Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field

doi:10.1088/1674-1056/28/8/083101

Abstract

We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schrödinger equation (TDSE) in spherical coordinates. This method is realized by combining constructing block diagonal matrices through using the real space product formula (RSPF) with splitting out diagonal sub-matrices for short iterative Lanczos (SIL) propagator. The numerical implementation of the solver guarantees efficient parallel computing for the simulation of real physical problems such as high harmonic generation (HHG) in these interaction systems.

Keywords: time-dependent Schrö dinger equation, Strong laser fields, Parallel numerical solver

Received: 26 March 2019
Revised: 20 May 2019
Accepted manuscript online:

PACS:	31.15.A-	(Ab initio calculations)
	32.30.Bv	(Radio-frequency, microwave, and infrared spectra)

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11534004, 11627807, 11774131, and 11774130) and the Scientific and Technological Project of Jilin Provincial Education Department in the Thirteenth Five-Year Plan, China (Grant No. JJKH20170538KJ).

Corresponding Authors: Da-Jun Ding
E-mail: dajund@jlu.edu.cn

Cite this article:

Sheng-Peng Zhou(周胜鹏), Ai-Hua Liu(刘爱华), Fang Liu(刘芳), Chun-Cheng Wang(王春成), Da-Jun Ding(丁大军) Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field 2019 Chin. Phys. B 28 083101

[1]	Corkum P B 1993 Phys. Rev. Lett. 71 1994
[2]	Faisal F H M 1973 J. Phys. B 6 L89
[3]	Reiss H R 1980 Phys. Rev. A 22 1786
[4]	HuP B, Liu J and Chen S 1997 Phys. Lett. A 236 533
[5]	Li M M, Geng J, Liu H, Deng Y, Wu C, Peng L, Gong Q and Liu Y 2014 Phys. Rev. Lett. 112 113002
[6]	Liu M M, Li M, Wu C, Gong Q, Staudte A and Liu Y 2016 Phys. Rev. Lett. 116 163004
[7]	Tal-Ezer H and Kosloff R 1984 J. Chem. Phys. 81 3967
[8]	Feit M D, Fleck J A Jr and Steiger A 1982 J. Comput. Phys. 47 412
[9]	Kosloff R 1994 Ann. Rev. Phys. Chem. 45 145
[10]	Kosloff D and Kosloff R 1983 J. Comput. Phys. 52 35
[11]	Goldstein G and Baye D 2004 Phys. Rev. E 70 056703
[12]	Lauvergnat D, Blasco S, Chapuisat X and Nauts A 2007 J. Chem. Phys. 126 204103
[13]	Kormann K, Holmgren S and Karlsson H O 2008 J. Chem. Phys. 128 184101
[14]	Sun Z and Yang W 2011 J. Chem. Phys. 134 041101
[15]	Lee Y, Wu J, Jiang T and Chen Y 2008 Phys. Rev. A 77 013414
[16]	Hu S X, Collins L A and Schneider B I 2009 Phys. Rev. A 80 023426
[17]	Gainullin I K and Sonkin M A 2015 Comput. Phys. Commun. 188 68
[18]	Patchkovskii S and Muller H G 2016 Comput. Phys. Commun. 199 153
[19]	Yu D, Cong S and Sun Z 2015 Chem. Phys. 458 41
[20]	Guan X, Bartschat K and Schneider B I 2008 Phys. Rev. A 77 043421
[21]	Balzer K, Bauch S and Bonitz M 2010 J. Phys.: Conf. Ser. 220 012020
[22]	Zhang Y and Zhang X 2015 Chin. Phys. B 24 123101
[23]	Zhang Y, Tang L, Zhang X and Shi T 2016 Chin. Phys. B 25 103101
[24]	Lu R, Zhang P and Han K 2008 Phys. Rev. E 77 066701
[25]	Park T J and Light J C 1986 J. Chem. Phys. 85 5870
[26]	Schneider B I and Collins L A 2005 J. Non-Cryst. Solids 351 1551
[27]	Schneider B I, Collins L A and Hu S X 2006 Phys. Rev. E 73 036708
[28]	Bauer D and Koval P 2006 Comput. Phys. Commun. 174 396
[29]	Suzuki M 1985 J. Math. Phys. 26 601
[30]	Suzuki M 1991 J. Math. Phys. 32 400
[31]	Hu S X 2010 Phys. Rev. E 81 056705
[32]	Rescigno T N and McCurdy C W 2000 Phys. Rev. A 62 032706
[33]	Lin C Y and Ho Y K 2011 Phys. Rev. A 84 023407
[34]	Zhou S, Yang Y and Ding D 2016 Front. Phys. 11 113201
[35]	Jiang W and Tian X 2017 Opt. Express 25 26832
[36]	Tong X M and Lin C D 2005 J. Phys. B 38 2593
[37]	Bian X, Huismans Y, Smirnova O, Yuan K, Vrakking M J J and Bandrauk A D 2011 Phys. Rev. A 84 043420
[38]	Liu A and Thumm U 2015 Phys. Rev. A 91 043416
[39]	Zhang Z, Peng L Y, Xu M H, Starace A F, Morishita T and Gong Q 2011 Phys. Rev. A 84 043409

[1]	Electron localization of linear symmetric molecular ion H₃²⁺ Zheng-Mao Jia(贾正茂), Zhi-Nan Zeng(曾志男), Ru-Xin Li(李儒新). Chin. Phys. B, 2017, 26(1): 013203.
[2]	Two-photon double ionization of helium by chirped few-cycle attosecond pulses: From nonsequential to sequential regime Yao Tong(童瑶), Wei-Chao Jiang(姜维超), Pan Wu(伍攀), Liang-You Peng(彭良友). Chin. Phys. B, 2016, 25(7): 073202.
[3]	Charge transfer of He²⁺ with H in a strong magnetic field Liu Chun-Lei (刘春雷), Zou Shi-Yang (邹士阳), He Bin (何斌), Wang Jian-Guo (王建国). Chin. Phys. B, 2015, 24(9): 093402.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field

Cite this article:

Online attention