囚禁单离子的量子阻尼运动

李金晴; 罗云荣; 海文华

doi:10.7498/aps.66.233701

摘要

用包含偶极和四极虚势能项的非厄米哈密顿算符来描述Paul阱中囚禁阻尼单离子在静电场下的量子运动.通过导出和分析系统的精确解，得到在PT对称和不对称情形下的不同实能谱与稳定量子态，以及PT不对称情形的虚能谱和衰减量子态，同时给出相应于不同态的参数区域和存活概率.结果发现该非厄米系统外场参数能惟一确定量子稳定态并导致波函数形态变化，据此提出非相干操控相应量子跃迁的方法.让量子态衰减导致的离子位置期待值的衰减与经典阻尼谐振子的衰减一致，得到虚势能参数与经典阻尼参数的对应关系.所得结果将进一步丰富具有广泛应用背景的囚禁离子动力学.

关键词:

Abstract

Classical motion of a single damped ion confined in a Paul trap is usually described by a damped harmonic oscillator model. We report the treatment of quantum damping motion of the system via a non-Hermitian Hamiltonian with dipole and quadrupole imaginary potential. By deriving and analyzing the exact solution of the system, we obtain the different real energy spectra and stable quantum states for the PT symmetry and asymmetry cases, as well as the imaginary spectrum and decaying quantum state for the PT asymmetry case. The corresponding imaginary energy parameter region and the survival probability are investigated. We find that the non-Hermitian system parameters of the external filed uniquely determine the quantum stable states and lead to the new characteristic of the morphology of wave function. Based on these properties, we propose a method of incoherently manipulating quantum transitions between the quantum stable states. By setting the decayed expectation value of ion position to be the same as the decayed displacement of the classical damped harmonic oscillator, we obtain the correspondence between the imaginary potential strength and the classical damping parameters. The results will enrich the quantum dynamics of the damped trapped ions, which may be useful in a wide application field.

Keywords:

作者及机构信息

1.
湖南师范大学物理系, 低维量子结构与调控教育部重点实验室, 湖南省量子效应及其应用协同创新中心, 长沙 410081

通信作者: 海文华, whhai2005@aliyun.com

基金项目: 国家自然科学基金（批准号：11475060）、湖南省研究生科研创新项目（批准号：CX2017B222）和湖南省自然科学基金（批准号：2017JJ3208）资助的课题.

Authors and contacts

1.
Synergetic Innovation Center for Quantum Effects and Applications of Hunan Province, Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics, Hunan Normal University, Changsha 410081, China

Corresponding author: Hai Wen-Hua, whhai2005@aliyun.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11475060), the Hunan Provincial Innovation Foundation for Postgraduate and Graduate Degree Thesis, China (Grant No. CX2017B222), and the Hunan Provincial Natural Science Foundation of China (Grant No. 2017JJ3208).

参考文献

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[21]	Eleuch H, Rotter I 2017 Phys. Rev. A 95 022117
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[23]	Li J H, Yu R, Ding C L, Wu Y 2016 Phys. Rev. A 93 023814
[24]	Santra R, Cederbaum L S 2002 Phys. Rep. 368 1
[25]	Longhi S 2016 Europhys. Lett. 115 61001
[26]	Jin L, Song Z 2009 Phys. Rev. A 80 052107
[27]	Jin L, Song Z 2010 Phys. Rev. A 81 032109
[28]	Zhong H H, Hai W H, Lu G B, Li Z J 2011 Phys. Rev. A 84 013401
[29]	Xiao K W, Hai W H, Liu J 2012 Phys. Rev. A 85 013410
[30]	Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401
[31]	Chen Z J, Ning X J 2003 Acta Phys. Sin. 52 2683 (in Chinese)[陈增军, 宁西京 2003 52 2683]
[32]	Baradaran M, Panahi H 2017 Chin. Phys. B 26 060301
[33]	Wang X Y, Chen H Z, Li Y, Li B, Ma R M 2016 Chin. Phys. B 25 124211
[34]	Graefe E M, Höning M, Korsch H J 2010 J. Phys. A:Math. Theor. 43 075306
[35]	Caldeira A O, Leggett A J 1985 Phys. Rev. A 31 1059
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[37]	Casati G, Guarneri I, Maspero G 2000 Phys. Rev. Lett. 84 63
[38]	Wimberger S, Krug A, Buchleitner A 2002 Phys. Rev. Lett. 89 263601
[39]	Mizrahi J, Senko C, Neyenhuis B, Johnson K G, Campbell W C, Conover C W S, Monroe C 2013 Phys. Rev. Lett. 110 203001
[40]	Chen Q, Hai K, Hai W H 2010 J. Phys. A:Math. Theor. 43 455302
[41]	Hai K, Luo Y R, Chong G S, Chen H, Hai W H 2017 Quantum Inf. Comput. 17 456
[42]	Chen Y H, She L, Wang M, Yang Z H, Liu H, Li J M 2016 Chin. Phys. B 25 120601
[43]	Yang M R, Hai W H, Lu G B, Zhong H H 2010 Acta Phys. Sin. 59 2406 (in Chinese)[杨美蓉, 海文华, 鲁耿彪, 钟宏华 2010 59 2406]

施引文献

[1]	Wineland D J 2013 Rev. Mod. Phys. 85 1103
[2]	Duan L M, Monroe C 2010 Rev. Mod. Phys. 82 1209
[3]	Singer K, Poschinger U, Murphy M, Ivanov P, Ziesel F, Calarco T, Schmidt-Kaler F 2010 Rev. Mod. Phys. 82 2609
[4]	Leibfried D, Blatt R, Monroe C, Wineland D 2003 Rev. Mod. Phys. 75 281
[5]	Soderberg K A B, Monroe C 2010 Rep. Prog. Phys. 73 036401
[6]	DeVoe R G, Hoffnagle J, Brewer R G 1989 Phys. Rev. A 39 4362
[7]	Blmel R 1995 Phys. Rev. A 51 620
[8]	Nam Y S, Jones E B, Blmel R 2014 Phys. Rev. A 90 013402
[9]	Weiss D K, Nam Y S, Blmel R 2016 Phys. Rev. A 93 043424
[10]	Hai W H, Duan Y W, Zhu X W, Shi L, Luo X L, He C S 1997 Acta Phys. Sin. 46 2217 (in Chinese)[海文华, 段宜武, 朱熙文, 施磊, 罗学立, 何春山 1997 46 2217]
[11]	Mihalcea B M, Vişan G G 2010 Phys. Scr. T 140 014057
[12]	Peng H W 1980 Acta Phys. Sin. 29 1084 (in Chinese)[彭桓武 1980 29 1084]
[13]	Gzyl H 1983 Phys. Rev. A 27 2297
[14]	Akerman N, Kotler S, Glickman Y, Dallal Y, Keselman A, Ozeri R 2010 Phys. Rev. A 82 061402
[15]	Fidio C D, Vogel W 2000 Phys. Rev. A 62 031802
[16]	Gong S J, Zhou F, Wu H Y, Wan W, Chen L, Feng M 2015 Chin. Phys. Lett. 32 013201
[17]	Bazrafkan M R, Ashrafi S M, Naghdi F 2014 Chin. Phys. Lett. 31 070303
[18]	Klimov A B, Romero J L, Delgado J, Sánchez-Soto L L 2004 Opt. Commun. 230 393
[19]	Jiang Z, Chen P X 2012 Acta Phys. Sin. 61 014209 (in Chinese)[蒋智, 陈平形 2012 61 014209]
[20]	Bushev P, Rotter D, Wilson A, Dubin F, Becher C, Eschner J, Blatt R, Steixner V, Rabl P, Zoller P 2006 Phys. Rev. Lett. 96 043003
[21]	Eleuch H, Rotter I 2017 Phys. Rev. A 95 022117
[22]	Dattoli G, Torre A, Mignani R 1990 Phys. Rev. A 42 1467
[23]	Li J H, Yu R, Ding C L, Wu Y 2016 Phys. Rev. A 93 023814
[24]	Santra R, Cederbaum L S 2002 Phys. Rep. 368 1
[25]	Longhi S 2016 Europhys. Lett. 115 61001
[26]	Jin L, Song Z 2009 Phys. Rev. A 80 052107
[27]	Jin L, Song Z 2010 Phys. Rev. A 81 032109
[28]	Zhong H H, Hai W H, Lu G B, Li Z J 2011 Phys. Rev. A 84 013401
[29]	Xiao K W, Hai W H, Liu J 2012 Phys. Rev. A 85 013410
[30]	Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401
[31]	Chen Z J, Ning X J 2003 Acta Phys. Sin. 52 2683 (in Chinese)[陈增军, 宁西京 2003 52 2683]
[32]	Baradaran M, Panahi H 2017 Chin. Phys. B 26 060301
[33]	Wang X Y, Chen H Z, Li Y, Li B, Ma R M 2016 Chin. Phys. B 25 124211
[34]	Graefe E M, Höning M, Korsch H J 2010 J. Phys. A:Math. Theor. 43 075306
[35]	Caldeira A O, Leggett A J 1985 Phys. Rev. A 31 1059
[36]	Gu Y 1996 Quantum Chaos (Shanghai:Shanghai Scientific and Technological Education Press) (in Chinese)[顾雁 1996 量子混沌 (上海:上海科技教育出版社)]
[37]	Casati G, Guarneri I, Maspero G 2000 Phys. Rev. Lett. 84 63
[38]	Wimberger S, Krug A, Buchleitner A 2002 Phys. Rev. Lett. 89 263601
[39]	Mizrahi J, Senko C, Neyenhuis B, Johnson K G, Campbell W C, Conover C W S, Monroe C 2013 Phys. Rev. Lett. 110 203001
[40]	Chen Q, Hai K, Hai W H 2010 J. Phys. A:Math. Theor. 43 455302
[41]	Hai K, Luo Y R, Chong G S, Chen H, Hai W H 2017 Quantum Inf. Comput. 17 456
[42]	Chen Y H, She L, Wang M, Yang Z H, Liu H, Li J M 2016 Chin. Phys. B 25 120601
[43]	Yang M R, Hai W H, Lu G B, Zhong H H 2010 Acta Phys. Sin. 59 2406 (in Chinese)[杨美蓉, 海文华, 鲁耿彪, 钟宏华 2010 59 2406]

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