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Journal of Physics B Atomic Molecular and Optical Physics

Giant cross-Kerr nonlinearity in a six-level inhomogeneously broadened atomic medium

Le Van Doai

Published Sep 23, 2019• 13 citations
Publisher

Abstract

Abstract We study the enhancement of cross-Kerr nonlinearity in a six-level inverted-Y-type inhomogeneously broadened atomic medium. The explicit analytical expressions for first- and third-order susceptibilities and cross-Kerr nonlinear coefficient are found in the presence of Doppler broadening. The analytical model is applied to 87 Rb atoms and it is shown that under the electromagnetically induced transparency (EIT) condition, the cross-Kerr nonlinearity is enhanced at multiple frequencies around three EIT windows. The amplitude and sign of the cross-Kerr nonlinear coefficient of the probe field are controlled by changing the parameters of the coupling field. The effect of Doppler broadening leads to a reduction in the transparent efficiency and thus reduces the amplitude of the cross-Kerr nonlinear coefficient. The analytical model can be used to easily fit the experimental observations at different temperatures and support future studies related to the cross-Kerr nonlinear effect.

DOI
10.1088/1361-6455/ab46eb

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Abstract We study the enhancement of cross-Kerr nonlinearity in a six-level inverted-Y-type inhomogeneously broadened atomic medium. The explicit analytical expressions for first- and third-order susceptibilities and cross-Kerr nonlinear coefficient are found in the presence of Doppler broadening. The analytical model is applied to 87 Rb atoms and it is shown that under the electromagnetically induced transparency (EIT) condition, the cross-Kerr nonlinearity is enhanced at multiple frequencies around three EIT windows. The amplitude and sign of the cross-Kerr nonlinear coefficient of the probe field are controlled by changing the parameters of the coupling field. The effect of Doppler broadening leads to a reduction in the transparent efficiency and thus reduces the amplitude of the cross-Kerr nonlinear coefficient. The analytical model can be used to easily fit the experimental observations at different temperatures and support future studies related to the cross-Kerr nonlinear effect.
In this work, we study the influence of Doppler broadening on cross-Kerr nonlinearity in a four-level inverted-Y atomic system under electromagnetically induced transparency (EIT) condition. The first- and third-susceptibilities in the presence of Doppler effect are derived as a function of probe, signal and coupling beams and temperature of medium. Under EIT condition, cross-Kerr nonlinearity is enhanced several orders of magnitude compared to that without EIT. The Doppler effect leads to a reduction in the transparent efficiency and thus reduces the amplitude of cross-Kerr nonlinear coefficient. For hot atomic gaseous medium, such consideration of the Doppler effect may be useful for experimental observations and apply to photonic devices operating at different temperature conditions.
We proposed a model for manipulating giant cross-Kerr nonlinearity in an atomic gaseous medium consisting of six-level inverted-Y systems. The absorption, dispersion, and cross-Kerr nonlinear coefficients of the medium are derived as analytical functions of the parameters of probe, coupling, and signal fields. It is shown that the cross-Kerr nonlinearity is enhanced significantly in three transparent windows under electromagnetically induced transparency (EIT). Furthermore, the cross-Kerr nonlinearity can be manipulated between positive and negative values by controlling intensity and/or frequency of the coupling laser. Such controllable giant cross-Kerr nonlinearity with the analytical interpretation is convenient to find experimental parameters and is useful for studying applications of controllable multi-channel quantum phase gates.
We present an analytical model for cross-Kerr nonlinear coefficient in a four-level N-type atomic medium under Doppler broadening. The model is applied to 87Rb atoms to analyze the dependence of the cross-Kerr nonlinear coefficient on the external light field and the temperature of atomic vapor. The analysis shows that in the absence of electromagnetically induced transparency (EIT) the cross-Kerr nonlinear coefficient is zero, but it is significantly enhanced when the EIT is established. It means that the cross-Kerr effect can be turned on/off when the external light field is on or off. Simultaneously, the amplitude and the sign of the cross-Kerr nonlinear coefficient are easily changed according to the intensity and frequency of the external light field. The amplitude of the cross-Kerr nonlinear coefficient remarkably decreases when the temperature of atomic medium increases. The analytical model can be convenient to fit experimental observations and applied to photonic devices.
In this paper, we propose an analytical model to study the effect of Doppler broadening on self-Kerr nonlinearity in a five-level ladder-type atomic system. First- and third-order susceptibilities and the self-Kerr nonlinear coefficient are found as the function of temperature and parameters of laser fields. The analytical model is applied to hot $^{85}{\rm Rb}$85Rb and $^{87}{\rm Rb}$87Rb atoms, and it is shown that under the electromagnetically induced transparency (EIT) effect, the self-Kerr nonlinear coefficient is enhanced around three transparent spectral regions. When the temperature of atomic vapor increases (i.e., Doppler width increases), the depth and width of the EIT windows decrease accordingly, and therefore the amplitude of the Kerr nonlinear coefficient decreases significantly. In addition, because the frequency gaps between hyperfine levels of upper excited state ${{5\rm D}_{5/2}}$5D5/2 of $^{85}{\rm Rb}$85Rb atoms are much smaller than those of $^{87}{\rm Rb}$87Rb atoms, the EIT windows as well as the nonlinear dispersion curves for $^{85}{\rm Rb}$85Rb atoms are closer than those for $^{87}{\rm Rb}$87Rb atoms as the Doppler effect presents. The analytical results agree well with the experimental observation when reducing to a three-level atomic system. The analytical model can be used to easily fit the experimental observations of self-Kerr nonlinearity in a five-level atomic system under different temperature conditions and apply to a variety of applications relating to all-optical-switching techniques.
We study enhancement of cross-Kerr nonlinearity in four-level N-type atomic system by the analytical method. The results apply to the 87Rb atoms and show that in the presence of the EIT effect (i.e., the presence of coupling laser field), the Kerr nonlinear coefficient is enhanced several order of magnitudes (about 10-6 cm2/W) around the EIT window. That is, on the Kerr nonlinear graph the two positive and negative values are found on both sides of the resonant frequency. The amplitude and sign of the Kerr nonlinear coefficient can be controlled versus the intensity or frequency of the coupling laser field. Analytical results are useful for experimental observation and related applications.
The analytical expression for the self-Kerr nonlinear coefficient in a three-level V-type atomic medium is found in the presence of the Doppler effect. Based on the analytical results, we have analyzed the enhancement and control of the Kerr nonlinear coefficient under the condition of electromagnetically induced transparency. It is shown that the Kerr nonlinear coefficient is significantly enhanced around the resonant frequency of both the probe and coupling fields. Simultaneously, the magnitude and sign of the Kerr nonlinear coefficient are controlled with respect to the intensity and frequency of the coupling laser field. The amplitude of the Kerr nonlinear coefficient decreases remarkably as temperature increases (i.e., the Doppler width increases). The analytical model can find potential applications in photonic devices and can explain experimental observations of the Kerr nonlinear coefficient at different temperatures.