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

Applied Sciences

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

Liping Hao, Yongmei Xue, Jiabei Fan, Yuechun Jiao, Jianming Zhao, Suotang Jia

Published Apr 25, 2019• 11 citations
Publisher

Abstract

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.

DOI
10.3390/app9081720

Related papers

Rydberg electromagnetically induced transparency and Autler–Townes splitting in a weak radio-frequency electric field*

Liping Hao, Yongmei Xue, Jiabei Fan +3 more

Abstract We utilize an electromagnetically induced transparency (EIT) of a three-level cascade system involving Rydberg state in a room-temperature cell, formed with a cesium 6S1/2–6P3/2–66S1/2 scheme, to investigate the Autler–Townes (AT) splitting resulting from a 15.21-GHz radio-frequency (RF) field that couples the | 66 S 1 / 2 〉 → | 65 P 1 / 2 〉 Rydberg transition. The radio-frequency electric field induced AT splitting, γ AT, is defined as the peak-to-peak distance of an EIT-AT spectrum. The dependence of AT splitting γ AT on the probe and coupling Rabi frequency, Ωp and Ωc, is investigated. It is found that the EIT-AT splitting strongly depends on the EIT linewidth that is related to the probe and coupling Rabi frequency in a weak RF-field regime. Using a narrow linewidth EIT spectrum would decrease the uncertainty of the RF field measurements. This work provides new experimental evidence for the theoretical framework in [J. Appl. Phys. 121, 233106 (2017)].

Chinese Physics B•May 1, 2019•13 citations

Microwave electromagnetically induced transparency and Aulter-Townes spectrum of cesium Rydberg atom

Fan Jia-Bei, Jiao Yue-Chun, Hao Li-Ping +3 more

We present an electromagnetically induced transparency and Aulter-Townes (EIT-AT) spectrum of a Rydberg three-level atom that is dressed with a microwave field in a room-temperature cesium cell. The EIT is a quantum coherent effect produced by the interaction of atoms with electromagnetic waves, which leads to the decrease of the absorption for a weak resonant probe laser. AT splitting refers to the phenomenon, that the absorption line splits when an electromagnetic field that is in resonance or near resonance acts on the transition of atoms. Rydberg atoms are extremely sensitive to an external electric field due to their large polarizabilities and microwave transition dipole moments, which can be used to measure the external field. In this work, a Rydberg three-level EIT is used to detect Rydberg atom and AT splitting induced by the microwave field. Cesium levels 6S1/2, 6P3/2 and 50S1/2 constitute a Rydberg three-level system, in which a weak probe laser locking to the transition from 6S1/2 to 6P3/2 couples ground-state transition and the strong coupling laser resonates on the Rydberg transition from 6P2/3 to 50S1/2. The two Rydberg levels 50S1/2 and 50P1/2 are coupled with the microwave field at a frequency of 30.852 GHz, leading to the AT splitting of EIT line and forming an EIT-AT spectrum, which is used to measure the electric field amplitude of microwave. In order to further study the EIT-AT splitting characteristics of the Rydberg levels, we carry out a series of measurements by changing the microwave field. The experimental results show a broadened EIT-AT signal for the weak field range and the four-peak spectrum for the strong field, which is attributed to the inhomogeneity of the microwave field. The microwave in cesium cell, emitted by a function generator, shows inhomogeneous behavior such that the atoms interacting with the laser field experience the different fields, leading to the line broadened and multi-peak EIT-AT spectra. For the microwave transition of nS1/2-nP1/2 in this paper, a pair of EIT-AT lines should be obtained for an electric field value. The broadening of the EIT-AT spectrum and the multi-peak structure here are due to the inhomogeneity of the microwave field measurement. We propose a method to increase the spatial resolution by reducing the length of cesium cell. The result in this work provides a method of measuring the field amplitude and monitoring the distribution of microwave electric field, meanwhile the spatial resolution of the measurements can be improved by reducing the size of the cell.

Acta Physica Sinica•Jan 1, 2018•14 citations

Microwave field sensor based on cold cesium Rydberg three-photon electromagnetically induced spectroscopy

Yuan-Yuan 圆圆 Wu 吴, Yunhui He, Yue-Chun Jiao +1 more

Abstract We present the electromagnetically induced transparency (EIT) spectra of cold Rydberg four-level cascade atoms consisting of the 6S1/2 → 6P3/2 → 7S1/2 → 60P3/2 scheme. A coupling laser drives the Rydberg transition, a dressing laser couples two intermediate levels and a weak probe laser probes the EIT signal. We numerically solve the Bloch equations and investigate the dependence of the probe transmission rate signal on the coupling and dressing lasers. We find that the probe transmission rate can display an EIT or electromagnetically induced absorption (EIA) profile, depending on the Rabi frequencies of the coupling and dressing lasers. When we increase the Rabi frequency of the coupling laser and keep the Rabi frequency of the probe and dressing laser fixed, flipping of the EIA to EIT spectrum occurs at the critical coupling Rabi frequency. When we apply a microwave field coupling the transition 60P3/2 → 61S1/2, the EIT spectrum shows Autler–Townes splitting, which is employed to measure the microwave field. The theoretical measurement sensitivity can be 1.52 × 10−2 nV⋅cm−1⋅Hz−1/2 at the EIA–EIT flipping point.

Chinese Physics B•Aug 30, 2024•3 citations

Spatial distribution measurement of the microwave electric field strength via the Autler-Townes effect of Rydberg atom

Jiasheng Liu, Hao Zhang, Zhenfei Song +2 more

We demonstrate the high-resolution spatial feature measurement of microwave electric field using an cesium atomic vapor cell based on the electromagnetically induced transparency (EIT) spectrum of133Cs Rydberg atom. The microwave electric field with the frequency of 6.95 GHz couples the transition of 47D5/2→48P3/2 Rydberg states. The EIT spectrum of a 6S1/2-6P3/2-47D5/2 ladder system will split by the Autler-Townes(AT) effect under the microwave electric field. The dependence of AT splitting separation on the microwave electric fields strength is observed. Moreover, we present the imaging of the spatial feature of microwave electric field in the atomic vapor cell. The theoretical maximum spatial resolution is about λMw/430.

IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization•Jul 1, 2016•1 citation

Transition from electromagnetically induced transparency to Autler–Townes splitting in cold cesium atoms

Liping Hao, Yuechun Jiao, Yongmei Xue +4 more

Electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS) are two similar yet distinct phenomena that modify the transmission of a weak probe field through an absorption medium in the presence of a coupling field, featured in a variety of three-level atomic systems. In many applications it is important to distinguish EIT from ATS splitting. We present EIT and ATS spectra in a three-level cascade system, involving cold cesium atoms in the Rydberg state. The EIT linewidth, γ EIT , defined as the full width at half maximum of the transparency window, and the ATS splitting, γ ATS , defined as the peak-to-peak distance between AT absorption peaks, are used to delineate the EIT and ATS regimes and to characterize the transition between the regimes. In the cold-atom medium, in the weak-coupler (EIT) regime γ EIT ≈ A + B ( + , where Ω c and Ω p are the coupler and probe Rabi frequencies, Γ eg is the spontaneous decay rate of the intermediate 6P 3/2 level, and parameters A and B that depend on the laser linewidth. We explore the transition into the strong-coupler (ATS) regime, which is characterized by the relation γ ATS ≈ Ω c . The experiments are in agreement with numerical solutions of the Master equation. Our analysis accounts for non-ideal conditions that exist in typical realizations of Rydberg-EIT, including laser-frequency jitter, Doppler mismatch of the utilized two-color Rydberg EIT system, and strong probe fields. The obtained criteria to distinguish cold-atom EIT from ATS are readily accessible and applicable in practical implementations.

arXiv:1709.00144•New Journal of Physics•Jul 5, 2018•44 citations

Magnetic-field-induced splitting of Rydberg Electromagnetically Induced Transparency and Autler-Townes spectra in 87 Rb vapor cell

Xinheng Li, Yue Cui, Jianhai Hao +6 more

We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87 Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each m F state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the theoretical calculations agree qualitatively with experimental results. The Rydberg atom microwave electric field sensor performance was enhanced by making use of the splitting interval between the two maximum absolute m F states separated by the static magnetic field, which was attributed to the stronger Clebsch-Gordon coefficients between the extreme m F states and the frequency detuning of the microwave electric field under the static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.

Optics Express•Oct 17, 2023•24 citations
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.
Abstract We utilize an electromagnetically induced transparency (EIT) of a three-level cascade system involving Rydberg state in a room-temperature cell, formed with a cesium 6S1/2–6P3/2–66S1/2 scheme, to investigate the Autler–Townes (AT) splitting resulting from a 15.21-GHz radio-frequency (RF) field that couples the | 66 S 1 / 2 〉 → | 65 P 1 / 2 〉 Rydberg transition. The radio-frequency electric field induced AT splitting, γ AT, is defined as the peak-to-peak distance of an EIT-AT spectrum. The dependence of AT splitting γ AT on the probe and coupling Rabi frequency, Ωp and Ωc, is investigated. It is found that the EIT-AT splitting strongly depends on the EIT linewidth that is related to the probe and coupling Rabi frequency in a weak RF-field regime. Using a narrow linewidth EIT spectrum would decrease the uncertainty of the RF field measurements. This work provides new experimental evidence for the theoretical framework in [J. Appl. Phys. 121, 233106 (2017)].
We present an electromagnetically induced transparency and Aulter-Townes (EIT-AT) spectrum of a Rydberg three-level atom that is dressed with a microwave field in a room-temperature cesium cell. The EIT is a quantum coherent effect produced by the interaction of atoms with electromagnetic waves, which leads to the decrease of the absorption for a weak resonant probe laser. AT splitting refers to the phenomenon, that the absorption line splits when an electromagnetic field that is in resonance or near resonance acts on the transition of atoms. Rydberg atoms are extremely sensitive to an external electric field due to their large polarizabilities and microwave transition dipole moments, which can be used to measure the external field. In this work, a Rydberg three-level EIT is used to detect Rydberg atom and AT splitting induced by the microwave field. Cesium levels 6S1/2, 6P3/2 and 50S1/2 constitute a Rydberg three-level system, in which a weak probe laser locking to the transition from 6S1/2 to 6P3/2 couples ground-state transition and the strong coupling laser resonates on the Rydberg transition from 6P2/3 to 50S1/2. The two Rydberg levels 50S1/2 and 50P1/2 are coupled with the microwave field at a frequency of 30.852 GHz, leading to the AT splitting of EIT line and forming an EIT-AT spectrum, which is used to measure the electric field amplitude of microwave. In order to further study the EIT-AT splitting characteristics of the Rydberg levels, we carry out a series of measurements by changing the microwave field. The experimental results show a broadened EIT-AT signal for the weak field range and the four-peak spectrum for the strong field, which is attributed to the inhomogeneity of the microwave field. The microwave in cesium cell, emitted by a function generator, shows inhomogeneous behavior such that the atoms interacting with the laser field experience the different fields, leading to the line broadened and multi-peak EIT-AT spectra. For the microwave transition of nS1/2-nP1/2 in this paper, a pair of EIT-AT lines should be obtained for an electric field value. The broadening of the EIT-AT spectrum and the multi-peak structure here are due to the inhomogeneity of the microwave field measurement. We propose a method to increase the spatial resolution by reducing the length of cesium cell. The result in this work provides a method of measuring the field amplitude and monitoring the distribution of microwave electric field, meanwhile the spatial resolution of the measurements can be improved by reducing the size of the cell.
Abstract We present the electromagnetically induced transparency (EIT) spectra of cold Rydberg four-level cascade atoms consisting of the 6S1/2 → 6P3/2 → 7S1/2 → 60P3/2 scheme. A coupling laser drives the Rydberg transition, a dressing laser couples two intermediate levels and a weak probe laser probes the EIT signal. We numerically solve the Bloch equations and investigate the dependence of the probe transmission rate signal on the coupling and dressing lasers. We find that the probe transmission rate can display an EIT or electromagnetically induced absorption (EIA) profile, depending on the Rabi frequencies of the coupling and dressing lasers. When we increase the Rabi frequency of the coupling laser and keep the Rabi frequency of the probe and dressing laser fixed, flipping of the EIA to EIT spectrum occurs at the critical coupling Rabi frequency. When we apply a microwave field coupling the transition 60P3/2 → 61S1/2, the EIT spectrum shows Autler–Townes splitting, which is employed to measure the microwave field. The theoretical measurement sensitivity can be 1.52 × 10−2 nV⋅cm−1⋅Hz−1/2 at the EIA–EIT flipping point.
We demonstrate the high-resolution spatial feature measurement of microwave electric field using an cesium atomic vapor cell based on the electromagnetically induced transparency (EIT) spectrum of133Cs Rydberg atom. The microwave electric field with the frequency of 6.95 GHz couples the transition of 47D5/2→48P3/2 Rydberg states. The EIT spectrum of a 6S1/2-6P3/2-47D5/2 ladder system will split by the Autler-Townes(AT) effect under the microwave electric field. The dependence of AT splitting separation on the microwave electric fields strength is observed. Moreover, we present the imaging of the spatial feature of microwave electric field in the atomic vapor cell. The theoretical maximum spatial resolution is about λMw/430.
Electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS) are two similar yet distinct phenomena that modify the transmission of a weak probe field through an absorption medium in the presence of a coupling field, featured in a variety of three-level atomic systems. In many applications it is important to distinguish EIT from ATS splitting. We present EIT and ATS spectra in a three-level cascade system, involving cold cesium atoms in the Rydberg state. The EIT linewidth, γ EIT , defined as the full width at half maximum of the transparency window, and the ATS splitting, γ ATS , defined as the peak-to-peak distance between AT absorption peaks, are used to delineate the EIT and ATS regimes and to characterize the transition between the regimes. In the cold-atom medium, in the weak-coupler (EIT) regime γ EIT ≈ A + B ( + , where Ω c and Ω p are the coupler and probe Rabi frequencies, Γ eg is the spontaneous decay rate of the intermediate 6P 3/2 level, and parameters A and B that depend on the laser linewidth. We explore the transition into the strong-coupler (ATS) regime, which is characterized by the relation γ ATS ≈ Ω c . The experiments are in agreement with numerical solutions of the Master equation. Our analysis accounts for non-ideal conditions that exist in typical realizations of Rydberg-EIT, including laser-frequency jitter, Doppler mismatch of the utilized two-color Rydberg EIT system, and strong probe fields. The obtained criteria to distinguish cold-atom EIT from ATS are readily accessible and applicable in practical implementations.
We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87 Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each m F state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the theoretical calculations agree qualitatively with experimental results. The Rydberg atom microwave electric field sensor performance was enhanced by making use of the splitting interval between the two maximum absolute m F states separated by the static magnetic field, which was attributed to the stronger Clebsch-Gordon coefficients between the extreme m F states and the frequency detuning of the microwave electric field under the static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.