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Journal of the Optical Society of America B

Manipulating giant cross-Kerr nonlinearity at multiple frequencies in an atomic gaseous medium

Le Van Doai, Nguyen Le Thuy An, Dinh Xuan Khoa, Vu Ngọc Sau, Nguyen Huy Bang

Published Sep 24, 2019• 14 citations
Publisher

Abstract

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.

DOI
10.1364/josab.36.002856

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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.
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 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.
We found the analytical expression for cross-Kerr nonlinear coefficient in a four-level Y-type atomic system. The analytical model is applied to 85Rb atoms and shown that under electromagnetically induced transparency, cross-Kerr nonlinear coefficient is enhanced by several orders of magnitude. At the same time, the amplitude and the sign of cross-Kerr nonlinear coefficient are controlled with respect to the intensity and the frequency of the coupling laser field. The analytical model can be useful to explain the experimental results and to study related effects in nonlinear optics. Full Text: PDF ReferencesC. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, P. Tombesi, "Polarization Qubit Phase Gate in Driven Atomic Media", Phys. Rev. Lett. 90, 197902 (2003). CrossRef C. Zhu, G. Huang, "Giant Kerr Nonlinearity, Controlled Entangled Photons and Polarization Phase Gates in Coupled Quantum-Well Structures", Opt. Express 19, 23364 (2011). CrossRef C. Hang, G. Huang, "Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet", Opt. Express 18(3), 2952 (2010). CrossRef M. Fleischhauer, I. Mamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media", Rev. Mod. Phys. 77, 633 (2005). CrossRef H. Schmidt, And A. Imamogdlu, "Giant Kerr nonlinearities obtained by electromagnetically induced transparency", Opt. Lett., 21(23), 1936 (1996). CrossRef H. Kang And Y. Zhu, Phys. "Observation of Large Kerr Nonlinearity at Low Light Intensities", Rev. Lett., 91, 093601 (2003). CrossRef J. Kou, R. G. Wan, Z. H. Kang, H. H. Wang, L. Jiang, X. J. Zhang, Y. Jiang, and J. Y. Gao, "EIT-assisted large cross-Kerr nonlinearity in a four-level inverted-Y atomic system", J. Opt. Soc. Am. B. 27(10), 2035 (2010). CrossRef X. Yang, S. Li, C. Zhang, and H. Wang, "Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system", J. Opt. Soc. Am. B. 26(7), 1423 (2009). CrossRef C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti and P. Tombesi, "Polarization Qubit Phase Gate in Driven Atomic Media", Phys. Rev. Lett. 90, 197902 (2003). CrossRef H. Sun, Y. Niu, S. Jin and S. Gong, "Phase control of cross-phase modulation with electromagnetically induced transparency", J. Phys. B: At. Mol. Opt. Phys. 40, 3037 (2007). CrossRef L.V. Doai, P.V. Trong, D.X. Khoa, and N.H. Bang, "Electromagnetically induced transparency in five-level cascade scheme of 85Rb atoms: An analytical approach", Optik, 125, 3666 (2014). CrossRef D. X. Khoa, P. V. Trong, L. V. Doai and N. H. Bang, "Electromagnetically induced transparency in a five-level cascade system under Doppler broadening: an analytical approach", Phys, Scr. 91, 035401 (2016). CrossRef D.X. Khoa, L.C. Trung, P.V. Thuan, L.V. Doai and N.H. Bang, "Measurement of dispersive profile of a multiwindow electromagnetically induced transparency spectrum in a Doppler-broadened atomic medium", J. Opt. Soc. Am. B 34 (6), 1255 (2017). CrossRef D. X. Khoa, L. V. Doai, D. H. Son, and N. H. Bang, "Enhancement of self-Kerr nonlinearity via electromagnetically induced transparency in a five-level cascade system: an analytical approach", J. Opt. Soc. Am. B., 31, 1330 (2014). CrossRef L.V. Doai, N.L.T. An, D.X. Khoa, V.N. Sau and N.H. Bang, "Manipulating giant cross-Kerr nonlinearity at multiple frequencies in an atomic gaseous medium", J. Opt. Soc. Am. B 36, 2856 (2019). CrossRef D. X. Khoa, L. V. Doai, L. N. M. Anh, L. C. Trung, P. V. Thuan, N. T. Dung, and N. H. Bang, "Optical bistability in a five-level cascade EIT medium: an analytical approach", J. Opt. Soc. Am. B, Vol. 33, 735 (2016). CrossRef N. T. Anh, L. V. Doai, and N. H. Bang, "Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity", J. Opt. Soc. Am. B 35, 1233 (2018). CrossRef N. T. Anh, L. V. Doai, D. H. Son, and N. H. Bang, "Manipulating multi-frequency light in a five-level cascade EIT medium under Doppler broadening", Optik 171, 721 (2018). CrossRef D.A. Steck, Rb85 D Line Data: http://Steck.Us/Alkalidata/rubidium85numbers.pdf CrossRef
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.
Abstract We propose an analytical model to study the effect of giant Kerr nonlinearity on group velocity of probe light in a six-level inverted-Y atomic system under electromagnetically induced transparency (EIT). In this scheme, a nonlinearity of the medium is enhanced greatly around in three spectral regions corresponding to transparent windows. As a consequence, such a giant Kerr nonlinearity of the medium changes significantly group index for probe light which can obstruct light slowdown. Moreover, this model shows also that the probe propagation can switch between subluminal and superluminal modes in three EIT windows by adjusting the parameters of the signal and coupling fields. Such analytical model is not only convenient for considering the influence of laser parameters on group velocity but is also easy used to fit the experimental results.
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.