Abstract
We propose a degenerate V-type inhomogeneously broadening atomic model for Kerr nonlinear control under the support of an external magnetic field. The magnetic field is used as a control knob to convert the medium from transparency to absorption at the resonance center. It is shown that the magnitude and sign of the Kerr nonlinearity index are manipulated by the magnetic field. Especially, we can easily convert the Kerr nonlinearity index from the positive peak into a negative peak, and from zero value can be transferred to enhanced positive or negative peaks simply only by changing the direction or strength of the magnetic field. In addition, the Kerr nonlinearity index under the influence of the temperature, the intensity, and detuning of the control field is also considered. The proposed model can be useful for applications in optical switching and nonlinear optical devices as well as possible experimental implementations.
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References
Anh, N.T., Doai, L.V., Bang, N.H.: Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity. J. Opt. Soc. Am. B 35, 1233–1239 (2018)
Anh, N.T., Thanh, T.D., Bang, N.H., Dong, H.M.: Microwave assisted all-optical switching in a four-level atomic system. Pramana - J. Phys. 95, 1–8 (2021)
Asadpour, S.H.: Goos–Hänchen shifts due to spin-orbit coupling in the carbon nanotube quantum dot nanostructures. Appl. Opt. 56, 2201–2208 (2017)
Asadpour, S.H., Hamedi, H.R.: Giant Kerr nonlinearity in an n-doped semiconductor quantum well. Opt. Quant. Electron. 45, 11–20 (2013)
Asadpour, S.H., Soleimani, H.R.: Impact of exciton spin relaxation (ESR) on Kerr nonlinearity in a quantum well nanostructure. Phys. B 449, 77–84 (2014)
Asadpour, S.H., Sahrai, M., Soltani, A., Hamedi, H.R.: Enhanced Kerr nonlinearity via quantum interference from spontaneous emission. Phys. Lett. A 376, 147–152 (2012)
Bang, N.H., Khoa, D.X., Son, D.H., Doai, L.V.: Effect of Doppler broadening on giant self-Kerr nonlinearity in a five-level ladder-type system. J. Opt. Soc. Am. B 36(11), 3151–3158 (2019)
Bang, N.H., Khoa, D.X., Doai, L.V.: Controlling self-Kerr nonlinearity with an external magnetic field in a degenerate two-level inhomogeneously broadened medium. Phys. Lett. A 384, 126234 (2020)
Boller, K.J., Imamoglu, A., Harris, S.E.: Observation of electromagnetically induced transparency. Phys. Rev. Lett. 66, 2593 (1991)
Chang, D.E., Vuletic, V., Lukin, M.D.: Quantum nonlinear optics photon by photon. Nat. Photon. 8, 685–694 (2014)
Chen, Y., Bai, Z., Huang, G.: Ultraslow optical solitons and their storage and retrieval in an ultracold ladder-type atomic system. Phys. Rev. A 89, 023835 (2014)
Dong, H.M., Bang, N.H.: Controllable optical switching in a closed-loop three-level lambda system. Phy. Scr. 94, 115510 (2019)
Dong, H.M., Doai, L.V., Sau, V.N., Khoa, D.X., Bang, N.H.: Propagation of laser pulse in a three-level cascade atomic medium under conditions of electromagnetically induced transparency. Photon. Lett. Pol. 8, 73 (2016)
Dong, H.M., Doai, L.V., Bang, N.H.: Pulse propagation in an atomic medium under spontaneously generated coherence, incoherent pumping, and relative laser phase. Opt. Commun. 426, 553 (2018)
Dong, H.M., Nga, L.T.Y., Bang, N.H.: Optical switching and bistability in a degenerated two-level atomic medium under an external magnetic field. Appl. Opt. 58(16), 4192–1499 (2019)
Dong, H.M., Nga, L.T.Y., Khoa, D.X., Bang, N.H.: Controllable ultraslow optical solitons in a degenerated two-level atomic medium under EIT assisted by a magnetic field. Sci. Rep. 10(1), 15298 (2020)
Dong, H.M., Bang, N.H., Khoa, D.X., Doai, L.V.: All-optical switching via spontaneously generated coherence, relative phase and incoherent pumping in a V-type three-level system. Opt. Commun. 507, 127731 (2022)
Firstenberg, O., Peyronel, T., Liang, Q.Y., Gorshkov, A.V., Lukin, M.D., Vuletic, V.: Attractive photons in a quantum nonlinear medium. Nature 502, 71–75 (2013)
Fleischhauer, M., Imamoglu, A., Marangos, J.P.: Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633 (2005)
Gao, H., Sun, H., Fan, S., Zhang, H.: Phase control of Kerr nonlinearity in V-type system with spontaneously generated coherence. J. Mod. Opt. 63, 598–604 (2016)
Goren, A.D., Wilson-Gordon, M., Rosenbluh, H.: Friedmann, Sub-Doppler and subnatural narrowing of an absorption line induced by interacting dark resonances in a tripod system. Phys. Rev. A 69, 063802 (2004)
Hamedi, H.R., Gharamaleki, A.H., Sahrai, M.: Colossal Kerr nonlinearity based on electromagnetically induced transparency in a five-level double-ladder atomic system. Appl. Opt. 22, 5892 (2016)
Han, Y., Xiao, J., Liu, Y., Zhang, C., Wang, H., Xiao, M., Peng, K.: Interacting dark states with enhanced nonlinearity in an ideal four-level tripod atomic system. Phys. Rev. A 77, 023824 (2008)
Harris, S.E.: Electromagnetically induced transparency. Phys. Today 50, 36 (1997)
Hau, L.V., Harris, S.E., Dutton, Z., Bejroozi, C.H.: Light speed reduction to 17 meters per second in an ultracold atomic gas. Nature 397, 594–598 (1999)
Haus, H.A., Wong, W.S.: Solitons in optical communications. Rev. Mod. Phys. 68(2), 423–444 (1996)
Jiang, W.J., Song, J.P., Zheng, H.B., Wu, C., Yin, B.Y., Zhang, Y.: Enhancement of Kerr nonlinearity via spontaneously generated coherence in a four-level N-type atomic system. Opt. Commun. 282, 101–105 (2009)
Joshi, M.X.: Controlling Steady-State and Dynamical Properties of Atomic Optical Bistability. World Scientific, Singapore (2012)
Kang, H., Zhu, Y.: Observation of large Kerr nonlinearity at low light intensities. Phys. Rev. Lett. 91, 093601 (2003)
Khoa, D.X., Dong, H.M., Doai, L.V., Bang, N.H.: Propagation of laser pulse in a three-level cascade inhomogeneously broadened medium under electromagnetically induced transparency conditions. Optik 131, 497–505 (2017)
Khordad, R.: Effects of magnetic field and geometrical size on the interband light absorption in a quantum pseudodot system. Solid State Sci. 12, 1253–1256 (2010)
Khordad, R.: Effects of the magnetic field direction and anisotropy on the interband light absorption of an asymmetric quantum dot. J. Math. Phys. 54, 062102 (2013)
Khordad, R., Sedehi, H.R.R., Ghanbari, A.: Influence of non-uniform magnetic field on magnetic susceptibility, heat capacity, electronic and optical properties of a charged particle. Opt. Quant. Electron. 53, 1–12 (2021)
Kis, Z., Demeter, G., Janszky, J.: Pulse propagation in a dressed, degenerate system. J. Opt. Soc. Am. B 30, 829–837 (2013)
Li, J., Yu, R., Si, L., Yang, X.: Propagation of twin light pulses under magneto-optical switching operations in a four-level inverted-Y atomic medium. J. Phys. B: At. Mol. Opt. Phys. 43, 065502 (2010)
Liang, H., Niu, Y., Deng, L., Gong, S.: Enhancement of Kerr nonlinearity completely without absorption. Phys. Lett. A 381, 3978–3982 (2017)
Nakajima, T.: Enhanced nonlinearity and transparency via autoionizing resonance. Opt. Lett. 25, 847–849 (2000)
Niu, Y., Gong, S.: Enhancing Kerr nonlinearity via spontaneously generated coherence. Phys. Rev. A 73, 053811 (2006)
Peyronel, T., Firstenberg, O., Liang, Q.Y., Hofferberth, S., Gorshkov, A.V., Pohl, T., Lukin, M.D., Vuletic, V.: Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57–60 (2012)
Raczynski, M., Rzepecka, J., Zaremba, S.Z.: Kaniasty, Polariton picture of light propagation and storing in a tripod system. Opt. Commun. 260, 73–80 (2006)
Rebic, S., Vitali, D., Ottaviani, C., Tombesi, P., Artoni, M., Cataliotti, F., Corbalan, R.: Polarization phase gate with a tripod atomic system. Phys. Rev. A 70, 032317 (2004)
Sahrai, M., Gharamaleki, A.H.: Phase dependent Kerr nonlinearity via quantum interference. Eur. Phys. J. D 73, 1–7 (2019)
Schmidt, H., Imamoglu, A.: Giant Kerr nonlinearities obtained by electromagnetically induced transparency. Opt. Lett. 21, 1936–1938 (1996)
Sevinli, S., Henkel, N., Ates, C., Pohl, T.: Nonlocal nonlinear optics in cold Rydberg gases. Phys. Rev. Lett. 107, 153001 (2011)
Sheng, J., Yang, X., Wu, H., Xiao, M.: Modified self Kerr nonlinearity in a four-level N-type atomic system. Phys. Rev. A 84, 053820 (2011)
Steck, D.A.: 87Rb D line data. https://steck.us/alkalidata(2019)
Thanh, T.D., Anh, N.T., Hien, N.T.T., Dong, H.M., Hao, N.X., Khoa, D.X., Bang, N.H.: Subluminal and superluminal light pulse propagation under an external magnetic field in a vee-type three-level atomic medium. Photon. Lett. Pol. 13(1), 4–6 (2021)
Tsai, P.J., Wei, Y.C., Wu, B.H., Lin, S.X., Chen, Y.C.: Theoretical study of a memory-based optical converter with degenerate Zeeman states. Phys. Rev. A 100, 063843 (2019)
Vafafard, A., Sahrai, M., Hamedi, H.R., et al.: Tunneling induced two-dimensional phase grating in a quantum well nanostructure via third and fifth orders of susceptibility. Sci. Rep. 10, 1–10 (2020)
Venkataraman, V., Saha, K., Gaeta, A.L.: Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing. Nat. Photon. 7, 138–141 (2013)
Wang, H., Goorskey, D., Xiao, M.: Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system. Phys. Rev. Lett. 87, 073601 (2001)
Wu, Y., Deng, L.: Ultraslow bright and dark optical solitons in a cold three-state medium. Opt. Lett. 29, 2064–2066 (2004)
Yan, X.A., Wang, L.Q., Yin, B.Y., Jiang, W.J., Zheng, H.B., Song, J.P., Zhang, Y.P.: Effect of spontaneously generated coherence on Kerr nonlinearity in a four-level atomic system. Phys. Lett. A 372, 6456–6460 (2008)
Yan, X., Wang, L., Yin, B., Song, J.: Enhanced self-Kerr nonlinearity in spontaneous emission. J. Opt. Soc. Am. B 26, 1862–1868 (2009)
Yang, X.D., Li, S.J., Zhang, C.H., Wang, H.: Enhanced cross-Kerr nonlinearity via electromagnetically induced transparency in a four-level tripod atomic system. J. Opt. Soc. Am. B 26, 1423–1434 (2009)
Zhu, Z., Chen, A.X., Yang, W.X., Lee, R.K.: Phase knob for switching steady-state behaviors from bistability to multistability via spontaneously generated coherence. J. Opt. Soc. Am. B 31, 2061–2067 (2014)
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Hoang Minh, D., Thai Doan, T. & Nguyen Tuan, A. Controllable Kerr nonlinearity in a degenerate V-type inhomogeneously broadening atomic medium aided by a magnetic field. Opt Quant Electron 54, 225 (2022). https://doi.org/10.1007/s11082-022-03593-z
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DOI: https://doi.org/10.1007/s11082-022-03593-z