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Scientific Reports

Optical response in six-level 85Rb and 87Rb atomic media

Le Quang Trung, Hoang Bich Ngoc, Nguyen Thanh An, Ho Nguyen An, Dang Khanh Huyen, Nguyen Huy Bang, Hoang Dinh Hai, Le Van Doai

Published Jun 5, 2026• 0 citations
Publisher

Abstract

In this work, we analytically investigate the optical response including absorption, dispersion, and group index of a six-level atomic system under electromagnetically induced transparency (EIT). A key advantage of this configuration is its ability to simultaneously generate four transparency windows at distinct frequency regions using only two controlling laser fields. The analytical model is applied to both 87 Rb and 85 Rb atoms in cold and hot conditions, enabling exploration under various experimental environments. The results provide a comprehensive picture of the fundamental optical properties of 87 Rb and 85 Rb atomic systems with the six-level configuration, offering useful insights for experimental predictions and potential applications.

DOI
10.1038/s41598-025-29380-w

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Using matrix theory,the absorption and dispersion properties of a lamda-type four-level system driven by two coherent fields are investigated.The result obtained by means of numerical method indicates that by adjusting the intensity of Rabi frequencies of the coherent field in the steady state,double or single electromagnetically induced transparency(EIT) can appear explicitly in this system.And the explanations of these phenomena are given by using the dressed states.In the double electromagnetically induced transparency,the location of transparent windows can be manipulated by controlling the detuning of the driving field.Additionally,it is also found that the medium shows a large refractive index at each transparency window,and the group velocity of the probe laser can be enhanced.

Optics & Optoelectronic Technology•Jan 1, 2009•0 citations
In this work, we analytically investigate the optical response including absorption, dispersion, and group index of a six-level atomic system under electromagnetically induced transparency (EIT). A key advantage of this configuration is its ability to simultaneously generate four transparency windows at distinct frequency regions using only two controlling laser fields. The analytical model is applied to both 87 Rb and 85 Rb atoms in cold and hot conditions, enabling exploration under various experimental environments. The results provide a comprehensive picture of the fundamental optical properties of 87 Rb and 85 Rb atomic systems with the six-level configuration, offering useful insights for experimental predictions and potential applications.
The control of light group velocity via electromagnetically induced transparency (EIT) has opened up potential applications in photonic technologies such as information encoding, quantum processing, and optical switching. For traditional three-level atomic systems only allow light control within a narrow frequency range, limiting multi-channel applications. To overcome this limitation, this study focuses on multi-frequency group velocity control in a 87Rb atomic medium under the influence of an external magnetic field. By combining the semiclassical theory with analytical methods, we derive the expressions for the absorption, dispersion, and group index of a four-level atomic system. Based on these results, we investigate the influence of the magnetic field and laser parameters on the absorption, dispersion, and group index. The findings not only shed light on the mechanism for controlling multi-frequency light, but also suggest potential directions for developing flexible photonic devices that meet the future demands of multi-channel information processing. Keywords: Electromagnetically induced transparency; light group velocity; external magnetic field; four-level atomic configuration
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.
This dissertation reports experimental studies of nonlinear optical effects manifested by electromagnetically induced transparency (EIT) in cold Rb atoms. The cold Rb atoms are confined in a magneto-optic trap (MOT) obtained with the standard laser cooling and trapping technique. Because of the near zero Doppler shift and a high phase density, the cold Rb sample is well suited for studies of atomic coherence and interference and related applications, and the experiments can be compared quantitatively with theoretical calculations. It is shown that with EIT induced in the multi-level Rb system by laser fields, the linear absorption is suppressed and the nonlinear susceptibility is enhanced, which enables studies of nonlinear optics in the cold atoms with slow photons and at low light intensities. Three independent experiments are described and the experimental results are presented. First, an experimental method that can produce simultaneously co-propagating slow and fast light pulses is discussed and the experimental demonstration is reported. Second, it is shown that in a three-level Rb system coupled by multi-color laser fields, the multi-channel two-photon Raman transitions can be manipulated by the relative phase and frequency of a control laser field. Third, a scheme for all-optical switching near single photon levels is developed. The scheme is based on the phase-dependent multi-photon interference in a coherently coupled four-level system. The phase dependent multi-photon interference is observed and switching of a single light pulse by a control pulse containing ∼20 photons is demonstrated. These experimental studies reveal new phenomena manifested by quantum coherence and interference in cold atoms, contribute to the advancement of fundamental quantum optics and nonlinear optics at ultra-low light intensities, and may lead to the development of new techniques to control quantum states of atoms and photons, which will be useful for applications in quantum measurements and quantum photonic devices.
Abstract We report the observation of electromagnetically induced transparency (EIT) in a six-level Λ -type system in atomic Rb vapor containing both 87 Rb and 85 Rb. The experimental observation includes five velocity selective optically pumped (VSOP) absorption dips for both 87 Rb and 85 Rb. The EIT signal appears on the background of one such VSOP absorption dips. The measured EIT linewidth ( ) shows sub-natural ( ) values for both lower and higher values of pump Rabi-frequencies. The density matrix based theoretical model for the six-level system is developed and solved numerically by taking into account the Doppler broadening. A complete analytical solution (non perturbative) for a three level Λ -type system has been obtained and compared with the experimentally observed sub-natural EIT linewidth. The simulated spectra are in good agreement with the experimental findings.
In this paper, we study the formation of two electromagnetically induced transparency (EIT) windows in a four-level lambda atomic system with Doppler broadening. The depth and the width of the EIT windows are easily changed by adjusting the intensity of the controlling laser fields. Meanwhile, the position of the EIT windows is also easily shifted by changing the frequency of the laser fields. In particular, by turning on or off one of the two coupling laser fields, the probe field response can be switched between one or two EIT window regimes, i.e., it is possible to switch between absorption and transparency regimes, and vice versa. In addition, our analytical model also allows one to investigate the influence of temperature (or Doppler width) on EIT windows, which is necessary for experimental observations as well as related applications at room temperature.
Using matrix theory,the absorption and dispersion properties of a lamda-type four-level system driven by two coherent fields are investigated.The result obtained by means of numerical method indicates that by adjusting the intensity of Rabi frequencies of the coherent field in the steady state,double or single electromagnetically induced transparency(EIT) can appear explicitly in this system.And the explanations of these phenomena are given by using the dressed states.In the double electromagnetically induced transparency,the location of transparent windows can be manipulated by controlling the detuning of the driving field.Additionally,it is also found that the medium shows a large refractive index at each transparency window,and the group velocity of the probe laser can be enhanced.