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In the past few years, many interesting optical phenomena, such as electromagnetically induced transparency, coherent optical control of a biexciton, slow light and optical solitons, have been investigated in single quantum dot (QD). However, in an actual semiconductor device there exist many quantum dots (QDs). Recently, QD molecule, which is comprised of double semiconductor QDs coupled by tunneling coupling, has been proposed. In this new semiconductor structure, many complex but interesting phenomena have been discovered. In fact, three QD molecules may also be composed of three QDs, which can be coupled by interdot tunneling coupling. For the three semiconductor QDs molecules, the influence of the interdot tunneling coupling strength must be considered. So, in this paper, with considering that a weak, -linear-polarized probe field can form left- and right-polarized components under the control of the parallel magnetic field, and when they are combined with the tunneling coupling among the QDs, an electromagnetically induced transparency medium of a five-level M configuration semiconductor three QDs is proposed. Subsequently, the nonlinear Faraday rotation in the semiconductor three QDs is analytically studied. For the linear case, the linear dispersion relation is driven by a method of multiple scales. Then, by studying the linear optical properties, it is found that the system exhibits a single tunneling induced transparency window due to the quantum destructive interference effect driven by the interdot tunneling coupling under appropriate conditions, and the width of the tunneling induced transparency window can be effectively controlled by the strength of the interdot tunneling coupling. Meanwhile, the switch regulatory effect, which changes from the anomalous dispersion regime to the normal dispersion regime, is likely to be achieved by changing the strength of the interdot tunneling coupling. For the nonlinear case, two coupled nonlinear Schrdinger equations, which govern the evolutions of left- and right-polarized components of the weak, -linear-polarized probe field under the applied longitudinal magnetic field, are derived. By studying the nonlinear properties, it is shown that a large nonlinear Faraday rotation angle can be obtained due to the quantum interference effect which is induced by the interdot tunneling coupling with a very low absorption of the weak, -linear-polarized probe field. In addition, it is also found that the nonlinear Faraday rotation direction is opposite to line Faraday rotation for the same magnetic field. What is more, the nonlinear Faraday rotation angle grows bigger than the linear Faraday rotation. These results mean that the Faraday rotation of the three semiconductor QDs with the electromagnetically induced transparency can be more effectively controlled by the nonlinear effect.
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Keywords:
- semiconductor quantum dot /
- nonlinear Faraday rotation /
- electromagnetically induced transparency
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[2] Wang B, Li S J, Ma J, Wang H, Peng K C, Xiao M 2006 Phys. Rev. A 73 051801
[3] Peng Z H, Zou J, Liu X J, Xiao Y J, Kuang L M 2012 Phys. Rev. A 86 034305
[4] Liu Q, Gross S, Dekker P, Withford M J, Steel M J 2014 Opt. Express 22 28037
[5] Yu Z, Fan S 2009 Nat. Photon. 3 91
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[19] Vaseghi B, Mohebi N 2013 J. Lumin. 134 352
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[23] Chen Q C 2014 Chin. Phys. B 23 124212
[24] Yang W X, Lee R K 2008 Europhys. Lett. 83 14002
[25] She Y C, Zheng X J, Wang D L, Zhang W X 2013 Opt. Express 21 17392
[26] Chen Y, Chen Z M, Huang G X 2015 Phys. Rev. A 91 023820
[27] Luo X Q, Wang D L, Zhang Z Q, Ding J W, Liu W M 2011 Phys. Rev. A 84 033803
[28] She Y C, Zhang W X, Wang D L 2011 Acta Phys. Sin. 60 064205 (in Chinese)[佘彦超, 张蔚曦, 王登龙2011 60 064205]
[29] Gammon D, Snow E S, Shanabrook B V, Katzer D S, Park D 1996 Science 273 87
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[1] Faraday M 1846 Philos. Mag. 28 294
[2] Wang B, Li S J, Ma J, Wang H, Peng K C, Xiao M 2006 Phys. Rev. A 73 051801
[3] Peng Z H, Zou J, Liu X J, Xiao Y J, Kuang L M 2012 Phys. Rev. A 86 034305
[4] Liu Q, Gross S, Dekker P, Withford M J, Steel M J 2014 Opt. Express 22 28037
[5] Yu Z, Fan S 2009 Nat. Photon. 3 91
[6] Hang C, Huang G X 2007 Chin. Opt. Lett. 5 47
[7] Zhu C J, Deng L, Hagley E W 2013 Phys. Rev. A 88 023854
[8] He Y M, Wei Y J, He Y, Xiong F L, Chen K, Zhao Y, Lu Z Y 2014 Sci. Sin. Inform. 44 394 (in Chinese)[何玉明, 魏宇佳, 贺煜, 熊飞雷, 陈凯, 赵勇, 陆朝阳2014中国科学信息科学 44 394]
[9] Zeng K H, Wang D L, She Y C, Zhang W X 2013 Acta Phys. Sin. 62 147801 (in Chinese)[曾宽宏, 王登龙, 佘彦超, 张蔚曦2013 62 147801]
[10] Bai Y F, Yang W X, Han D A, Yu X Q 2012 Chin. Phys. B 21 114208
[11] Hao X Y, Zheng A S, Wang Y, Li X G 2012 Commun. Theor. Phys. 57 866
[12] Wu Y, Yang X X 2007 Phys. Rev. B 76 054425
[13] Tian S C, Wan R G, Tong C Z, Ning Y Q 2014 J. Opt. Soc. Am. B 31 2681
[14] Ding C L, Yu R, Li J H, Hao X Y, Wu Y 2014 Phys. Rev. A 90 043819
[15] Borges H S, Sanz L, Villas-Boas J M, Diniz Neto O O, Alcalde A M 2012 Phys. Rev. B 85 115425
[16] Hang C, Huang G X 2008 Phys. Rev. A 77 033830
[17] Sun H, Fan S L, Feng X L, Wu C F, Gong S Q, Huang G X, Oh C H 2012 Opt. Express 20 8485
[18] Anisimov P M, Dowling J P, Sanders B C 2011 Phys. Rev. Lett. 107 163604
[19] Vaseghi B, Mohebi N 2013 J. Lumin. 134 352
[20] Songmuang R, Kiravittaya S, Schmidt O G 2003 Appl. Phys. Lett. 82 2892
[21] Beirne G J, Hermannstädter C, Wang L, Rastelli A, Schmidt O G, Michler P 2006 Phys. Rev. Lett. 96 137401
[22] Yang W, Sun D L, Zhou L, Wang J, Zhan M S 2014 Acta Phys. Sin. 63 153701(in Chinese)[杨威, 孙大立, 周林, 王谨, 詹明生2014 63 153701]
[23] Chen Q C 2014 Chin. Phys. B 23 124212
[24] Yang W X, Lee R K 2008 Europhys. Lett. 83 14002
[25] She Y C, Zheng X J, Wang D L, Zhang W X 2013 Opt. Express 21 17392
[26] Chen Y, Chen Z M, Huang G X 2015 Phys. Rev. A 91 023820
[27] Luo X Q, Wang D L, Zhang Z Q, Ding J W, Liu W M 2011 Phys. Rev. A 84 033803
[28] She Y C, Zhang W X, Wang D L 2011 Acta Phys. Sin. 60 064205 (in Chinese)[佘彦超, 张蔚曦, 王登龙2011 60 064205]
[29] Gammon D, Snow E S, Shanabrook B V, Katzer D S, Park D 1996 Science 273 87
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