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

Real-imaginary spectrum decomposition of the transparency spectra in microwave dressed Rydberg systems

Wenyu Niu, Lu Qin, Zeyun Shi, Yingying Zhang, Shiqiang Xia, Xue-Jing Feng, Qi Wang, Jingxue Liu, Zhijun Zhao, Zunlue Zhu, Weibin Li, Xing-Dong Zhao

Published May 20, 2024• 0 citations
Publisher

Abstract

To distinguish the contributions of electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in their applications in precision laser spectroscopy, we propose a real-imaginary spectrum decomposition method to investigate the transparency spectra in a four-level microwave (MW) dressed Rydberg system. We show that the opening transparency windows in the absorption spectra of probe field is a prominent character by EIT, EIT-ATS crossover, and ATS when the MW field is turned off and the intensity of the control field is adjusted. When the MW field is turned on and gradually increased, the EIT is destroyed and disappears. In addition, the most prominent characters that open a transparency window are the EIT-ATS crossover and the ATS. Then, if we further increase the intensity of the MW field, we find that the transparency windows open mainly due to the ATS. Compared to the previous considerations of this issue, which were limited to three-level systems, our four-level scheme reported here is useful for understanding the features of quantum interference in multilevel atomic systems, and has potential applications to study enhanced sensitivity, measurement spectroscopic, quantum processing, quantum communication, and transmission.

DOI
10.1364/oe.520789

Related papers

Distinction of electromagnetically induced transparency and Autler-Towners splitting in a Rydberg-involved ladder-type cold atom system

Zhonghua Ji, Yuechun Jiao, Yongmei Xue +3 more

Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two similar quantum coherent phenomena but have different mechanisms and applications. Akaike information criteria (AIC), an objective method to discriminate EIT and ATS from an experimental viewpoint, has been employed in a variety of systems. Here we use AIC method to quantitively discriminate a series of spectra of cold atoms in a Rydberg-involved upper-driving ladder-type. The derived weights of EIT and ATS reflect that our spectra change from EIT-ATS intermediate region to ATS-dominated region along Rabi frequency of coupling field increases. We find that there are two factors affecting EIT-ATS weights in a Rydberg-involved three-level system: dephasing rate, induced by the interactions among Rydberg atoms, makes the EIT-ATS crossover move to the direction of low Rabi frequency of coupling field and the experimental noise makes the difference between EIT and ATS weights reduce at elsewhere. Our investigation could provide a meaningful reference for the observations and applications of Rydberg-involved quantum coherent spectroscopy.

Optics Express•Mar 22, 2021•13 citations

Mixture of Electromagnetically Induced Transparency and Autler–Townes Splitting in a Five-Level Atomic System*

Xiao-Yun 晓 芸 Zhang 张, Shan 山 Wu 吴, Hai‐Chao Li

Abstract Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.

Communications in Theoretical Physics•Feb 1, 2017•3 citations

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

Crossover from electromagnetically induced transparency to Autler–Townes splitting in open ladder systems with Doppler broadening

Chaohua Tan, Guoxiang Huang

We propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio kc/kp≈−1, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where kc (kp) is the wavenumber of control (probe) field. Furthermore, when kc/kp is far from −1, EIT can occur, but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na2 molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.

arXiv:1311.2149•Journal of the Optical Society of America B•Mar 4, 2014•34 citations

Pole analysis of EIT-AT spectrum with Rydberg atoms

Meng Shi, Yuechun Jiao, Jianming Zhao

We investigate the electromagnetically induced transparency (EIT) and Autler Townes (AT) splitting spectrum with a four-level Rydberg atom by pole analysis of the probe coherence. A pair of poles corresponding to the two peaks of the spectral splitting is observed. The spectral split or the pole positions are affected by the microwave intensity (MW) and the detuning between the probe and the coupling laser. In the absence of any detuning, the two poles coincide and separate again on the imaginary axis of the complex detuning plane at weak MW field. The two poles do not coincide when the probe (coupling) laser is detuned for scanning the coupling (probe) laser frequency. However, under finite detuning, the two poles approach the nearest distance in the absence of any splitting and are separated again in the direction parallel to the imaginary axis. The spectral analysis of the poles provides an alternate way to establish the relationship between the splitting and the intensity of MW, which may play a role in the application of atomic-based MW measurements.

Optics Express•Oct 19, 2021•3 citations

Analytical model for transient evolution of an EIT-AT spectrum with Rydberg atoms

Fang Li

An analytical model of an electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting spectrum with a four-level Rydberg atom was presented, and equations were derived to explain the dependence of the transient absorption for a probe laser on light and microwave (MW) fields. The analytical solution of absorption for the probe laser Im [ χ ( t )] shows that it depends on the spontaneous decay rate from level |2〉 to level |1〉, Rabi frequencies of the control and MW fields. For 87 Rb atoms, a stronger control laser shortens the steady-state time window and a stronger MW field will lead to a higher oscillation frequency shown in analytical and numerical results. The time-dependent EIT-AT splitting spectrum is also investigated, and the stable splitting distance shows a linear dependence on the continuous MW E-field strength.

Optics Letters•Jan 23, 2025•5 citations
To distinguish the contributions of electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in their applications in precision laser spectroscopy, we propose a real-imaginary spectrum decomposition method to investigate the transparency spectra in a four-level microwave (MW) dressed Rydberg system. We show that the opening transparency windows in the absorption spectra of probe field is a prominent character by EIT, EIT-ATS crossover, and ATS when the MW field is turned off and the intensity of the control field is adjusted. When the MW field is turned on and gradually increased, the EIT is destroyed and disappears. In addition, the most prominent characters that open a transparency window are the EIT-ATS crossover and the ATS. Then, if we further increase the intensity of the MW field, we find that the transparency windows open mainly due to the ATS. Compared to the previous considerations of this issue, which were limited to three-level systems, our four-level scheme reported here is useful for understanding the features of quantum interference in multilevel atomic systems, and has potential applications to study enhanced sensitivity, measurement spectroscopic, quantum processing, quantum communication, and transmission.
Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two similar quantum coherent phenomena but have different mechanisms and applications. Akaike information criteria (AIC), an objective method to discriminate EIT and ATS from an experimental viewpoint, has been employed in a variety of systems. Here we use AIC method to quantitively discriminate a series of spectra of cold atoms in a Rydberg-involved upper-driving ladder-type. The derived weights of EIT and ATS reflect that our spectra change from EIT-ATS intermediate region to ATS-dominated region along Rabi frequency of coupling field increases. We find that there are two factors affecting EIT-ATS weights in a Rydberg-involved three-level system: dephasing rate, induced by the interactions among Rydberg atoms, makes the EIT-ATS crossover move to the direction of low Rabi frequency of coupling field and the experimental noise makes the difference between EIT and ATS weights reduce at elsewhere. Our investigation could provide a meaningful reference for the observations and applications of Rydberg-involved quantum coherent spectroscopy.
Abstract Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.
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 propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio kc/kp≈−1, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where kc (kp) is the wavenumber of control (probe) field. Furthermore, when kc/kp is far from −1, EIT can occur, but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na2 molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.
We investigate the electromagnetically induced transparency (EIT) and Autler Townes (AT) splitting spectrum with a four-level Rydberg atom by pole analysis of the probe coherence. A pair of poles corresponding to the two peaks of the spectral splitting is observed. The spectral split or the pole positions are affected by the microwave intensity (MW) and the detuning between the probe and the coupling laser. In the absence of any detuning, the two poles coincide and separate again on the imaginary axis of the complex detuning plane at weak MW field. The two poles do not coincide when the probe (coupling) laser is detuned for scanning the coupling (probe) laser frequency. However, under finite detuning, the two poles approach the nearest distance in the absence of any splitting and are separated again in the direction parallel to the imaginary axis. The spectral analysis of the poles provides an alternate way to establish the relationship between the splitting and the intensity of MW, which may play a role in the application of atomic-based MW measurements.
An analytical model of an electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting spectrum with a four-level Rydberg atom was presented, and equations were derived to explain the dependence of the transient absorption for a probe laser on light and microwave (MW) fields. The analytical solution of absorption for the probe laser Im [ χ ( t )] shows that it depends on the spontaneous decay rate from level |2〉 to level |1〉, Rabi frequencies of the control and MW fields. For 87 Rb atoms, a stronger control laser shortens the steady-state time window and a stronger MW field will lead to a higher oscillation frequency shown in analytical and numerical results. The time-dependent EIT-AT splitting spectrum is also investigated, and the stable splitting distance shows a linear dependence on the continuous MW E-field strength.