Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams

doi:10.1088/1674-1056/28/1/010306

中国物理B ›› 2019, Vol. 28 ›› Issue (1): 10306-010306.doi: 10.1088/1674-1056/28/1/010306

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams

Jun Wen(文军), Jian-Qi Zhang(张建奇), Lei-Lei Yan(闫磊磊), Mang Feng(冯芒)

1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
2 School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2018-09-18 修回日期:2018-11-14 出版日期:2019-01-05 发布日期:2019-01-05
通讯作者: Mang Feng E-mail:mangfeng@wipm.ac.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11734018, 11674360, 11404377, and 91636220).

Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams

Jun Wen(文军)^1,2, Jian-Qi Zhang(张建奇)¹, Lei-Lei Yan(闫磊磊)¹, Mang Feng(冯芒)¹

1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
2 School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2018-09-18 Revised:2018-11-14 Online:2019-01-05 Published:2019-01-05
Contact: Mang Feng E-mail:mangfeng@wipm.ac.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11734018, 11674360, 11404377, and 91636220).

摘要/Abstract

摘要：

Trapped ions, under electromagnetic confinement and Coulomb repulsion, can behave as non-interacting particles in one-dimensional lattices. Here we explore analytically the possible effects regarding Anderson localization in a chain of trapped ions experiencing laser Bessel beams. Under an experimentally feasible condition, we predict an analytical form of the energy-dependent mobility edges, which is verified to be in good agreement with the exact numerical results except for the top band. Some other important properties regarding the phonon localization in the ion chain are also discussed both analytically and numerically. Our results are relevant to experimental observation of localization-delocalization transition in the ion trap and helpful for deeper understanding of the rich phenomena due to long-range phonon hopping.

关键词: mobility edge, localization, eigenstates, critical values

Abstract:

Key words: mobility edge, localization, eigenstates, critical values

中图分类号: (Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)

03.75.Lm

05.50.+q (Lattice theory and statistics) 64.60.Cn (Order-disorder transformations) 63.20.-e (Phonons in crystal lattices)

文军, 张建奇, 闫磊磊, 冯芒. Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams[J]. 中国物理B, 2019, 28(1): 10306-010306.

Jun Wen(文军), Jian-Qi Zhang(张建奇), Lei-Lei Yan(闫磊磊), Mang Feng(冯芒). Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams[J]. Chin. Phys. B, 2019, 28(1): 10306-010306.

参考文献 31

[1]	Anderson P W 1958 Phys. Rev. 109 1492 doi: 10.1103/PhysRev.109.1492
[2]	Lahini Y, Pugatch R, Pozzi F, Sorel M, Morandotti R, Davidson N and Silberberg Y 2009 Phys. Rev. Lett. 103 013901 doi: 10.1103/PhysRevLett.103.013901
[3]	Roati G, Errico C D, Fallani L, Fattori M, Fort C, Zaccanti M, Modugno G, Modugno M and Inguscio M 2008 Nature 453 895 doi: 10.1038/nature07071
[4]	Billy J, Josse V, Zuo Z C, Bernard A, Hambrecht B, Lugan P, Clément D, Plencia L S, Bouyer P and Aspect A 2008 Nature 453 891 doi: 10.1038/nature07000
[5]	Lye J E, Fallani L, Fort C, Guarrera V, Modugno M, Wiersam D S and Inguscio M 2007 Phys. Rev. A 75 061603 doi: 10.1103/PhysRevA.75.061603
[6]	Shadrivov I V, Bliokh K Y, Bliokh Y P, Freilikher V and Kivshar Y S 2010 Phys. Rev. Lett. 104 123902 doi: 10.1103/PhysRevLett.104.123902
[7]	Conti C 2012 Phys. Rev. A 86 061801(R)
[8]	Eleuch H, Hilke M, and MacKenzie R 2017 Phys. Rev. A 95 062114 doi: 10.1103/PhysRevA.95.062114
[9]	Sheinfux H H, Lumer Y, Ankonina G, Genack A Z, Bartal G and Segev M 2017 Science 356 953 doi: 10.1126/science.aah6822
[10]	Aubry S and André G 1979 Ann, Isr. Phys. Soc. 3 133
[11]	Kraus Y E and Zilberber O 2012 Phys. Rev. Lett 109 116404 doi: 10.1103/PhysRevLett.109.116404
[12]	Liu F, Ghosh S and Chong Y D 2015 Phys. Rev. B 91 014108 doi: 10.1103/PhysRevB.91.014108
[13]	Ke Y G, Qin X Z, Mei F, Zhong H H, Kivshar Y S and Lee C H 2016 Laser & Photonics Reviews 10 995
[14]	Albert M and Leboeuf P 2010 Phys. Rev. A 81 013614 doi: 10.1103/PhysRevA.81.013614
[15]	Bermudez A, Martin-Delgado A and Porras D 2010 New J. Phys. 12 123016 doi: 10.1088/1367-2630/12/12/123016
[16]	Modugno M 2009 New J. Phys. 11 033023 doi: 10.1088/1367-2630/11/3/033023
[17]	Gopalakrishnan S 2017 Phys. Rev. B 96 054202 doi: 10.1103/PhysRevB.96.054202
[18]	Sarma S D, He S and Xie X C 1998 Phys. Rev. Lett. 61 2144
[19]	Biddle J and Sarma S D 2009 Phys. Rev. Lett. 104 070601
[20]	Zhang W, Yang R, Zhao Y, Duan S, Zhang P and Ulloa S E 2010 Phys. Rev. B 81 214202 doi: 10.1103/PhysRevB.81.214202
[21]	Biddle J, Jr D J P, Wang B and Sarma S D 2011 Phys. Rev. B 83 075105 doi: 10.1103/PhysRevB.83.075105
[22]	Dufour G and Orso G 2102 Phys. Rev. Lett. 109 155306
[23]	Liu X M, Du Z Z, Cheng W W and Liu J M 2015 Int. J. Theor. Phys. 54 30033
[24]	Qin P Q, Yin C H and Chen S 2014 Phys. Rev. B 90 054303
[25]	Lin G D, Zhu S L, Islam R, Kim K, Chang M S, Korenblit S, Monroe C and Duan L M 2009 Europhys. Lett. 86 60004 doi: 10.1209/0295-5075/86/60004
[26]	Bermudez A, Bruderer M and Plenio M B 2013 Phys. Rev. Lett. 111 040601 doi: 10.1103/PhysRevLett.111.040601
[27]	Reamm M, Pruttivarasin T and Häffner H 2014 New J. Phys. 16 063062 doi: 10.1088/1367-2630/16/6/063062
[28]	Abdelrahman A, Khosravani O, Gessner M, Buchleitner A, Breuer H P, Gorman D, Masuda R, Pruttivarasin T, Ramm M, Schindler P and Häffner H 2017 Nat. Commun. 8 15712 doi: 10.1038/ncomms15712
[29]	Wen J, Zhang J Q, Yan L L, Chen L, Cai X M and Feng M 2018 Phys. Rev. A 98 013829 doi: 10.1103/PhysRevA.98.013829
[30]	Blümel R and Smilansky U 1984 Phys. Rev. Lett. 52 137 doi: 10.1103/PhysRevLett.52.137
[31]	Amico L, Fazio R, Osterloh A and Vedral V 2008 Rev. Mod. Phys. 80 517 doi: 10.1103/RevModPhys.80.517

Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams

Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams

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