动态光子晶体中V型三能级原子的自发辐射

邢容; 谢双媛; 许静平; 羊亚平

doi:10.7498/aps.66.014202

摘要

研究了动态各向同性光子晶体中V型三能级原子的自发辐射，主要讨论了光子晶体能带带边频率受到阶跃调制和三角函数周期调制两种情况下，调制参数对占据数演化的控制作用，以及此过程中量子相干效应带来的影响.结果表明，阶跃调制时，调制发生后原子上能级劈裂出来的束缚缀饰态数目只取决于原子的跃迁频率和此时的带边频率，且与具有相同参数条件的静态情形下的相同.调制发生时刻对其后原子上能级占据数的长时演化情况有影响.随系统初态的不同，量子相干效应既可导致调制之后占据数迅速衰减，也可使原子上能级保留较多的占据数.三角函数周期调制时，原子上能级总占据数在足够长的时间之后随时间做频率近似等于调制频率的有衰减的准周期振荡.衰减率与调制频率有关，也因量子相干效应而受系统初态以及偶极矩夹角的影响.

关键词:

Abstract

The spontaneous emission from a V-type three-level atom embedded in an isotropic photonic crystal with dynamic photonic band edge is studied. We consider the situation where the atom interacts with all possible radiation modes, and calculate numerically the evolution of atomic population without using Markov approximation. The calculation method can be used in related researches. In the present paper, we mainly discuss the effects of modulation parameters and the quantum interference on spontaneous emission when the band edge is modulated with step function or triangle function. We hope that the results can contribute to the applications in the dynamic photonic crystal environment in controlling the spontaneous emission via the quantum interference. The results show that in the step-modulated situation, the number of the photon-atom bound dressed states after the modulation has happened depends on atomic transition frequencies and the band edge frequency at that time, and is identical to the one in the unmodulated situation with the same parameters. The long-time evolution of the atomic population is affected by the time when the modulation happens. Depending on the system initial state, after the modulation has happened, the quantum interference can weaken the probability amplitude components corresponding to the photon-atom bound dressed states, and cause the upper-level population to decay quickly from a great value to a value near zero; or on the contrary, it can strengthen the bound dressed states, and make the upper levels retain a high population. In the modulated situation with trigonometric functions, after long enough time, the total upper-level population presents a decaying quasi-periodic oscillation behaviour. And the evolution of the total upper-level population tends to synchronize with the modulation, so the frequency of the quasi-periodic oscillation is approximately equal to the modulation frequency. But, the quantum interference can destroy the synchronization under some conditions. The decay rate of the total upper-level population is affected by the modulation frequency, and also by the initial state of the system and the angle between two dipole moment because of the quantum interference.

Keywords:

作者及机构信息

1.
同济大学物理科学与工程学院先进微结构材料教育部重点实验室, 上海 200092

通信作者: 谢双媛, xieshuangyuan@tongji.edu.cn

基金项目: 国家自然科学基金（批准号：11074188，11274242）、国家自然科学基金委员会-中国工程物理研究院联合基金（批准号：U1330203）和国家重点基础研究计划特别基金（批准号：2011CB922203，2013CB632701）资助的课题.

Authors and contacts

1.
Ministry of Education Key Laboratory of Advanced Microstructure Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

Corresponding author: Xie Shuang-Yuan, xieshuangyuan@tongji.edu.cn

Funds: Project supported by the National Natural Science Foundation of China（Grant Nos. 11074188, 11274242), the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics（Grant No. U1330203) and the National Key Basic Research Special Foundation of China（NKBRSFC)（Grant Nos. 2011CB922203, 2013CB632701).

参考文献

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[3]	Zhu S Y, Chan R C F, Lee C P 1995 Phys. Rev. A 52 710
[4]	Paspalakis E, Kylstra N J, Knight P L 1999 Phys. Rev. A 60 R33
[5]	Angelakis D G, Paspalakis E, Knight P L 2001 Phys. Rev. A 64 013801
[6]	Du C G, Hu Z F, Hou C F, Li S Q 2002 Chin. Phys. Lett. 19 338
[7]	Yang Y P, Zhu S Y, Zubairy M S 1999 Opt. Commun. 166 79
[8]	Yang Y P, Zhu S Y 2000 Phys. Rev. A 61 043809
[9]	Yang Y P, Zhu S Y 2000 J. Mod. Opt. 47 1513
[10]	Zhu S Y, Chen H, Huang H 1997 Phys. Rev. Lett. 79 205
[11]	Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[12]	John S 1987 Phys. Rev. Lett. 58 2486
[13]	John S, Wang J 1990 Phys. Rev. Lett. 64 2418
[14]	John S, Wang J 1991 Phys. Rev. B 43 12772
[15]	John S, Quang T 1994 Phys. Rev. A 50 1764
[16]	Yang Y P, Lin Z X, Xie S Y, Feng W G, Wu X 1999 Acta Phys. Sin. 48 603 （in Chinese)[羊亚平, 林志新, 谢双媛, 冯伟国, 吴翔1999 48 603]
[17]	Xie S Y, Yang Y P, Wu X 2001 Eur. Phys. J. D 13 129
[18]	Quang T, Woldeyohannes M, John S, Agarwal G S 1997 Phys. Rev. Lett. 79 5238
[19]	Wang X H, Gu B Y 2005 Appl. Phys. Lett. 86 051103
[20]	Zhang L F, Huang J P 2010 Chin. Phys. B 19 024213
[21]	Liu S Y, Du J J, Lin Z F, Wu R X, Chui S T 2008 Phys. Rev. B 78 155101
[22]	Manzanares-Martinez J, Ramos-Mendieta F, Halevi P 2005 Phys. Rev. B 72 035336
[23]	Hu X Y, Zhang Q, Liu Y H, Cheng B Y, Zhang D Z 2003 Appl. Phys. Lett. 83 2518
[24]	Leonard S W, van Driel H M, Schilling J, Wehrspohn R B 2002 Phys. Rev. B 66 161102
[25]	Jia F, Xie S Y, Yang Y P 2006 Acta Phys. Sin. 55 5835 （in Chinese)[贾飞, 谢双媛, 羊亚平2006 55 5835]
[26]	Pisipati U, Almakrami I M, Joshi A, Serna J D 2012 Am. J. Phys. 80 612
[27]	Yang Y P, Xu J P, Li G X, Chen H 2004 Phys. Rev. A 69 053406
[28]	Law C K, Zhu S Y, Zubairy M S 1995 Phys. Rev. A 52 4095
[29]	Linington I E, Garraway B M 2006 J. Phys. B:At. Mol. Opt. Phys. 39 3383
[30]	Linington I E, Garraway B M 2008 Phys. Rev. A 77 033831
[31]	Kofman A G, Kurizki G 2001 Phys. Rev. Lett. 87 270405
[32]	Linz P 1985 Analytical and Numerical Methods for Volterra Equations（Philadelphia:Society for Industrial and Applied Mathematics) Chapter 7
[33]	Xia H R, Ye C Y, Zhu S Y 1996 Phys. Rev. Lett. 77 1032

施引文献

[1]	Scully M O, Zubairy M S 1997 Quantum Optics（Cambridge:Cambridge University Press) Chapter 7
[2]	Fleischhauer M, Imamoglu A, Marangos J 2005 Rev. Mod. Phys. 77 633
[3]	Zhu S Y, Chan R C F, Lee C P 1995 Phys. Rev. A 52 710
[4]	Paspalakis E, Kylstra N J, Knight P L 1999 Phys. Rev. A 60 R33
[5]	Angelakis D G, Paspalakis E, Knight P L 2001 Phys. Rev. A 64 013801
[6]	Du C G, Hu Z F, Hou C F, Li S Q 2002 Chin. Phys. Lett. 19 338
[7]	Yang Y P, Zhu S Y, Zubairy M S 1999 Opt. Commun. 166 79
[8]	Yang Y P, Zhu S Y 2000 Phys. Rev. A 61 043809
[9]	Yang Y P, Zhu S Y 2000 J. Mod. Opt. 47 1513
[10]	Zhu S Y, Chen H, Huang H 1997 Phys. Rev. Lett. 79 205
[11]	Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[12]	John S 1987 Phys. Rev. Lett. 58 2486
[13]	John S, Wang J 1990 Phys. Rev. Lett. 64 2418
[14]	John S, Wang J 1991 Phys. Rev. B 43 12772
[15]	John S, Quang T 1994 Phys. Rev. A 50 1764
[16]	Yang Y P, Lin Z X, Xie S Y, Feng W G, Wu X 1999 Acta Phys. Sin. 48 603 （in Chinese)[羊亚平, 林志新, 谢双媛, 冯伟国, 吴翔1999 48 603]
[17]	Xie S Y, Yang Y P, Wu X 2001 Eur. Phys. J. D 13 129
[18]	Quang T, Woldeyohannes M, John S, Agarwal G S 1997 Phys. Rev. Lett. 79 5238
[19]	Wang X H, Gu B Y 2005 Appl. Phys. Lett. 86 051103
[20]	Zhang L F, Huang J P 2010 Chin. Phys. B 19 024213
[21]	Liu S Y, Du J J, Lin Z F, Wu R X, Chui S T 2008 Phys. Rev. B 78 155101
[22]	Manzanares-Martinez J, Ramos-Mendieta F, Halevi P 2005 Phys. Rev. B 72 035336
[23]	Hu X Y, Zhang Q, Liu Y H, Cheng B Y, Zhang D Z 2003 Appl. Phys. Lett. 83 2518
[24]	Leonard S W, van Driel H M, Schilling J, Wehrspohn R B 2002 Phys. Rev. B 66 161102
[25]	Jia F, Xie S Y, Yang Y P 2006 Acta Phys. Sin. 55 5835 （in Chinese)[贾飞, 谢双媛, 羊亚平2006 55 5835]
[26]	Pisipati U, Almakrami I M, Joshi A, Serna J D 2012 Am. J. Phys. 80 612
[27]	Yang Y P, Xu J P, Li G X, Chen H 2004 Phys. Rev. A 69 053406
[28]	Law C K, Zhu S Y, Zubairy M S 1995 Phys. Rev. A 52 4095
[29]	Linington I E, Garraway B M 2006 J. Phys. B:At. Mol. Opt. Phys. 39 3383
[30]	Linington I E, Garraway B M 2008 Phys. Rev. A 77 033831
[31]	Kofman A G, Kurizki G 2001 Phys. Rev. Lett. 87 270405
[32]	Linz P 1985 Analytical and Numerical Methods for Volterra Equations（Philadelphia:Society for Industrial and Applied Mathematics) Chapter 7
[33]	Xia H R, Ye C Y, Zhu S Y 1996 Phys. Rev. Lett. 77 1032

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