1 Institute of Mathematics, College of Science, Shantou University, Shantou 515063, China; 2 School of Science, Hainan University, Haikou 570288, China; 3 Research Center for Advanced Optics and Photoelectronics, Department of Physics, College of Science, Shantou University, Shantou 515063, China; 4 Faculty of Science, Xi'an Aeronautical University, Xi'an 710077, China
Abstract The semiclassical method based on Feynman's path-integral is in favor of uncovering the quantum tunneling effect, the classical trajectory description of the electron, and the quantum phase information, which can present an intuitive and transparent physical image of electron's propagation in comparison with the ab initio time-dependent Schrödinger equation. In this review, we introduce the basic theoretical concepts and development of several semiclassical methods as well as some of their applications in strong-field physics. Special emphasis is placed on extracting time delay on attosecond scale by the combination of the semiclassical method with phase of phase method. Hundreds of millions of trajectories are generally adopted to obtain a relatively high-resolution photoelectron spectrum, which would take a large amount of time. Here we also introduce several optimization approaches of the semiclassical method to overcome the time-consuming problem of violence calculation.
(Multiphoton ionization and excitation to highly excited states)
Fund: Project supported by the National Natural Science Foun dation of China (Grants Nos. 91950101, 12074240, and 12104285), Sino-German Mobility Programme (Grant No. M- 0031), the High Level University Projects of the Guangdong Province, China (Mathematics, Shantou University), and the Open Fund of the State Key Laboratory of High Field Laser Physics (SIOM).
Corresponding Authors:
Wei-Feng Yang, Xiao-Hong Song
E-mail: wfyang@hainanu.edu.cn;song_xiaohong@hainanu.edu.cn
Cite this article:
Xun-Qin Huo(火勋琴), Wei-Feng Yang(杨玮枫), Wen-Hui Dong(董文卉), Fa-Cheng Jin(金发成), Xi-Wang Liu(刘希望), Hong-Dan Zhang(张宏丹), and Xiao-Hong Song(宋晓红) Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics 2022 Chin. Phys. B 31 033101
[1] Maiman T H 1960 Nature187 493 [2] Voronov G S and Delone N B 1965 JETP Lett.1 66 [3] Voronov G S, Delone G A, Delone N B and Kudrevatova O V 1965 JETP Lett.2 377 [4] Agostini P, Barjot G, Bonnal J, Mainfray G, Manus C and Morellec J 1968 IEEE J. Quantum Electron.4 667 [5] Agostini P, Fabre F, Mainfray G, Petite G and Rahman N K 1979 Phys. Rev. Lett.42 1127 [6] Shore B W and Knight P L 1987 J. Phys. B20 413 [7] Mcpherson A, Gibson G, Jara H, Johann U, Luk T S, McIntyre I A, Boyer K and Rhodes C K 1987 J. Opt. Soc. Am. B4 595 [8] Wang Y L, Yu S G, Lai X Y, Liu X J and Chen J 2017 Phys. Rev. A95 063406 [9] Yang W F, Zhang H T, Lin C, Xu J W, Sheng Z H, Song X H, Hu S L and Chen J 2016 Phys. Rev. A94 043419 [10] Lai X Y and Liu X J 2020 Chin. Phys. B29 013205 [11] Wu C Y, Yang Y D, Liu Y Q, Gong Q H, Wu M, Liu X, Hao X L, Li W D, He X T and Chen J 2012 Phys. Rev. Lett.109 043001 [12] Yang W F, Li J, Jia W B, Zhang H D, Liu X W, Zhu M, Song X H and Chen J 2021 Phys. Rev. A103 053105 [13] Xiong W H, Xiao X R, Peng L Y and Gong Q H 2016 Phys. Rev. A94 013417 [14] Peng L Y, Jiang W C, Geng J W, Xiong W H and Gong Q H 2015 Phys. Rep.575 1 [15] Song X H, Zuo R X, Yang S D, Li P C, Meier T and Yang W F 2019 Opt. Express27 2225 [16] Guan Z, Zhou X X and Bian X B 2016 Phys. Rev. A93 033852 [17] Wang F, He L X, Zhai C Y, Shi W J, Zhang Q B, Lan P F and Lu P X 2015 Phys. Rev. A92 063839 [18] Song Q Y, Lu P F, Gong X C, Ji Q Y, Lin K, Zhang W B, Ma J Y, Zeng H P and Wu J 2017 Phys. Rev. A95 013406 [19] Zhang W B, Lu P F, Gong X C, Li H, Ji Q Y, Lin K, Ma J Y, Li H X, Sun F H, Qiang J J, Chen F, Tong J H and Wu J 2020 Phys. Rev. A101 033401 [20] Xie H Q, Lei H B, Li G H, Zhang Q, Wang X W, Zhao J, Chen Z M, Yao J P, Chen Y and Zhao Z X 2020 Phys. Rev. Research2 023329 [21] Zhang H D, Liu X W, Jin F C, Zhu M, Yang S D, Dong W H, Song X H and Yang W F 2021 Chin. Phys. Lett.38 063201 [22] Li W K, Lei Y, Li X, Yang T, Du M, Jiang Y, Li J L, Luo S Z, Liu A H, He L H, Ma P, Zhang D D and Ding D J 2021 Chin. Phys. Lett.38 053202 [23] Wang X W, Wang L, Xiao F, Zhang D W, Lü Z H, Yuan J M and Zhao Z X 2020 Chin. Phys. Lett.37 023201 [24] Yuan J Y, Ma Y X, Li R Y, Ma H Y, Zhang Y Z, Ye D F, Zhenjie Shen Z J, Yan T M, Wang X C, Weidemüller M and Jiang Y H 2020 Chin. Phys. Lett.37 053201 [25] Zuo R X, Trautmann A, Wang G F, Hannes W R, Yang S D, Song X H, Meier T, Ciappina M, Duc H T and Yang W F 2021 Ultrafast Science2021 9861923 [26] Keldysh L V 1964 Zh. Eksp. Teor. Fiz.47 1945 [27] Keldysh L V 1965 Sov. Phys. JETP20 1307 (Engl. transl.) [28] Faisal F H M 1973 J. Phys. B6 L89 [29] Reiss H R 1980 Phys. Rev. A22 1786 [30] Perelomov A M, Popov V S and Terentév M V 1966 Zh. Eksp. Teor. Fiz.50 1393 [31] Perelomov A M, Popov V S and Terent'ev M V 1966 Sov. Phys. JETP23 924 (Engl. transl.) [32] Ammosov M V, Delone N B and Krainov V P 1986 Zh. Eksp.Teor. Fiz.91 2008 [33] Ammosov M V, Delone N B and Krainov V P 1986 Sov. Phys. JETP64 1191 (Engl. transl.) [34] Feynman R P 1948 Rev. Mod. Phys.20 367 [35] Feynman R P and Hibbs A R 1965 Quantum Mechanics and Path Integrals (New York:McGraw-Hill) [36] Bian X B, Huismans Y, Smirnova O, Yuan K J, Vrakking M and Bandrauk A D 2011 Phys. Rev. A84 043420 [37] Ben S, Wang T, Xu T T, Guo J and Liu X S 2016 Opt. Express24 7525 [38] Xu T T, Ben S, Wang T, Zhang J, Guo J and Liu X S 2015 Phys. Rev. A92 033405 [39] Liu A H and Thumm U 2015 Phys. Rev. Lett.115 183002 [40] Liu A H and Thumm U 2014 Phys. Rev. A89 063423 [41] Bauer D and Koval P 2006 Comput. Phys. Commun.174 396 [42] Mosert V and Bauer D 2016 Comput. Phys. Commun.207 452 [43] Cormier E and Lambropoulos P 1997 J. Phys. B30 77 [44] Patchkovskii S and Muller H G 2016 Comput. Phys. Commun.199 153 [45] Corkum P B, Burnett N H and Brunel F 1989 Phys. Rev. Lett.62 1259 [46] Corkum P B. 1993 Phys. Rev. Lett.71 1994 [47] Brabec T, Ivanov M Y and Corkum P B 1996 Phys. Rev. A54 R2551 [48] Hu B, Liu J and Chen S G 1997 Phys. Lett. A236 533 [49] Li M, Geng J W, Liu H, Deng Y K, Wu C Y, Peng L Y, Gong Q H and Liu Y Q 2014 Phys. Rev. Lett.112 113002 [50] Geng J W, Qin L, Li M, Xiong W H, Liu Y Q, Gong Q H and Peng L Y 2014 J. Phys. B47 204027 [51] Song X H, Lin C, Sheng Z H, Liu P, Chen Z J, Yang W F, Hu S L, Lin C D and Chen J 2016 Sci. Rep.6 28392 [52] Yang W F, Zhang H T, Lin C, Xu J W, Sheng Z H, Song X H, Hu S L and Chen J 2016 Phys. Rev. A94 043419 [53] Huismans Y, Rouzée A, Gijsbertsen A, Jungmann J H, Smolkowska A S, Logman P S W M, Lépine F, Cauchy C, Zamith S, Marchenko T, Bakker J M, Berden G, Redlich B, van der Meer A F G, Muller H G, Vermin W, Schafer K J, Spanner M, Ivanov M Y, Smirnova O, Bauer D, Popruzhenko S V and Vrakking M J J 2011 Science331 61 [54] Song X H, Xu J W, Lin C, Sheng Z H, Liu P, Yu X H, Zhang H T, Yang W F, Hu S L, Chen J, Xu S P, Chen Y J, Quan W and Liu X J 2017 Phys. Rev. A95 033426 [55] Lin C, Zhang H T, Sheng Z H, Yu X H, Liu P, Xu J W, Song X H, Hu S L, Chen J and Yang W F 2016 Acta Phys. Sin.65 223207 (in Chinese) [56] Gordon W 1926 Z. Phys.40 117 [57] Volkov D M 1935 Z. Phys.94 250 [58] Arbó D G, Miraglia J E, Gravielle M S, Schiessl K, Persson E and Burgdörfer J 2008 Phys. Rev. A77 013401 [59] Popruzhenko S V 2014 J. Phys. B47 204001 [60] Popruzhenko S V and Bauer D 2008 J. Mod. Opt.55 2573 [61] Yan T M, Popruzhenko S V, Vrakking M J J and Bauer D 2010 Phys. Rev. Lett.105 253002 [62] Yan T M and Bauer D 2012 Phys. Rev. A86 053403 [63] Maxwell A S, Al-Jawahiry A, Das T and Faria C F D M 2017 Phys. Rev. A96 023420 [64] Maxwell A S, Al-Jawahiry A, Lai X Y and Faria C F D M 2018 J. Phys. B51 044004 [65] Lai X Y, Poli C, Schomerus H and Faria C F D M 2015 Phys. Rev. A92 043407 [66] Faria C F D M and Maxwell A S 2020 Rep. Prog. Phys.83 034401 [67] Xiao X R, Wang M X, Li M, Geng J W, Liu Y Q and Peng L Y 2016 Acta Phys. Sin.65 220203 (in Chinese) [68] Brabec T, Ivanov M Y and Corkum P B 1996 Phys. Rev. A54 R2551 [69] Saliéres P 2001 Science292 902 [70] Bauer D, Milošević D B and Becker 2005 Phys. Rev. A72 023415 [71] Becker W, Grasbon F, Kopold R, Milošević D B, Paulus G G and Walther H 2002 Adv. At. Mol. Opt. Phys.48 35 [72] Jašarević A, Hasović E, Kopold R, Becker W and Milošević D B 2020 J. Phys. A53 125201 [73] Wang C L Xia L X, Yao H B and Li W L 2017 Chin. Phys. B26 043201 [74] Fu Y Z, Zhao S F and Zhou X X 2012 Chin. Phys. B21 113101 [75] Yudin G and Ivanov M 2001 Phys. Rev. A64 13409 [76] Hickstein D D, Ranitovic P, Witte S, Tong X M and Kapteyn H C 2012 Phys. Rev. Lett.109 073004 [77] Korneev P A, Popruzhenko S V, Goreslavski S P, Becker W, Paulus G G, Feti B and Miloevi D B 2012 New J. Phys.14 055019 [78] Korneev P A, Popruzhenko S V, Goreslavski S P, Yan T M, Bauer D and Becker W 2012 Phys. Rev. Lett.108 223601 [79] Rudenko A, Zrost K, Schröter C D, de Jesus V L B, Feuerstein B, Moshammer R and Ullrich J 2004 J. Phys. B37 L407 [80] Gopal R, Simeonidis K, Moshammer R, Ergler T and Kling M F 2009 Phys. Rev. Lett.103 053001 [81] Möller M, Meyer F, Sayler A M, Paulus G G, Kling M F, Schmidt B E, Becker W and Milošević D B 2014 Phys. Rev. A90 023412 [82] Kang H P, Maxwell A S and Trabert D 2020 Phys. Rev. A102 013109 [83] Arbó D G, Nagele S, Tong X M, Xie X, Kitzler M and Burgdörfer J 2014 Phys. Rev. A89 043414 [84] Xie X, Roither S, Gräfe S, Kartashov D, Persson E, Lemell Ch, Zhang Li, Schöffler M S, Baltuška A, Burgdörfer J and Kitzler M 2013 New J. Phys.15 043050 [85] Mauritsson J, Dahlström J M, Mansten E and Fordell T 2009 J. Phys. B42 134003 [86] Schumacher D W, Weihe F, Muller H G and Bucksbaum P B 1994 Phys. Rev. Lett.73 1344 [87] Zipp L J, Natan A and Bucksbaum P H 2014 Optica1 361 [88] Natan A, Zipp L J and Bucksbaum P H 2016 Int. Conf. on Ultrafast Phenomena (Optical Society of America) p. UM2B.6 [89] Skruszewicz S, Tiggesbäumker J, Meiwes-Broer K H, Arbeiter M, Fennel T and Bauer D 2015 Phys. Rev. Lett.115 043001 [90] Foerster M, Paschen T, Krueger M, Lemell C, Wachter G Libisch F, Madlener T, Burgdörfer J and Hommelhoff P 2016 Phys. Rev. Lett.117 217601 [91] Porat G, Alon G, Rozen S, Pedatzur O, Krüger M, Azoury D, Natan A, Orenstein G, Bruner B D, Vrakking M J J and Dudovich N 2018 Nat. Commun.9 2805 [92] Würzler D, Skruszewicz S, Sayler A M, Zille D, Möller M, Wustelt P, Zhang Y, Tiggesbäumker J and Paulus G G 2020 Phys. Rev. A101 033416 [93] Almajid M A, Zabel M, Skruszewicz S, Tiggesbäumker J and Bauer D 2017 J. Phys. B50 194001 [94] Tulsky V A, Krebs B, Tiggesbaumker J and Bauer D 2020 J. Phys. B53 7 [95] Tulsky V A, Almajid M A and Bauer D 2018 Phys. Rev. A98 053433 [96] Song X H, Shi G L, Zhang G J, Xu J W, Lin C, Chen J and Yang W F 2018 Phys. Rev. Lett.121 103201 [97] Kraus P M, Tolstikhin O I, Baykusheva D, Rupenyan A, Schneider J, Bisgaard C Z, Morishita T, Jensen F, Madsen L B and Wörner H J 2015 Nat. Commun.6 7039 [98] Camus N, Yakaboylu E, Fechner L, Klaiber M, Laux M, Mi Y, Hatsagorsyan K Z, Pfeifer T, Keitel C H and Moshammer R 2017 Phys. Rev. Lett.119 023201 [99] Tan J, Li Y, Zhou Y M, He M R, Chen Y B, Li M and Lu P X 2018 Optical and Quantum Electronics50 57 [100] Zhou Y M, Tolstikhin O I and Toru Morishita T 2016 Phys. Rev. Lett.116 173001 [101] Tan J, Zhou Y M, He M R, Ke Q H, Liang J T, Li Y, Li M and Lu P X 2019 Phys. Rev. A99 033402 [102] Tan J, Zhou Y M, He M R, Chen Y B, Ke Q H, Liang J T, Zhu X S, Li M and Lu P X 2018 Phys. Rev. Lett.121 253203 [103] Huppert M, Jordan I, Baykusheva D, Conta A V and Wörner H J 2016 Phys. Rev. Lett.117 093001 [104] Tao Z, Chen C, Szilvási T, Keller M, Mavrikakis M, Kapteyn H and Murnane M 2016 Science353 62 [105] Petretti S, Vanne Y V, Saenz A, Castro A and Decleva P 2010 Phys. Rev. Lett.104 223001 [106] Schultze M, Fieß M, Karpowicz N, Gagnon J, Korbman M, Hofstetter M, Neppl S, Cavalieri A L, Komninos Y, Mercouris Th, Nicolaides C A, Pazourek R, Nagele S, Feist J, Burgdörfer J, Azzeer A M, Ernstorfer R, Kienberger R, Kleineberg U, Goulielmakis E, Krausz F and Yakovlev V S 2010 Science328 1658 [107] Pazourek R, Nagele S and Burgdörfer J 2015 Rev. Mod. Phys.87 765 [108] Pazourek R, Nagele S and Burgdörfer J 2013 Faraday Discuss.163 353 [109] Baykusheva D and Wörner H J 2021 Molecular Spectroscopy and Quantum Dynamics (Elsevie) pp. 113——161 [110] Freeman R R, Bucksbaum P H, Milchberg H, Darack S, Schumacher D and Geusic M E 1987 Phys. Rev. Lett.59 1092 [111] Su J, Ni H, Jaroń-Becker A and Becker A 2014 Phys. Rev. Lett.113 263002 [112] Gong X C, Lin C, He F, Song Q Y, Lin K, Ji Q Y, Zhang W B, Ma J Y, Lu P F, Liu Y Q, Zeng H P, Yang W F and Wu J 2017 Phys. Rev. Lett.118 143203 [113] Maharjan C M, Alnaser A S, Litvinyuk I, Ranitovic P and Cocke C L 2006 J. Phys. B39 1955 [114] Freeman R R and Bucksbaum P H 1991 J. Phys. B24 325 [115] Woolf H (Ed.) 1980 Some strangeness in the proportion (Addison-Wesley, Reading, MA) p. 376 [116] Popruzhenko S V, Paulus G G and Bauer D 2008 Phys. Rev. A77 053409 [117] Yang S D, Song X H, Liu X W, Zhang H D, Shi G L, Yu X H, Tang Y J, Chen J and Yang W 2020 Laser Phys. Lett.17 095301 [118] Xiao X R, Wang M X, Xiong W H and Peng L Y 2016 Phys. Rev. E94 053310 [119] Liu X W, Zhang G J, Li J, Shi G L, Zhou M Y, Huang B Q, Tang Y J, Song X H and Yang W F 2020 Phys. Rev. Lett.124 113202 [120] Silver D, Huang A, Maddison C J, Guez A, Sifre L, van den Driessche G, Schrittwieser J, Antonoglou I, Panneershelvam V, Lanctot M, Dieleman S, Grewe D, Nham J, Kalchbrenner N, Sutskever I, Lillicrap T, Leach M, Kavukcuoglu K, Graepel T and Hassabis D 2016 Nature529 484 [121] Silver D, Schrittwieser J, Simonyan K, Antonoglou I, Huang A, Guez A, Hubert T, Baker L, Lai M, Bolton A, Chen Y, Lillicrap T, Hui F, Sifre L, Driessche G V D, Graepel T and Hassabis D 2017 Nature550 354 [122] Segler M H S, Preuss M and Waller M P 2018 Nature555 604 [123] Ouyang W, Aristov A, Lelek M, Hao X and Zimmer C 2018 Nat. Biotechnol36 460 [124] Giri S K, Saalmann U and Rost J M 2020 Phys. Rev. Lett.124 113201
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