improved by about 3 times compared with the common EIT scheme. After the Doppler averaging, the minimum detectable MW E-field strength is about 5 times larger than that without Doppler effect. Also, we investigate other effects on the sensitivity of the system.
The effects of Rydberg interactions, such as van der Waals and dipole–dipole interactions, on the probe absorption, cavity transmission, and reflection in a microwave (MW)-mediated pump–probe laser-driven atom–cavity system are theoretically investigated. The results demonstrate that the nonlinear probe absorption is enhanced by increasing intra-cavity photon numbers and is significantly influenced by the external MW field. Notably, the presence of the MW field alters the characteristics of Autler–Townes (AT) peaks in the absorption spectra and modifies the transmission windows in the cavity-transmitted or reflected intensity profiles. These alterations may facilitate the optimization of Rydberg atom-based MW sensing in atomic environments. Furthermore, we show that the variations in cavity length can considerably affect the smallest detectable MW electric field. The resolution of transmitted and reflected signals is improved under the strong pump field condition. Finally, an MW electric field measurement technique based on the phases of cavity-transmitted and reflected light is proposed, considering the influence of Rydberg interactions.
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 discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.