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Physica Scripta

Influence of spontaneously generated coherence on absorption, dispersion, and group index in a five-level cascade atomic system

Le Nguyen Mai Anh, Nguyen Huy Bang, Nguyen Van Phu, Dinh Xuan Khoa, Nguyen Thi Ngan, Bui Thu Huyen, Le Van Doai

Published Mar 2, 2023• 4 citations
Publisher

Abstract

Abstract By solving the density matrix equations in the steady state, we have derived analytical expressions for the absorption, dispersion, and group index of a five-level cascade-type atomic system as functions of laser intensity and frequency, spontaneously generated coherence (SGC), and relative phase of applied fields. The influences of SGC and relative phase on absorption, dispersion, and group index of this system under electromagnetically induced transparency (EIT) are studied. It is shown that the three EIT windows of system become deeper and narrower as the strength of SGC increases. These lead to an increase in the slope and the amplitude of the dispersion curves at three EIT windows. As a result, the amplitude of the group index at these three EIT windows also becomes larger when the strength of SGC increases. In particular, the group index can easily be switched between negative and positive values i.e., the light propagation can easily be converted between superluminal to subluminal modes by adjusting the strength of SGC, relative phase or the coupling laser intensity.

DOI
10.1088/1402-4896/acc0ab

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Abstract By solving the density matrix equations in the steady state, we have derived analytical expressions for the absorption, dispersion, and group index of a five-level cascade-type atomic system as functions of laser intensity and frequency, spontaneously generated coherence (SGC), and relative phase of applied fields. The influences of SGC and relative phase on absorption, dispersion, and group index of this system under electromagnetically induced transparency (EIT) are studied. It is shown that the three EIT windows of system become deeper and narrower as the strength of SGC increases. These lead to an increase in the slope and the amplitude of the dispersion curves at three EIT windows. As a result, the amplitude of the group index at these three EIT windows also becomes larger when the strength of SGC increases. In particular, the group index can easily be switched between negative and positive values i.e., the light propagation can easily be converted between superluminal to subluminal modes by adjusting the strength of SGC, relative phase or the coupling laser intensity.
Abstract We present a comparative study of the control of group velocity in three-level atomic systems including Λ-, Ladder-, and V-types via spontaneously generated coherence (SGC) and relative phase of laser fields. In the steady regime, expressions of group index are derived as an analytical function of controllable parameters related to SGC and relative phase. It is shown that the group velocity can be further slowed down or speeded up under SGC in which modifications of group velocity due to the SGC in Λ- and V-systems are stronger than that in Ladder-system. In particular, when interference strength of SGC p increases from 0.7 to 1.0, the light propagation is switched from superluminal to subluminal modes (for Λ- and Ladder-systems) or from subluminal to superluminal modes (for V-system). In the presence of relative phase, the group velocity changes between subluminal and superluminal modes with a period of 2π. In resonant region, the largest positive value of group index reaches at the relative phase φ = π while the largest negative value of group index reaches at φ = 0 and 2π for the Λ- and Ladder-systems, otherwise, for the V-system the largest positive group index occurs at φ = 0 and 2π, and the largest negative group index occurs at φ = π .
The dispersion and the absorption properties of a closed three-level Λ system with incoherent pumping have been studied when both dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) play a significant role. We analyze the interplay between the dynamically induced coherence (DIC) and the spontaneously generated coherence (SGC) on the absorption spectrum to induce different nonlinear processes like amplification without population inversion (AWI), electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA). By changing the probe field Rabi frequency the response of the system can switch over from one nonlinear process to other and hence the probe field Rabi frequency can be used as a knob for switching different nonlinear responses. By changing the relative phase of two fields the response of the system switches over from EIA to EIT or EIT to AWI which can be used as optical switch. Choosing appropriate value of the relative phase and the probe field Rabi frequency, the dispersion and hence the propagation of the probe pulse can be controlled efficiently. Therefore these parameters can be used as a knob to manipulate light propagation from subluminal to superluminal. Exact analytical expressions for the coherences and populations in the steady state limit have been derived (keeping all orders of system parameters) to generalize the analysis. Any restrictions over the system parameters have been avoided to make it applicable to various atomic and molecular systems.
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 paper investigates the effects of spontaneously generated coherence(SGC) on the probe absorption in the Y-type four-level atomic system driven by three fields.It finds that the probe absorption at the resonance center shows the different phenomena with the SGC effects.When SGC produces the destructive interference on the probe absorption,the absorption at the resonance center is reduced with the SGC enhancement and the gain appears there.When SGC produces the constructive interference on the probe absorption,the absorption at the resonance center is enhanced with the SGC enhancement.That is electromagnetically induced absorption(being abbreviated EIA);the intensity of double electromagnetically induced transparency(being abbreviated EIT);at both sides of the resonance is increased,and the windows get wider.At the same time,the linewidth of the absorption at the resonance center becomes narrow and the transparent windows at both sides of the resonance get wider when the spontaneous decay rate of energy levels |3〉→|2〉 and 4〉→|2〉 is decreased at the ratio of the spontaneous decay rate of energy levels |3〉→|2〉 and |4〉→|2〉 being constant.
In this work, we present an analytical method to achieve giant Kerr nonlinearity without absorption in a five-level atomic medium. By using iterative perturbation technique on density matrix equations, we have derived the analytical expressions of nonlinear susceptibility and Kerr nonlinear coefficient in the presence of spontaneously generated coherence (SGC) and relative phase between applied laser fields. It shows that, this five-level atomic medium exhibits multiple electromagnetically induced transparency (EIT) at three different frequencies, at the same time, the Kerr nonlinear coefficient is enhanced around three transparent spectral regions; in each such EIT region appears a pair of positive-negative peaks of Kerr nonlinear coefficient. In particular, these nonlinear peaks are moved to the center of the EIT windows via SGC. This means that the Kerr nonlinear coefficient is enhanced with completely suppressed absorption at different transparency frequencies. Furthermore, the magnitude and the sign of the Kerr nonlinear coefficient are easily controlled according to the SGC strength, the coupling laser intensity, and the relative phase between applied laser fields. Such a giant nonlinear medium can be useful for photonic devices working in the resonant frequency region without absorption. As a typical application, this giant Kerr nonlinear material has been applied to an interferometer for the formation of optical bistability, and showed the appearance of OB at the resonant frequency with significantly reduced threshold intensity and OB width.
This article presents a coherent phenomenon called spontaneously generated coherence (SGC) under the regime of electromagnetically induced transparency (EIT) in a three-coupled multiple quantum wells. We demonstrate that the presence of SGC in these quantum wells lead to intriguing modifications in the transparency window within the absorption spectrum. At the same time, modification of the dispersive nature is also demonstrated which enables the feasibility of the system in diverse applications based on light propagation. The absorption and dispersion responses are found to be varied by the individual strength of the first and second control fields in presence as well as in absence of SGC in the EIT regime. The positional shifting of the transparency window and simultaneous modifications in the dispersive profiles by tuning the control field detunings of both the first and second control fields are also revealed. Some absorption and dispersion contours are illustrated for getting better insights into the modifications of the optical responses via SGC. Finally, by manipulating the strength of the SGC parameter, we observe the changes in the respective position of the transparency window and dispersion curve. It is expected that the current investigations will pave novel ways for innovative applications in quantum communications, and fabrication of advanced photonic devices.