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Physica Scripta

The effect of giant Kerr nonlinearity on group velocity in a six-level inverted-Y atomic system

Le Van Doai

Published Oct 30, 2019• 7 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ab5288

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The analytical expression for the group index in a degenerated three-level lambda-type atomic system is derived as a function of the parameters of laser fields and external magnetic field. The influence of the external magnetic field on the group index is investigated. It is shown that by changing the magnitude or sign of the external magnetic field, the transparency window with normal dispersion switches to enhanced absorption with anomalous dispersion at the line center and hence the light propagation can be converted between subluminal and superluminal modes. Full Text: PDF ReferencesR. W. Boyd, "Slow and fast light: fundamentals and applications", J. Mod. Opt. 56 (2009) 1908-1915 CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, "Observation of electromagnetically induced transparency", Phys. Rev. Lett. 66 (1991) 2593. CrossRef A. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption", Phys. Rev. A 59 (1999) 4732-4735. CrossRef L. V. Hau, S. E. Harris, Z. Dutton, C. H. Bejroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas", Nature 397, 594 (1999) CrossRef L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation", Nature 406 (6793), 277-279 (2000) CrossRef A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hammer, "Observation of Ultraslow and Stored Light Pulses in a Solid", Phys. Rev. Lett. 88, 023602 (2002). CrossRef K. Bencheikh, E. Baldit, S. Briaudeau, P. Monnier, J. A. Levenson, and G. Mélin, "Slow light propagation in a ring erbium-doped fiber", Opt. Express 18 (25), 25642-25648 (2010). CrossRef E. E. Mikhailov, V. A. Sautenkov, I. Novikova, G. R. Welch, "Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas", Phys. Rev. A 69, 063808 (2004). CrossRef E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, G.R. Welch, "Absorption resonance and large negative delay in rubidium vapor with a buffer gas", J. Opt. Soc. Am. B 21, 425 (2004). CrossRef A. M Akulshin and R. J McLean, "Fast light in atomic media", J. Opt. 12 (2010) 104001. CrossRef Vineet Bharti, Vasant Natarajan, "Sub- and super-luminal light propagation using a Rydberg state", Opt. Comm. 392 (2017) 180-184. 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 (2018) 721-727. 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 (2018) 1233. CrossRef N.H. Bang, L.N.M. Anh, N.T. Dung and L.V. Doai, "Comparative Study of Light Manipulation in Three-Level Systems Via Spontaneously Generated Coherence and Relative Phase of Laser Fields*", Commun. Theor. Phys. 71 (2019) 947-954. CrossRef L.V. Doai, "The effect of giant Kerr nonlinearity on group velocity in a six-level inverted-Y atomic system", Physica Scripta 95 (2020) 035104 (7pp). CrossRef P. Kaur and A. Wasan, "Effect of magnetic field on the optical properties of an inhomogeneously broadened multilevel Λ-system in Rb vapor", Eur. Phys. J. D 71 (2017) 78. CrossRef H. Cheng, H. -M. Wang, S. -S. Zhang, P. -P. Xin, J. Luo and H. -P. Liu, "Electromagnetically induced transparency of 87Rb in a buffer gas cell with magnetic field", J. Phys. B: At. Mol. Opt. Phys. 50 (2017) 095401. CrossRef C. Mishra, A. Chakraborty, A. Srivastava, S. K. Tiwari, S. P. Ram, V. B. Tiwari and S. R. Mishr, "lectromagnetically induced transparency in Λ-systems of 87Rb atom in magnetic field", J. Mod. Opt. 65 (2018) 2269-2277. CrossRef S. H. Asadpour, H. R. Hamedi and H. R. Soleimani, "Slow light propagation and bistable switching in a graphene under an external magnetic field", Laser Phys. Lett. 12 (2015) 045202. CrossRef R. Karimi, S. H. Asadpour, S. Batebi and h. R. Soleimani, "Manipulation of pulse propagation in a four-level quantum system via an elliptically polarized light in the presence of external magnetic field", Mod. Phys. Lett. B 29 (2015) 1550185. CrossRef

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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.
We propose a model to manipulate group velocity of a multi-frequency probe light in an electromagnetically induced transparency medium consisting of five-level cascade-type atoms associated with a giant self-Kerr nonlinearity. An analytic expression of group index for the probe light is derived as a function of parameters of the probe and coupling fields, atomic density, and lifetimes of excited atomic states. In the presence of the self-Kerr, both probe and controlling fields can be used as knobs to manipulate the probe light between the subluminal and superluminal propagation modes in three separated frequency regions. The theoretical model agrees with experimental observation, and it is helpful to find the optimized parameters and related applications. Furthermore, by using such a cascade excitation scheme, it could be possible to choose the uppermost excited electronic states having long lifetimes, as Rydberg states, to slow the light down to a few mm/s.
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.
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.
The analytical expression for the group index in a degenerated three-level lambda-type atomic system is derived as a function of the parameters of laser fields and external magnetic field. The influence of the external magnetic field on the group index is investigated. It is shown that by changing the magnitude or sign of the external magnetic field, the transparency window with normal dispersion switches to enhanced absorption with anomalous dispersion at the line center and hence the light propagation can be converted between subluminal and superluminal modes. Full Text: PDF ReferencesR. W. Boyd, "Slow and fast light: fundamentals and applications", J. Mod. Opt. 56 (2009) 1908-1915 CrossRef K.J. Boller, A. Imamoglu, S.E. Harris, "Observation of electromagnetically induced transparency", Phys. Rev. Lett. 66 (1991) 2593. CrossRef A. Lezama, S. Barreiro, and A. M. Akulshin, "Electromagnetically induced absorption", Phys. Rev. A 59 (1999) 4732-4735. CrossRef L. V. Hau, S. E. Harris, Z. Dutton, C. H. Bejroozi, "Light speed reduction to 17 metres per second in an ultracold atomic gas", Nature 397, 594 (1999) CrossRef L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation", Nature 406 (6793), 277-279 (2000) CrossRef A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, P. R. Hammer, "Observation of Ultraslow and Stored Light Pulses in a Solid", Phys. Rev. Lett. 88, 023602 (2002). CrossRef K. Bencheikh, E. Baldit, S. Briaudeau, P. Monnier, J. A. Levenson, and G. Mélin, "Slow light propagation in a ring erbium-doped fiber", Opt. Express 18 (25), 25642-25648 (2010). CrossRef E. E. Mikhailov, V. A. Sautenkov, I. Novikova, G. R. Welch, "Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas", Phys. Rev. A 69, 063808 (2004). CrossRef E. E. Mikhailov, V. A. Sautenkov, Y. V. Rostovtsev, G.R. Welch, "Absorption resonance and large negative delay in rubidium vapor with a buffer gas", J. Opt. Soc. Am. B 21, 425 (2004). CrossRef A. M Akulshin and R. J McLean, "Fast light in atomic media", J. Opt. 12 (2010) 104001. CrossRef Vineet Bharti, Vasant Natarajan, "Sub- and super-luminal light propagation using a Rydberg state", Opt. Comm. 392 (2017) 180-184. 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 (2018) 721-727. 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 (2018) 1233. CrossRef N.H. Bang, L.N.M. Anh, N.T. Dung and L.V. Doai, "Comparative Study of Light Manipulation in Three-Level Systems Via Spontaneously Generated Coherence and Relative Phase of Laser Fields*", Commun. Theor. Phys. 71 (2019) 947-954. CrossRef L.V. Doai, "The effect of giant Kerr nonlinearity on group velocity in a six-level inverted-Y atomic system", Physica Scripta 95 (2020) 035104 (7pp). CrossRef P. Kaur and A. Wasan, "Effect of magnetic field on the optical properties of an inhomogeneously broadened multilevel Λ-system in Rb vapor", Eur. Phys. J. D 71 (2017) 78. CrossRef H. Cheng, H. -M. Wang, S. -S. Zhang, P. -P. Xin, J. Luo and H. -P. Liu, "Electromagnetically induced transparency of 87Rb in a buffer gas cell with magnetic field", J. Phys. B: At. Mol. Opt. Phys. 50 (2017) 095401. CrossRef C. Mishra, A. Chakraborty, A. Srivastava, S. K. Tiwari, S. P. Ram, V. B. Tiwari and S. R. Mishr, "lectromagnetically induced transparency in Λ-systems of 87Rb atom in magnetic field", J. Mod. Opt. 65 (2018) 2269-2277. CrossRef S. H. Asadpour, H. R. Hamedi and H. R. Soleimani, "Slow light propagation and bistable switching in a graphene under an external magnetic field", Laser Phys. Lett. 12 (2015) 045202. CrossRef R. Karimi, S. H. Asadpour, S. Batebi and h. R. Soleimani, "Manipulation of pulse propagation in a four-level quantum system via an elliptically polarized light in the presence of external magnetic field", Mod. Phys. Lett. B 29 (2015) 1550185. CrossRef
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.
We use four-level atomic system and control the wave propagation via forbidden decay rate. The Raman gain process becomes dominant on electromagnetically induced transparency (EIT) medium by increasing the forbidden decay rate via increasing the number of atoms [G.S. Agarwal and T.N. Dey, Phys. Rev. A 74 (2006) 043805 and K. Harada, T. Kanbashi, and M. Mitsunaga, Phys. Rev. A 73 (2006) 013803 ]. The behavior of wave propagation is dramatically changed from normal (subluminal) to anomalous (superluminal) dispersion by increasing the forbidden decay rate. The system can also give a control over the group velocity of the light propagating through the medium via Kerr field.