Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms

doi:10.1088/1674-1056/27/5/053401

Abstract We study the fractal rhythm in the ionization of Rydberg helium and lithium atoms in an electric field by using the semiclassical method. The fractal structures present a nested relationship layer by layer in the initial launch angles of the ionized electrons versus the escape time, which is defined as the rhythm attractor, and exhibit similar rhythm endings. The gradually enhanced chaotic regions of the escape time plots tend to broaden as the scaled energy increases. In addition, the fractal rhythm changes synchronously with the oscillations of the kinetic energy spectrum. We note that the intrinsic quality of the fractal rhythm is closely related to the kinetic energy distribution, that is, the inherent dynamic properties of the Hamiltonian equations have an impact on the fractal regularities. In addition, different ionizing closed trajectories exhibit iterate properties and the inherent beauty of symmetry. Our results and analysis can not only reveal new laws in the ionization of Rydberg atoms, but also promote the establishment of the dynamic mechanism of fractals.

Keywords: ionization dynamics Rydberg atoms fractal rhythm kinetic energy spectrum

Received: 05 August 2017
Revised: 12 January 2018
Accepted manuscript online:

PACS:	34.50.Fa	(Electronic excitation and ionization of atoms (including beam-foil excitation and ionization))
	05.45.Pq	(Numerical simulations of chaotic systems)
	03.65.Sq	(Semiclassical theories and applications)

Fund: Project supported by the Natural Science Foundation of Shandong Province,China (Grant No.ZR2014AM030).Xiangji Cai is also partially supported by the Program for Outstanding PhD Candidate of Shandong University,China.

Corresponding Authors: Yanhui Zhang
E-mail: yhzhang@sdnu.edu.cn

Cite this article:

Yanhui Zhang(张延惠), Xiulan Xu(徐秀兰), Lisha Kang(康丽莎), Xiangji Cai(蔡祥吉), Xu Tang(唐旭) Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms 2018 Chin. Phys. B 27 053401

[14]	Blondel C, Delsart C and Dulieu F 1996 Phys. Rev. Lett. 77 3755
[1]	Yang G C, Mao J M and Du M L 1999 Phys. Rev. A 59 2053
[15]	Nicole C, Offerhaus H L, Vrakking M J J, Lépine F and Bordas C 2002 Phys. Rev. Lett. 88 133001
[2]	Zhao L B and Delos J B 2010 Phys. Rev. A 81 053417
[16]	Lépine F, Bordas C, Nicole C and Vrakking M J J 2004 Phys. Rev. A 70 033417
[3]	Zhao L B and Delos J B 2010 Phys. Rev. A 81 053418
[17]	Nicole C, Sluimer I, Rosca-Pruna F, Warntjes M, Vrakking M, Bordas C, Texier F and Robicheaux F 2000 Phys. Rev. Lett. 85 4024
[4]	Hüpper B, Main J and Wunner G 1996 Phys. Rev. A 53 744
[18]	Ivanov I A, Nam C H and Kim K T 2016 Phys. Rev. A 93 043404
[5]	Lankhuijzen G M and Noordam L D 1996 Phys. Rev. Lett. 76 1784
[19]	Hüpper B, Main Jörg and Wunner G 1995 Phys. Rev. Lett. 74 2650
[6]	Zhou H, Li H Y, Gao S, Zhang Y H, Jia Z M and Lin S L 2008 Chin. Phys. B 17 4428
[7]	Wang D H 2011 Chin. Phys. B 20 013403
[20]	Xu X L, Zhang Y H, Cai X J, Zhao G P and Kang L S 2016 Chin. Phys. B 25 110301
[21]	Liu F L and Zhao L B 2017 Phys. Rev. A 95 043428
[8]	Du M L 1989 Phys. Rev. A 40 4983
[22]	Deng M, Gao W, Lu R, Delos J B, You L and Liu H P 2016 Phys. Rev. A 93 063411
[9]	Du M L and Delos J B 1988 Phys. Rev. A 38 1896
[23]	Stodolna A S, Lépine F, Bergeman T, Robicheaux F, Gijsbertsen A, Jungmann J H, Bordas C and Vrakking M J J 2014 Phys. Rev. Lett. 113 103002
[10]	Du M L and Delos J B 1987 Phys. Rev. Lett. 58 1731
[11]	Fabian L, Iva Březinová, Joachim B and Florian L 2013 Phys. Rev. E 88 022916
[24]	Chen X, Wu Y and Zhang J T 2017 Phys. Rev. A 95 013402
[25]	Wang L, Yang H F, Liu X J, Liu H P, Zhan M S and Delos J B 2010 Phys. Rev. A 82 022514
[12]	Zhao G P, Zhang Y H, Cai X J, Xu X L and Kang L S 2016 Physica E 84 10
[26]	Mitchell K A, Handley J P, Tighe B, Flower A and Delos J B 2004 Phys. Rev. A 70 043407
[13]	Yang B C, Delos J B and Du M L 2014 Phys. Rev. A 89 013417
[14]	Blondel C, Delsart C and Dulieu F 1996 Phys. Rev. Lett. 77 3755
[27]	Mitchell K A, Handley J P, Tighe B, Flower A and Delos J B 2004 Phys. Rev. Lett. 92 073001
[28]	Mitchell K A, Handley J P, Tighe B, Delos J B and Knudson S K 2003 Chaos:An Interdisciplinary Journal of Nonlinear Science 13 880
[15]	Nicole C, Offerhaus H L, Vrakking M J J, Lépine F and Bordas C 2002 Phys. Rev. Lett. 88 133001
[16]	Lépine F, Bordas C, Nicole C and Vrakking M J J 2004 Phys. Rev. A 70 033417
[29]	Mitchell K A, Handley J P, Delos J B and Knudson S K 2003 Chaos:An Interdisciplinary Journal of Nonlinear Science 13 892
[30]	Kotimäki V, Räsänen E, Hennig H and Heller E J 2013 Phys. Rev. E 88 022913
[17]	Nicole C, Sluimer I, Rosca-Pruna F, Warntjes M, Vrakking M, Bordas C, Texier F and Robicheaux F 2000 Phys. Rev. Lett. 85 4024
[18]	Ivanov I A, Nam C H and Kim K T 2016 Phys. Rev. A 93 043404
[31]	Yi X H, Bi J J, Liu R, Wang C K, Jiao Y and Li Z L 2016 Chin. Phys. B 25 128503
[19]	Hüpper B, Main Jörg and Wunner G 1995 Phys. Rev. Lett. 74 2650
[32]	Byrd T A and Delos J B 2014 Phys. Rev. E 89 022907
[20]	Xu X L, Zhang Y H, Cai X J, Zhao G P and Kang L S 2016 Chin. Phys. B 25 110301
[33]	Cai X J, Zhang Y H, Li Z L, Jiang G H, Yang Q N and Xu X Y 2013 Chin. Phys. B 22 020501
[34]	Mackay R S, Meiss J D and Percival I C 1984 Physica D 13 55
[21]	Liu F L and Zhao L B 2017 Phys. Rev. A 95 043428
[35]	Zhang Y H, Cai X J, Li Z L, Jiang G H, Yang Q N and Xu X Y 2013 Chin. Phys. Lett. 30 040501
[22]	Deng M, Gao W, Lu R, Delos J B, You L and Liu H P 2016 Phys. Rev. A 93 063411
[36]	Mitchell K A and Steck D A 2007 Phys. Rev. A 76 031403
[23]	Stodolna A S, Lépine F, Bergeman T, Robicheaux F, Gijsbertsen A, Jungmann J H, Bordas C and Vrakking M J J 2014 Phys. Rev. Lett. 113 103002
[37]	Friedman N, Kaplan A, Carasso D and Davidson N 2001 Phys. Rev. Lett. 86 1518
[24]	Chen X, Wu Y and Zhang J T 2017 Phys. Rev. A 95 013402
[38]	Mitchell K A and Delos J B 2006 Physica D:Nonlinear Phenomena 221 170
[25]	Wang L, Yang H F, Liu X J, Liu H P, Zhan M S and Delos J B 2010 Phys. Rev. A 82 022514
[26]	Mitchell K A, Handley J P, Tighe B, Flower A and Delos J B 2004 Phys. Rev. A 70 043407
[27]	Mitchell K A, Handley J P, Tighe B, Flower A and Delos J B 2004 Phys. Rev. Lett. 92 073001
[28]	Mitchell K A, Handley J P, Tighe B, Delos J B and Knudson S K 2003 Chaos:An Interdisciplinary Journal of Nonlinear Science 13 880
[29]	Mitchell K A, Handley J P, Delos J B and Knudson S K 2003 Chaos:An Interdisciplinary Journal of Nonlinear Science 13 892
[30]	Kotimäki V, Räsänen E, Hennig H and Heller E J 2013 Phys. Rev. E 88 022913
[31]	Yi X H, Bi J J, Liu R, Wang C K, Jiao Y and Li Z L 2016 Chin. Phys. B 25 128503
[32]	Byrd T A and Delos J B 2014 Phys. Rev. E 89 022907
[33]	Cai X J, Zhang Y H, Li Z L, Jiang G H, Yang Q N and Xu X Y 2013 Chin. Phys. B 22 020501
[34]	Mackay R S, Meiss J D and Percival I C 1984 Physica D 13 55
[35]	Zhang Y H, Cai X J, Li Z L, Jiang G H, Yang Q N and Xu X Y 2013 Chin. Phys. Lett. 30 040501
[36]	Mitchell K A and Steck D A 2007 Phys. Rev. A 76 031403
[37]	Friedman N, Kaplan A, Carasso D and Davidson N 2001 Phys. Rev. Lett. 86 1518
[38]	Mitchell K A and Delos J B 2006 Physica D:Nonlinear Phenomena 221 170

[1]	An all-optical phase detector by amplitude modulation of the local field in a Rydberg atom-based mixer Xiu-Bin Liu(刘修彬), Feng-Dong Jia(贾凤东), Huai-Yu Zhang(张怀宇), Jiong Mei(梅炅), Wei-Chen Liang(梁玮宸), Fei Zhou(周飞), Yong-Hong Yu(俞永宏), Ya Liu(刘娅), Jian Zhang(张剑), Feng Xie(谢锋), and Zhi-Ping Zhong(钟志萍). Chin. Phys. B, 2022, 31(9): 090703.
[2]	Highly sensitive detection of Rydberg atoms with fluorescence loss spectrum in cold atoms Xuerong Shi(师雪荣), Hao Zhang(张好), Mingyong Jing(景明勇), Linjie Zhang(张临杰), Liantuan Xiao(肖连团), Suotang Jia(贾锁堂). Chin. Phys. B, 2020, 29(1): 013201.
[3]	Tunable multistability and nonuniform phases in a dimerized two-dimensional Rydberg lattice Han-Xiao Zhang(张焓笑), Chu-Hui Fan(范楚辉), Cui-Li Cui(崔淬砺), Jin-Hui Wu(吴金辉). Chin. Phys. B, 2020, 29(1): 013204.
[4]	Properties of collective Rabi oscillations with two Rydberg atoms Dan-Dan Ma(马丹丹), Ke-Ye Zhang(张可烨), Jing Qian(钱静). Chin. Phys. B, 2019, 28(1): 013202.
[5]	Fractal dynamics in the ionization of helium Rydberg atoms Xiulan Xu(徐秀兰), Yanhui Zhang(张延惠), Xiangji Cai(蔡祥吉), Guopeng Zhao(赵国鹏), Lisha Kang(康丽莎). Chin. Phys. B, 2016, 25(11): 110301.
[6]	Nonlinear spectroscopy of barium in parallel electric and magnetic fields Yang Hai-Feng (杨海峰), Gao Wei (高伟), Cheng Hong (成红), Liu Hong-Ping (刘红平). Chin. Phys. B, 2014, 23(10): 103201.
[7]	Spectral decomposition at complex laser polarization configuration Yang Hai-Feng (杨海峰), Gao Wei (高伟), Cheng Hong (成红), Liu Hong-Ping (刘红平). Chin. Phys. B, 2013, 22(5): 053201.
[8]	The fractal structure in the ionization dynamics of Rydberg lithium atoms in a static electric field Deng Shan-Hong(邓善红), Gao Song(高嵩), Li Yong-Ping(李永平), Xu Xue-You(徐学友), and Lin Sheng-Lu(林圣路). Chin. Phys. B, 2010, 19(4): 040511.
[9]	Recombination during expansion of ultracold plasma Zhao Jian-Ming(赵建明), Zhang Lin-Jie(张临杰), Feng Zhi-Gang(冯志刚), Li Chang-Yong(李昌勇), and Jia Suo-Tang(贾锁堂). Chin. Phys. B, 2010, 19(4): 043202.
[10]	Measurement of quantum defect of nS and nD states using field ionization spectroscopy in ultracold cesium atoms Zhang Lin-Jie(张临杰), Feng Zhi-Gang(冯志刚), Li An-Ling(李安玲), Zhao Jian-Ming(赵建明), Li Chang-Yong(李昌勇), and Jia Suo-Tang(贾锁堂). Chin. Phys. B, 2009, 18(5): 1838-1842.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms

Cite this article:

Online attention