电磁感应透明介质中的频隙孤子
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摘要
近几十年来,关于光孤子在光信息处理和光通信领域中的应用已有大量的理论和实验研究。到目前为止,大多数光孤子都在传统被动光学介质,比如玻璃光纤中产生,其中为了避免不可控的光学衰减和失真,人们普遍采用远离共振的激发。但是,由于缺少间距足够宽的清晰的能级,这些被动光学介质中的非线性效应非常弱,所以需要很高强度的入射光来产生孤子。同时,缺少清晰的能级和相应的跃迁定则也使得对光孤子进行主动操控十分困难。
近年来,由于电磁感应透明(EIT)效应的发现,相干介质中的弱光非线性光学的研究引起了人们极大的兴趣。EIT的基本原理是利用光强度较大的控制光所诱导的原子量子态之间的干涉效应来消除共振介质对光强度较弱的入射探测光的吸收。EIT可使介质的色散特性产生重大改变,从而降低探测光的群速度。基于这些有趣的性质,在最近的研究中发现了一种新型的光孤子,称为超慢光孤子(USOS)。这种孤子在多能级共振介质中产生,它的传播速度比真空中的光速小许多数量级。这些成果为研究非线性光脉冲在多能级共振介质中的形成与传播开拓了新的方向。
如果在EIT系统中将连续波控制场改换成驻波控制场,则探测场的线性色散关系会由单一频带转变为多个频带,即形成带结构,而且这些带结构可以十分方便地进行人工调控。最近,理论和实验工作者在这方面开展了认真深入的研究,得到了许多有趣的结果。人们普遍认为在这个方向上的进一步研究可以为低光强度水平上进行量子态操控和量子信息存储提供新方法和新途径。
与以往的研究不同,本文考虑在控制场为驻波场的情形下探测场的弱非线性传播效应。以Λ-型三能级原子为模型,我们提出一种在共振介质中通过EIT技术产生光学频隙孤子的方法。我们将证明,通过调节系统参数,所得光孤子的振动频率可位于探测光场振动频率的禁带之内,而且产生这样的频隙孤子只需要很低的入射光强度。另外,这种频隙孤子物理特性可以很方便地进行人工调控。由于它们的独特性质,频隙孤子可作为性质良好的,没有畸变的光脉冲在光信息处理和光通讯工程领域中发展潜在的应用前景。
本文的主要内容和组织结构如下。第一章简要概述孤子和电磁感应透明现象及有关的基本概念。第二章介绍关于EIT介质中孤子的基本理论。第三章介绍关于Λ-型三能级原子系统在EIT构型下形成频隙孤子的基本研究结果,包括小频隙和大频隙两种情况下的频隙孤子。最后一章给出我们工作的总结。
In the past decades, considerable theoretical and experimental research activities have focused on the study of optical solitons due to their important applications in optical information processing and transmission. Up to now, most optical solitons are produced in passive optical media such as glass-based optical fibers, in which far-off resonance excitation schemes are generally employed in order to avoid unmanageable optical attenuation and distortion. However, due to the lack of distinctive energy levels, the nonlinear effect in such passive optical media is very weak, and hence a very high light intensity is required to form a soliton. In addition, the lack of distinctive energy levels and transition selection rules also makes an active control of such optical soliton difficult.
In recent years, due to the discovery of electromagnetically induced transparency (EIT), weak-light nonlinear optics in a coherent media has attracted many research attention and interests. The basic theory of EIT is using quantum coherence between atom states induced by a strong control light to eliminate the absorption of a weak probe light. EIT can significantly change the dispersion relation of the media and hence a magnificent reduction of group velocity of the probe light can be obtained. Based on these interesting features, in recent works it has been shown that a new type of optical soliton, called ultraslow optical soliton (or USOS), can form in a resonant multi-level media. And they can propagate in the media at velocity several magnitudes lower than they propagate in vacuum. Such study has opened a new research direction on nonlinear optical pulses formation and propagation in coherent multi-level media.
If we replace the continuous control wave in EIT with a standing wave, the linear dispersion relation of the probe light will be changed from a single line to a series of photonic band gap, and these gaps can be easily manipulated. Recently, many theoretical and experimental works have been done in this area and many interesting results have been found. It is widely expected that a further exploration in this direction may offer new tools of photonic state manipulation and quantum information processing at low-light level.
Different from the previous studies, in this work we consider when the control light has formed a standing wave that how the probe light propagates with weak nonlinearity. Based on a A-type three-level atomic scheme we present an optical gap soliton generation technique in a resonant media via EIT. We shall demonstrate that by modulating the parameters of the system, the oscillating frequency of the gap solitons found by us is within the forbidden gap of frequency spectrum of the probe field, and the incident light intensity needed here is very low. Further more, the physical property of such gap solitons can be easily manipulated in a controllable way. Because of their robust nature, gap solitons may become promising candidates of well-characterized, distortion-free optical pulses and hence have potential technological applications in optical information processing and telecommunication engineering.
The paper is arranged as follows. The first chapter gives a simple description of soliton and electromagnetically induced transparency, and the basic concepts related. In Chapter II we give the basic theory about EIT system and solitons formed in it. In Chapter III we present our study about gap solitons formed in a A-type three-level atomic system under EIT condition, including both small and large gap solitons. The last chapter gives a summary of our main results.
近年来,由于电磁感应透明(EIT)效应的发现,相干介质中的弱光非线性光学的研究引起了人们极大的兴趣。EIT的基本原理是利用光强度较大的控制光所诱导的原子量子态之间的干涉效应来消除共振介质对光强度较弱的入射探测光的吸收。EIT可使介质的色散特性产生重大改变,从而降低探测光的群速度。基于这些有趣的性质,在最近的研究中发现了一种新型的光孤子,称为超慢光孤子(USOS)。这种孤子在多能级共振介质中产生,它的传播速度比真空中的光速小许多数量级。这些成果为研究非线性光脉冲在多能级共振介质中的形成与传播开拓了新的方向。
如果在EIT系统中将连续波控制场改换成驻波控制场,则探测场的线性色散关系会由单一频带转变为多个频带,即形成带结构,而且这些带结构可以十分方便地进行人工调控。最近,理论和实验工作者在这方面开展了认真深入的研究,得到了许多有趣的结果。人们普遍认为在这个方向上的进一步研究可以为低光强度水平上进行量子态操控和量子信息存储提供新方法和新途径。
与以往的研究不同,本文考虑在控制场为驻波场的情形下探测场的弱非线性传播效应。以Λ-型三能级原子为模型,我们提出一种在共振介质中通过EIT技术产生光学频隙孤子的方法。我们将证明,通过调节系统参数,所得光孤子的振动频率可位于探测光场振动频率的禁带之内,而且产生这样的频隙孤子只需要很低的入射光强度。另外,这种频隙孤子物理特性可以很方便地进行人工调控。由于它们的独特性质,频隙孤子可作为性质良好的,没有畸变的光脉冲在光信息处理和光通讯工程领域中发展潜在的应用前景。
本文的主要内容和组织结构如下。第一章简要概述孤子和电磁感应透明现象及有关的基本概念。第二章介绍关于EIT介质中孤子的基本理论。第三章介绍关于Λ-型三能级原子系统在EIT构型下形成频隙孤子的基本研究结果,包括小频隙和大频隙两种情况下的频隙孤子。最后一章给出我们工作的总结。
In the past decades, considerable theoretical and experimental research activities have focused on the study of optical solitons due to their important applications in optical information processing and transmission. Up to now, most optical solitons are produced in passive optical media such as glass-based optical fibers, in which far-off resonance excitation schemes are generally employed in order to avoid unmanageable optical attenuation and distortion. However, due to the lack of distinctive energy levels, the nonlinear effect in such passive optical media is very weak, and hence a very high light intensity is required to form a soliton. In addition, the lack of distinctive energy levels and transition selection rules also makes an active control of such optical soliton difficult.
In recent years, due to the discovery of electromagnetically induced transparency (EIT), weak-light nonlinear optics in a coherent media has attracted many research attention and interests. The basic theory of EIT is using quantum coherence between atom states induced by a strong control light to eliminate the absorption of a weak probe light. EIT can significantly change the dispersion relation of the media and hence a magnificent reduction of group velocity of the probe light can be obtained. Based on these interesting features, in recent works it has been shown that a new type of optical soliton, called ultraslow optical soliton (or USOS), can form in a resonant multi-level media. And they can propagate in the media at velocity several magnitudes lower than they propagate in vacuum. Such study has opened a new research direction on nonlinear optical pulses formation and propagation in coherent multi-level media.
If we replace the continuous control wave in EIT with a standing wave, the linear dispersion relation of the probe light will be changed from a single line to a series of photonic band gap, and these gaps can be easily manipulated. Recently, many theoretical and experimental works have been done in this area and many interesting results have been found. It is widely expected that a further exploration in this direction may offer new tools of photonic state manipulation and quantum information processing at low-light level.
Different from the previous studies, in this work we consider when the control light has formed a standing wave that how the probe light propagates with weak nonlinearity. Based on a A-type three-level atomic scheme we present an optical gap soliton generation technique in a resonant media via EIT. We shall demonstrate that by modulating the parameters of the system, the oscillating frequency of the gap solitons found by us is within the forbidden gap of frequency spectrum of the probe field, and the incident light intensity needed here is very low. Further more, the physical property of such gap solitons can be easily manipulated in a controllable way. Because of their robust nature, gap solitons may become promising candidates of well-characterized, distortion-free optical pulses and hence have potential technological applications in optical information processing and telecommunication engineering.
The paper is arranged as follows. The first chapter gives a simple description of soliton and electromagnetically induced transparency, and the basic concepts related. In Chapter II we give the basic theory about EIT system and solitons formed in it. In Chapter III we present our study about gap solitons formed in a A-type three-level atomic system under EIT condition, including both small and large gap solitons. The last chapter gives a summary of our main results.
引文
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[28] M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094(2000).
[29] Chien Liu et al., Nature 409,490(2001).
[30] M. Bajcsy, A. S. Zibrov and M. D. Lukin, Nature 426, 638(2003).
[31] Alan C. Newell and Jerome V. Moloney, Nonlinear Optics (Wesley Publishing Company, 1992).
[32] A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springrer, Berlin, 2003).
[33] G Huang, L. Deng and M. G Payne, Phys. Rev. E 72, 016617(2005).
[34] G Huang et al, Phys. Rev. E 73, 056606(2006).
[35] C. Hang, G Huang and L. Deng, Phys. Rev. E 73,036607(2006).
[36] C. Hang, G Huang, and L. Deng, Phys. Rev. E 74,046601(2006).
[37] A. Andre and M. D. Lukin, Phys. Rev. Lett. 89,143602(2002).
[38] A. Andre et al, Phys. Rev. Lett. 94, 063902(2005).
[39] X. M. Su and B. S. Ham, Phys. Rev. A 71, 013821(2005).
[40] W. Jiang et al., arXiv:quant-ph/0511210.
[41] F. E. Zimmer et al., quant-ph/0602197.
[42] W. Chen and D. L. Mills, Phys. Rev. Lett. 58,160(1987).
[43] W. Chen and D. L. Mills, Phys Rev. B 36, 6269(1987).
[44] C. M. de Sterke and J. E. Sipe, Prog. Opt. XXXIII, 203(1994).
[45] R. E. Slusher and B. J. Eggleton, Nonlinear Photonic Crystals (Springer-Velarg, Berlin, 2003), and references therein.
[46] A. Jeffrey and T. Kawahara, Asymptotic Methods in Nonlinear Wave Theory (Pitman, London, 1982).
[47] H. Schimit and A. Imamohlu Opt. Lett. 21,1936(1996).
[48] A. B. Aceves and S. Wabnitz, Phys. Lett. A141, 37(1989).
[49] D. N. Christodoulides and R. I. Joseph, Phys. Rev. Lett. 62,1746(1989).
[50] D. J. Kaup and A. C. Newell, Lett. Nuovo Cim. 20, 325(1977).
[51] C. Martijn de Sterke and J. E. Sipe, Opt. Lett. Vol.13, No.2 (1988); C. Martijn de Sterke and J. E. Sipe, Phys. Rev. A38, 5149(1988).
[52] C. Martijn de Sterke and J. E. Sipe, Phys. Rev. A39, 5163 (1989).
[53] C. Martijn de Sterke and J. E. Sipe, Phys. Rev. A 42, 550(1990).
[54] C. Hang et al, Phys. Lett. A 74,012319(2006).
[55] S. E. Harris and Y. Yamamoto, Phys. Rev. Lett. 81, 3611(1998).
[56] M. Yan, E. G Rickey and Yifu Zhu, Phys. Rev. A 64, 041801(2001).
[57] H. Kang et al., Phys. Rev. A 73, 011802(2006).
[58] H. Y. Ling, H. Pu and B. Seaman, Phys. Rev. Lett. 93, 250403(2004).
[59] H. Y. Ling et al., Phys. Rev. A 75, 033615(2007).
[60] H. X. Chen etal, Phys. Rev. A58,1545(1998).
[61] M. V. Pack, R. M. Camacho and J. C. Howell, Phys. Rev. A 74, 013812(2006).
[62] H. J. Li, C. Hang and Guoxiang Huang, Phys. Lett. A, (2007) in press.
[63] F. S. Pavone et al., Opt. Lett. 22, 736(1997).
[64] S. Wielandy and A. L. Gaeta, Phys. Rev. Lett. 81,3359(1998).
[65] V. A. Sautenkov et al, Phys. Rev. A 62, 023810(2000).
[66] D. Cho et al., Phys. Rev. A 72, 023821 (2005).
[67] T. Hong et al, Phys. Rev. Lett. 94, 050801(2005).
[68] R. Santra et al, Phys. Rev. Lett. 94,173002(2005).
[69] T. Zanon-Willette et al, Phys. Rev. Lett. 97,233001(2006).
[70] W. Yang, A. Joshi and M. Xiao, Phys. Rev. Lett. 95, 093902(2005).
[71] G Huang et al, Phys. Rev. A 65, 053605(2002).
[72] G Huang et al, Phys. Rev. A 67, 023604(2003).