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

Journal of Physics B Atomic Molecular and Optical Physics

Study of multi-window electromagnetically induced transparency (EIT) and related dispersive signals in V-type systems in the Zeeman sublevels of hyperfine states of 87 Rb-D 2 line

Rohit Hazra, Md. Mabud Hossain

Published Oct 23, 2020• 11 citations
Publisher

Abstract

Abstract We have theoretically studied the multi-window electromagnetically induced transparency (EIT) and the related dispersive signals in multi-level V-type systems which are formed by the co-propagating circularly polarized pump ( σ − ) and probe ( σ + ) laser fields in the Zeeman sublevels of hyperfine states of 87 Rb-D 2 line. The optical Bloch equations (OBEs) are derived and numerically solved under the steady-state condition to obtain the probe absorption and dispersion spectra. We present the study of a single-window EIT for the three-level, double-window EIT for the four-level and triple-window EIT for the five-level V-type systems under both Doppler-free and Doppler-broadened conditions. The dispersive signals corresponding to the multi EIT windows for each system are also observed separately. From the knowledge of the slopes of the probe dispersion signals, we have calculated group index ( n g ) of the medium considering three different V-type schemes. The effect of temperature on the EIT, dispersion and group index profiles is also studied in detail. It is found that the amplitudes of EIT and dispersion signals and also the positive and negative values of n g are decreased as the temperature of the medium increases. To understand the Doppler-broadening effect on the group index profiles, we have considered three different velocity groups of atoms in the calculation of group index profiles. Moreover, the effects of probe intensity variation on the Doppler-broadened EIT and dispersive signals are studied extensively, and the conversions of EIT to EIA and dispersive positive slope to negative slope are observed under strong probe regime. Also, we have investigated the variation of dispersive slope and group index with the variation of probe intensity and probe frequency, respectively, at the multi-frequency position of the multi-window EIT. Finally, the switching between subluminal (slow light) to superluminal (fast light) propagation of light with the variation of both probe intensity and probe frequency is discussed in detail.

DOI
10.1088/1361-6455/abbd32

Related papers

Simulation of double electromagnetically induced transparency in a four-level V-type system: A comparative study of probe and pump transmissions

Rohit Hazra, Md. Mabud Hossain

In this paper, we present the theoretical study of double electromagnetically induced transparency (EIT) in a four-level V-type system which is formed by two co-propagating laser fields and the Zeeman sublevels of hyperfine transitions of 87Rb D2 line. The density matrix equations for the four-level V-type system are derived from the Liouville’s equation of motion and numerically solved under steady state condition to get the EIT signals. We consider both the probe and pump transmission spectra for the observation of double EIT signals under both Doppler free and Doppler broadened conditions. In case of Doppler free medium, two EIT peaks are formed in the two Lorentzian shape dips present in the both Doppler free probe and pump transmission spectra. When the medium becomes Doppler broadened, the two EIT peaks are formed in the probe transmission spectrum having Doppler broadened background, but the pump transmission spectrum gives two EIT peaks in the Doppler free background. The effect of probe intensity variation on the two EIT peaks is studied in case of Doppler broadened probe transmission spectrum. It is found that the heights of the EIT peaks decrease as the probe intensity increases, and interestingly one EIT peak converts into EIA (electromagnetically induced absorption) dip at some strong probe intensity value. The depth of the EIA dip is significantly increased as the intensity of the probe field increases. We also present the effect of probe intensity variation on the EIT peaks in the pump transmission spectrum and found that the EIT peak heights are increased as the probe intensity increases.

AIP conference proceedings•Jan 1, 2019•3 citations

Electromagnetically Induced Transparency Window in the System of Four-level Configuration

Wu Han-Hua

The absorption and dispersion properties of an N-type four-level system with Doppler(broadening) effect were investigated.In this system we considered two coherent fields and a probe field.When the second coherent field is absent,this system is a single three-level configuration,and the absorption line is just one clear electromagnetically induced transparency(EIT) window.While the second coherent field exists,there are two EIT windows which become wide and deep with the(coherent) intensity increasing.The position width and absorbance of the transparency windows can be manipulated by adjusting the detuning of the driving field.In addition,we also found that the medium shows a large refractive index at each transparency window,and the group velocity of the probe laser can be reduced.

Journal of Jilin University(Science Edition)•Jan 1, 2006•0 citations

Observation and theoretical simulation of dispersive properties of an electromagnetically induced transparent 87 Rb atomic medium

Arpita Das, Bankim Chandra Das, Shrabana Chakrabarti +2 more

Abstract The dispersive properties of 87 Rb atomic medium in electromagnetically induced transparency (EIT) have been studied experimentally as well as theoretically. To measure the dispersion signal, a balanced homodyne detection technique was used by forming a Mach–Zehnder interferometer. We studied the system in a Λ-type configuration. From the slope of the dispersive EIT signal, the group index ( n g ) of the atomic medium, the group velocity ( ) and the time delay ( ) of the light wave through the atomic medium were calculated. We measured the group index of the atomic medium from the dispersion signal and observed that it non-linearly depends on the pump power. This non-linearity signifies that to achieve the maximum reduced group velocity, optimization of the pump power is needed. We got the maximum reduction in the group velocity of the probe beam as m s −1 . The corresponding time delay was ns. To support our experimental observation, we have performed a theoretical simulation by taking the semi-classical approach of density matrix formalism of a Λ-type three level system. To get the probe response we solved the optical Bloch equation analytically assuming the Lorentzian velocity distribution of the atom. We have observed that our analytical solution matched exactly with the numerical solution. Our experimental observation of non-linear variation of the group index with the pump Rabi frequency matched quite well with both of our numerical and analytical simulations.

Laser Physics•Oct 23, 2018•3 citations

Measurement of dispersive profile of a multiwindow electromagnetically induced transparency spectrum in a Doppler-broadened atomic medium

Dinh Xuan Khoa, Trung Le Canh, Phan Van Thuan +2 more

We have measured the dispersive profile of a multiwindow electromagnetically induced transparency (EIT) spectrum in a medium consisting of Rb atoms in the presence of Doppler broadening. The atomic medium is excited by a strong coupling light and a weak probe laser light via the V-type transitions within the D2 manifold. Under the EIT effect, an anomalous dispersive region of the medium is basically modified into multinormal and anomalous dispersive regions. Furthermore, the slope and position of the dispersion can be controlled with the intensity and frequency of the coupling light. An analytic model is proposed to simulate the observed spectrum with a good agreement. Such controllable dispersive properties with their analytic description would be useful for finding applications related to multiwindow EIT phenomena.

Journal of the Optical Society of America B•May 24, 2017•31 citations

A theoretical study of the group refractive index n g in a four-level inverted Y-type system formed by 87Rb atom – laser radiation interaction

Rohit Hazra, Md. Mabud Hossain

Abstract We report a theoretical investigation of the dispersion resulting from electromagnetically induced transparency (EIT) and the associated group refractive index profiles n g of a four-level inverted Y-type system formed by the interaction of three optical fields (probe, pump and control) with 87Rb atoms. The density matrix equations are derived from the semi-classical Liouville’s equation and solved both numerically and analytically to study the coherent nonlinear optical properties of the medium. We first present the EIT, dispersion and corresponding group index profiles n g under the switch-on/off and on/off-resonance conditions of the pump and control lasers. In presence of both pump and control lasers, an enhancement of the EIT window, a sharp EIT spike and related steeper dispersion slopes are obtained at the line centre of the probe frequency detuning. The group index profiles with the variation of the strengths of individual applied optical fields are studied. The effect of the ground state decoherence rates on the group index profile is examined in detail. It is found that the manipulation of n g values and the corresponding group velocities ν g of the probe light can be easily controlled from subluminal to superluminal values or vice versa by changing the strengths of the applied fields and the ground state decoherence rates. Besides, the EIT-based ‘optical switching’ phenomenon in the medium is explained by studying the variation of the group index with the pump and control Rabi frequencies.

Quantum Electronics•Jul 28, 2021•2 citations

Electromagnetically induced transparency in five-level configurations under Doppler broadening

Ai Nguyen Van, Quynh Anh Thi Nguyen, Quang Hai Ho +9 more

Abstract Electromagnetically induced transparency (EIT) in five-level atomic systems is theoretically investigated for three representative configurations: M-, inverted-Y, and K-type systems driven by a weak probe field and three control laser fields. The different coupling schemes produce different quantum interference pathways and two-photon resonance conditions, leading to markedly different EIT spectra. The M-type configuration exhibits one, two, and three well-resolved transparency windows as successive control fields are introduced. In contrast, the inverted-Y configuration produces broader transparency windows because of the overlap of multiple interference channels, whereas the K-type configuration exhibits only a single EIT window when all control fields are resonant. Multiple transparency windows in the K-type system appear after introducing appropriate coupling-field detunings. Doppler broadening at room temperature significantly broadens the absorption spectrum and reduces the transparency depth, while preserving the number and positions of the EIT windows. These results demonstrate that the coupling scheme plays an important role in determining the formation and evolution of multi-window EIT spectra and identify the characteristics of the three five-level configurations for multi-channel quantum-optical applications, as well as for the experimental observation of EIT spectra in five-level configurations.

Physica Scripta•Sep 17, 2026•0 citations
Abstract We have theoretically studied the multi-window electromagnetically induced transparency (EIT) and the related dispersive signals in multi-level V-type systems which are formed by the co-propagating circularly polarized pump ( σ − ) and probe ( σ + ) laser fields in the Zeeman sublevels of hyperfine states of 87 Rb-D 2 line. The optical Bloch equations (OBEs) are derived and numerically solved under the steady-state condition to obtain the probe absorption and dispersion spectra. We present the study of a single-window EIT for the three-level, double-window EIT for the four-level and triple-window EIT for the five-level V-type systems under both Doppler-free and Doppler-broadened conditions. The dispersive signals corresponding to the multi EIT windows for each system are also observed separately. From the knowledge of the slopes of the probe dispersion signals, we have calculated group index ( n g ) of the medium considering three different V-type schemes. The effect of temperature on the EIT, dispersion and group index profiles is also studied in detail. It is found that the amplitudes of EIT and dispersion signals and also the positive and negative values of n g are decreased as the temperature of the medium increases. To understand the Doppler-broadening effect on the group index profiles, we have considered three different velocity groups of atoms in the calculation of group index profiles. Moreover, the effects of probe intensity variation on the Doppler-broadened EIT and dispersive signals are studied extensively, and the conversions of EIT to EIA and dispersive positive slope to negative slope are observed under strong probe regime. Also, we have investigated the variation of dispersive slope and group index with the variation of probe intensity and probe frequency, respectively, at the multi-frequency position of the multi-window EIT. Finally, the switching between subluminal (slow light) to superluminal (fast light) propagation of light with the variation of both probe intensity and probe frequency is discussed in detail.
In this paper, we present the theoretical study of double electromagnetically induced transparency (EIT) in a four-level V-type system which is formed by two co-propagating laser fields and the Zeeman sublevels of hyperfine transitions of 87Rb D2 line. The density matrix equations for the four-level V-type system are derived from the Liouville’s equation of motion and numerically solved under steady state condition to get the EIT signals. We consider both the probe and pump transmission spectra for the observation of double EIT signals under both Doppler free and Doppler broadened conditions. In case of Doppler free medium, two EIT peaks are formed in the two Lorentzian shape dips present in the both Doppler free probe and pump transmission spectra. When the medium becomes Doppler broadened, the two EIT peaks are formed in the probe transmission spectrum having Doppler broadened background, but the pump transmission spectrum gives two EIT peaks in the Doppler free background. The effect of probe intensity variation on the two EIT peaks is studied in case of Doppler broadened probe transmission spectrum. It is found that the heights of the EIT peaks decrease as the probe intensity increases, and interestingly one EIT peak converts into EIA (electromagnetically induced absorption) dip at some strong probe intensity value. The depth of the EIA dip is significantly increased as the intensity of the probe field increases. We also present the effect of probe intensity variation on the EIT peaks in the pump transmission spectrum and found that the EIT peak heights are increased as the probe intensity increases.
The absorption and dispersion properties of an N-type four-level system with Doppler(broadening) effect were investigated.In this system we considered two coherent fields and a probe field.When the second coherent field is absent,this system is a single three-level configuration,and the absorption line is just one clear electromagnetically induced transparency(EIT) window.While the second coherent field exists,there are two EIT windows which become wide and deep with the(coherent) intensity increasing.The position width and absorbance of the transparency windows can be manipulated by adjusting the detuning of the driving field.In addition,we also found that the medium shows a large refractive index at each transparency window,and the group velocity of the probe laser can be reduced.
Abstract The dispersive properties of 87 Rb atomic medium in electromagnetically induced transparency (EIT) have been studied experimentally as well as theoretically. To measure the dispersion signal, a balanced homodyne detection technique was used by forming a Mach–Zehnder interferometer. We studied the system in a Λ-type configuration. From the slope of the dispersive EIT signal, the group index ( n g ) of the atomic medium, the group velocity ( ) and the time delay ( ) of the light wave through the atomic medium were calculated. We measured the group index of the atomic medium from the dispersion signal and observed that it non-linearly depends on the pump power. This non-linearity signifies that to achieve the maximum reduced group velocity, optimization of the pump power is needed. We got the maximum reduction in the group velocity of the probe beam as m s −1 . The corresponding time delay was ns. To support our experimental observation, we have performed a theoretical simulation by taking the semi-classical approach of density matrix formalism of a Λ-type three level system. To get the probe response we solved the optical Bloch equation analytically assuming the Lorentzian velocity distribution of the atom. We have observed that our analytical solution matched exactly with the numerical solution. Our experimental observation of non-linear variation of the group index with the pump Rabi frequency matched quite well with both of our numerical and analytical simulations.
We have measured the dispersive profile of a multiwindow electromagnetically induced transparency (EIT) spectrum in a medium consisting of Rb atoms in the presence of Doppler broadening. The atomic medium is excited by a strong coupling light and a weak probe laser light via the V-type transitions within the D2 manifold. Under the EIT effect, an anomalous dispersive region of the medium is basically modified into multinormal and anomalous dispersive regions. Furthermore, the slope and position of the dispersion can be controlled with the intensity and frequency of the coupling light. An analytic model is proposed to simulate the observed spectrum with a good agreement. Such controllable dispersive properties with their analytic description would be useful for finding applications related to multiwindow EIT phenomena.
Abstract We report a theoretical investigation of the dispersion resulting from electromagnetically induced transparency (EIT) and the associated group refractive index profiles n g of a four-level inverted Y-type system formed by the interaction of three optical fields (probe, pump and control) with 87Rb atoms. The density matrix equations are derived from the semi-classical Liouville’s equation and solved both numerically and analytically to study the coherent nonlinear optical properties of the medium. We first present the EIT, dispersion and corresponding group index profiles n g under the switch-on/off and on/off-resonance conditions of the pump and control lasers. In presence of both pump and control lasers, an enhancement of the EIT window, a sharp EIT spike and related steeper dispersion slopes are obtained at the line centre of the probe frequency detuning. The group index profiles with the variation of the strengths of individual applied optical fields are studied. The effect of the ground state decoherence rates on the group index profile is examined in detail. It is found that the manipulation of n g values and the corresponding group velocities ν g of the probe light can be easily controlled from subluminal to superluminal values or vice versa by changing the strengths of the applied fields and the ground state decoherence rates. Besides, the EIT-based ‘optical switching’ phenomenon in the medium is explained by studying the variation of the group index with the pump and control Rabi frequencies.
Abstract Electromagnetically induced transparency (EIT) in five-level atomic systems is theoretically investigated for three representative configurations: M-, inverted-Y, and K-type systems driven by a weak probe field and three control laser fields. The different coupling schemes produce different quantum interference pathways and two-photon resonance conditions, leading to markedly different EIT spectra. The M-type configuration exhibits one, two, and three well-resolved transparency windows as successive control fields are introduced. In contrast, the inverted-Y configuration produces broader transparency windows because of the overlap of multiple interference channels, whereas the K-type configuration exhibits only a single EIT window when all control fields are resonant. Multiple transparency windows in the K-type system appear after introducing appropriate coupling-field detunings. Doppler broadening at room temperature significantly broadens the absorption spectrum and reduces the transparency depth, while preserving the number and positions of the EIT windows. These results demonstrate that the coupling scheme plays an important role in determining the formation and evolution of multi-window EIT spectra and identify the characteristics of the three five-level configurations for multi-channel quantum-optical applications, as well as for the experimental observation of EIT spectra in five-level configurations.