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

Fast simulation for interacting four-level Rydberg atoms: electromagnetically induced transparency and Autler-Townes splitting

Xinyi Y. I. Xu, Guoda Xie, Jin-Lou Ma, Lei Ying, Jinpeng Yuan, Zhixiang Huang, Wei E. I. Sha

Published May 24, 2024• 9 citations
Publisher

Abstract

Quantum sensing using Rydberg atoms is an emerging technology for precise measurement of electric fields. However, most existing computational methods are all based on a single-particle model and neglect Rydberg-Rydberg interaction between atoms. In this study, we introduce the interaction term into the conventional four-level optical Bloch equations. By incorporating fast iterations and solving for the steady-state solution efficiently, we avoid the computation of a massive 4 N × 4 N dimensional matrix. Additionally, we apply the Doppler frequency shift to each atom used in the calculation, eliminating the requirement for an additional Doppler iteration. These schemes allow for the calculation of the interaction between 7000 atoms around one minute. Based on the many-body model, we investigate the Rydberg-Rydberg interaction of Rydberg atoms under different atomic densities. Furthermore, we compare our results with the literature data of a three-level system and the experimental results of our own four-level system. The results demonstrate the validity of our model, with an effective error of 4.59% compared to the experimental data. Finally, we discover that the many-body model better predicts the linear range for measuring electric fields than the single-particle model, making it highly applicable in precise electric field measurements.

DOI
10.1364/oe.523897

Related papers

Fast Simulation of Many-Body Rydberg Atomic Systems for Quantum Sensing

Xinyi Y. I. Xu, Guoda Xie, Lei Ying +2 more

Quantum sensing based on Rydberg atoms is an emerging technology for electric-field measurement. Theoretical and numerical studies were generally limited by the many-body effect in atomic ensembles. In this work, we initially derived a many-body dynamic equation by incorporating the Rydberg- Rydberg interaction into the four-level optical Bloch equation. Particularly, we proposed a fast steady-state solution as an alternative to the transient one. As a result, we ingeniously replaced the computationally expensive matrix operations with a linearly iterative process, enabling rapid convergence within few steps while considering the Doppler frequency shift. This approach made it possible to simulate the interaction of 7000 atoms in less than a minute. Based on the many-body model, we investigated the phenomenon of electromagnetically induced transparency (EIT) and Autler- Townes (AT) splitting under varying atomic gas densities; and compared the numerical results with experimental data. The comparison revealed a relatively-low error of 4.59% for the EITAT simulation by the many-body model. Moreover, we found that the linear dynamic range of the quantum sensing shrinks when considering the many-body interaction.

Digest - IEEE Antennas and Propagation Society. International Symposium•Jul 14, 2024•0 citations

Solving the Detection Model of Rydberg Atomic Electric Field Based on Time Parallel Method

Ren-Di Tian, Wenjie Ding, Guoda Xie +1 more

Rydberg atoms are emerging as a powerful tool for quantum precision measurement, owing to their broad bandwidth and high sensitivity to microwave electric fields. These properties make Rydberg atoms a key focus of contemporary research in the field. To better understand their detection capabilities, a semiclassical model based on optical Bloch equations is developed. A time-parallel algorithm is then introduced to efficiently solve the system's equations, significantly improving computational performance. In the case of a four-level detection system, this algorithm achieves a 50-fold increase in efficiency compared to traditional iterative methods. The results highlight the effectiveness of the time-parallel approach in enhancing both computational speed and detection accuracy. This methodology provides a reliable theoretical framework that could drive future advancements in quantum precision measurement technologies.

International Conference on Microwave and Millimeter Wave Technology (ICMMT)•May 19, 2025•0 citations

Atomic spectra in a six-level scheme for electromagnetically induced transparency and Autler-Townes splitting in Rydberg atoms

Amy K. Robinson, Alexandra B. Artusio‐Glimpse, Matthew T. Simons +1 more

We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting in Rydberg rubidium atoms for a six-level excitation scheme. In this six-level system, one radio-frequency field simultaneously couples to two high-laying Rydberg states and results in interesting atomic spectra observed in the EIT lines. We present experimental results for several excitation parameters. We also present two theoretical models for this atomic system, where these two models capture different aspects of the observed spectra. One is a six-level model used to predict dominant spectral features and the other a more complex eight-level model used to predict the full characteristics of this system. Both models shows very good agreement with the experimental data.

arXiv:2009.13612•Physical Review A•Feb 5, 2021•45 citations

Enhanced sensing of 3.4 GHz microwave in multi-level Rydberg atomic system

Jingjing XUE, Ruonan LI, Hu Xuesong +3 more

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.

Acta Physica Sinica•Jan 1, 2025•1 citation

Enhanced sensing of 3.4 GHz microwave in multi-level Rydberg atomic system

Jingjing, Xue, Ruonan, Li, Hu Xuesong +3 more

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.

arXiv:2508.01260•Aug 2, 2025•0 citations

Nonlinearity of Microwave Electric Field Coupled Rydberg Electromagnetically Induced Transparency and Autler-Townes Splitting

Liping Hao, Yongmei Xue, Jiabei Fan +3 more

An electromagnetically induced transparency (EIT) of a cascade-three-level atom involving Rydberg level in a room-temperature cell, formed with a cesium 6S 1 / 2-6P 3 / 2-66 S 1 / 2 scheme, is employed to detect the Autler-Townes (AT) splitting resulted with a 15.21-GHz microwave field coupling the 66 S 1 / 2 → 65 P 1 / 2 transition. Microwave field induced AT splitting, f A T, is characterized by the distance of peak-to-peak of an EIT-AT spectrum. The f A T dependence on the microwave Rabi frequency, Ω M W , demonstrates two regions, the strong-coupling linear region, f A T ≈ Ω M W and the weak-coupling nonlinear region, f A T ≲ Ω M W. The f A T dependencies on the probe and coupling Rabi frequency are also investigated. Using small probe- and coupling-laser, the Rabi frequency is found to enlarge the linear regime and decrease the uncertainty of the microwave field measurements. The measurements agree with the calculations based on a four-level atomic model.

Applied Sciences•Apr 25, 2019•11 citations
Quantum sensing using Rydberg atoms is an emerging technology for precise measurement of electric fields. However, most existing computational methods are all based on a single-particle model and neglect Rydberg-Rydberg interaction between atoms. In this study, we introduce the interaction term into the conventional four-level optical Bloch equations. By incorporating fast iterations and solving for the steady-state solution efficiently, we avoid the computation of a massive 4 N × 4 N dimensional matrix. Additionally, we apply the Doppler frequency shift to each atom used in the calculation, eliminating the requirement for an additional Doppler iteration. These schemes allow for the calculation of the interaction between 7000 atoms around one minute. Based on the many-body model, we investigate the Rydberg-Rydberg interaction of Rydberg atoms under different atomic densities. Furthermore, we compare our results with the literature data of a three-level system and the experimental results of our own four-level system. The results demonstrate the validity of our model, with an effective error of 4.59% compared to the experimental data. Finally, we discover that the many-body model better predicts the linear range for measuring electric fields than the single-particle model, making it highly applicable in precise electric field measurements.
Quantum sensing based on Rydberg atoms is an emerging technology for electric-field measurement. Theoretical and numerical studies were generally limited by the many-body effect in atomic ensembles. In this work, we initially derived a many-body dynamic equation by incorporating the Rydberg- Rydberg interaction into the four-level optical Bloch equation. Particularly, we proposed a fast steady-state solution as an alternative to the transient one. As a result, we ingeniously replaced the computationally expensive matrix operations with a linearly iterative process, enabling rapid convergence within few steps while considering the Doppler frequency shift. This approach made it possible to simulate the interaction of 7000 atoms in less than a minute. Based on the many-body model, we investigated the phenomenon of electromagnetically induced transparency (EIT) and Autler- Townes (AT) splitting under varying atomic gas densities; and compared the numerical results with experimental data. The comparison revealed a relatively-low error of 4.59% for the EITAT simulation by the many-body model. Moreover, we found that the linear dynamic range of the quantum sensing shrinks when considering the many-body interaction.
Rydberg atoms are emerging as a powerful tool for quantum precision measurement, owing to their broad bandwidth and high sensitivity to microwave electric fields. These properties make Rydberg atoms a key focus of contemporary research in the field. To better understand their detection capabilities, a semiclassical model based on optical Bloch equations is developed. A time-parallel algorithm is then introduced to efficiently solve the system's equations, significantly improving computational performance. In the case of a four-level detection system, this algorithm achieves a 50-fold increase in efficiency compared to traditional iterative methods. The results highlight the effectiveness of the time-parallel approach in enhancing both computational speed and detection accuracy. This methodology provides a reliable theoretical framework that could drive future advancements in quantum precision measurement technologies.
We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting in Rydberg rubidium atoms for a six-level excitation scheme. In this six-level system, one radio-frequency field simultaneously couples to two high-laying Rydberg states and results in interesting atomic spectra observed in the EIT lines. We present experimental results for several excitation parameters. We also present two theoretical models for this atomic system, where these two models capture different aspects of the observed spectra. One is a six-level model used to predict dominant spectral features and the other a more complex eight-level model used to predict the full characteristics of this system. Both models shows very good agreement with the experimental data.
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.
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.
An electromagnetically induced transparency (EIT) of a cascade-three-level atom involving Rydberg level in a room-temperature cell, formed with a cesium 6S 1 / 2-6P 3 / 2-66 S 1 / 2 scheme, is employed to detect the Autler-Townes (AT) splitting resulted with a 15.21-GHz microwave field coupling the 66 S 1 / 2 → 65 P 1 / 2 transition. Microwave field induced AT splitting, f A T, is characterized by the distance of peak-to-peak of an EIT-AT spectrum. The f A T dependence on the microwave Rabi frequency, Ω M W , demonstrates two regions, the strong-coupling linear region, f A T ≈ Ω M W and the weak-coupling nonlinear region, f A T ≲ Ω M W. The f A T dependencies on the probe and coupling Rabi frequency are also investigated. Using small probe- and coupling-laser, the Rabi frequency is found to enlarge the linear regime and decrease the uncertainty of the microwave field measurements. The measurements agree with the calculations based on a four-level atomic model.