Progress in study of low-energy photoelectron in ultra-fast strong fields-analytical R-matrix theory based semiclassical trajectory method

Huang Wen-Xiao; Zhang Yi-Zhu; Yan Tian-Min; Jiang Yu-Hai

doi:10.7498/aps.65.223204

Abstract

The semi-classical method based on the recently developed analytical R-matrix theory is reviewed in this work. The method is described with the application to ultra-fast strong-field direct ionization of atoms with one active electron in a linearly polarized field[Torlina L, Smirnova O 2012 Phys. Rev. A 86 043408]. The analytical R-matrix theory separates the space into inner and outer regions, naturally allowing the possibility of an analytical or semi-analytical description of wave function in the outer region, which can be approximated by Eikonal-Volkov solutions while the inner region provides well-defined boundary conditions. Applying the stationary phase method, the calculation of the ionization amplitude is cast into a superposition of components from trajectories and their associated phase factors. The shape of the tunneling wave packets associated with different instants of ionization is presented. It shows the exponential cost of deviating from the optimal tunneling trajectory renders the tunneling wave packet a Gaussian shape surrounding the semi-classical trajectory. The intrinsically non-adiabatic corrections to the sub-cycle ionization amplitude in the presence of both the Coulomb potential and the laser field is shown to have different influences on the probability of ionization. As a specific study case, soft recollisions of the released electron near the ionic core is investigated by using pure light-driven trajectories with Coulomb-corrected phase factor[Pisanty E, Ivanov M 2016 Phys. Rev. A 93 043408]. Incorporating the Coulomb potential, it is found problematic to use the conventional integration contour as chosen in other methods with trajectory-based Coulomb corrections, because the integration contour may run into the Coulomb-induced branch cuts and hence the analyticity of the integrand fails. In order to overcome the problem, the evolution time of the post-tunneling electron is extended into the complex domain which allows a trajectory to have an imaginary component. As the soft recollision occurs, the calculation of the ionization amplitude requires navigating the branch cuts cautiously. The navigating scheme is found based on closest-approach times which are the roots of closest-approach times equations. The appropriately selected closest-approach times that always present in the middle of branch-cut gate may serve to circumvent these branch cuts. The distribution of the closest-approach times presents rich geometrical structures in both the classical and quantum domains, and intriguing features of complex trajectories emerge as the electron returns near the core. Soft recollisions responsible for the low-energy structures are embedded in the geometry, and the underlying emergence of near-zero energy structures is discussed with the prediction of possible observations in experiments.

Keywords:

Authors and contacts

1.
Shanghai Advanced Research Institute, Chinese Academy of Sciences, Shanghai 201210, China;
2.
University of Chinese Academy of Sciences, Beijing 100049, China;
3.
ShanghaiTech University, Shanghai 201210, China

Corresponding author: Yan Tian-Min, yantm@sari.ac.cn;jiangyh@sari.ac.cn ; Jiang Yu-Hai, yantm@sari.ac.cn;jiangyh@sari.ac.cn

Funds: Project supported by the National Basic Research Program of China (Grant No. 2013CB922200), the National Natural Science Foundation of China (Grant Nos. 11420101003, 11274232, 11604347, 61675213, 91636105), and the Shanghai Sailing Program, China (Grant No. 16YF1412600).

References

[1]	Blaga C I, Catoire F, Colosimo P, Paulus G G, Muller H G, Agostini P, DiMauro L F 2008Nat. Phys. 5 335
[2]	Quan W, Lin Z, Wu M, Kang H, Liu H, Liu X, Chen J, Liu J, He X T, Chen S G, Xiong H, Guo L, Xu H, Fu Y, Cheng Y, Xu Z Z 2009Phys. Rev. Lett. 103 093001
[3]	Liu C, Hatsagortsyan K Z 2010Phys. Rev. Lett. 105 113003
[4]	Liu C, Hatsagortsyan K Z 2011J. Phys. B:Atomic, Molecular and Optical Physics 44 095402
[5]	Liu C, Hatsagortsyan K Z 2012Phys. Rev. A 85 023413
[6]	Paulus G G, Becker W, Nicklich W, Walther H 1994J. Phys. B:Atomic, Molecular and Optical Physics 27 L703
[7]	Becker W, Grasbon F, Kopold R, Milošević D, Paulus G, Walther H 2002In Advances in Atomic, Molecular, and Optical Physics (edited by Walther B B A H) (Vol. 48) (Waltham:Academic Press) pp35-98
[8]	Miloševic D B, Ehlotzky F 1998J. Phys. B:Atomic, Molecular and Optical Physics 31 4149
[9]	Popruzhenko S, Bauer D 2008J. Mod. Opt. 55 2573
[10]	Yan T M, Popruzhenko S V, Vrakking M J J, Bauer D 2010Phys. Rev. Lett. 105 253002
[11]	Yan T M, Bauer D 2012Phys. Rev. A 86 053403
[12]	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, Chen J 2012Phys. Rev. Lett. 109 043001
[13]	Dura J, Camus N, Thai A, Britz A, Hemmer M, Baudisch M, Senftleben A, Schröter C D, Ullrich J, Moshammer R, Biegert J 2013Sci. Reports 3 2675
[14]	Pullen M G, Dura J, Wolter B, Baudisch M, Hemmer M, Camus N, Arne Senftleben, Schroeter C D, Moshammer R, Ullrich J, Biegert J 2014J. Phys. B:Atomic, Molecular and Optical Physics 47 204010
[15]	Wolter B, Lemell C, Baudisch M, Pullen M G, Tong X M, Hemmer M, Senftleben A, Schröter C D, Ullrich J, Moshammer R, Biegert J, Burgdörfer J 2014Phys. Rev. A 90 063424
[16]	Torlina L, Smirnova O 2012Phys. Rev. A 86 043408
[17]	Torlina L, Ivanov M, Walters Z B, Smirnova O 2012Phys. Rev. A 86 043409
[18]	Pisanty E, Ivanov M 2016Phys. Rev. A 93 043408
[19]	Kaushal J, Smirnova O 2013Phys. Rev. A 88 013421
[20]	Torlina L, Kaushal J, Smirnova O 2013Phys. Rev. A 88 053403
[21]	Smirnova O, Spanner M, Ivanov M 2006J. Phys. B:Atomic, Molecular and Optical Physics 39 S307
[22]	Walters Z B, Smirnova O 2010J. Phys. B:Atomic, Molecular and Optical Physics 43 161002
[23]	Caillat J, Zanghellini J, Kitzler M, Koch O, Kreuzer W, Scrinzi A 2005Phys. Rev. A 71 012712
[24]	Scrinzi A 2010Phys. Rev. A 81 053845
[25]	Tao L, Scrinzi A 2012New J. Phys. 14 013021
[26]	Kuchiev M Y 1987JETP Lett. 45 404
[27]	Corkum P B 1993Phys. Rev. Lett. 71 1994
[28]	Yudin G L, Ivanov M Y 2001Phys. Rev. A 63 033404
[29]	Chen Z, Le A T, Morishita T, Lin C D 2009Phys. Rev. A 79 033409
[30]	Le A T, Lucchese R R, Tonzani S, Morishita T, Lin C D 2009Phys. Rev. A 80 013401
[31]	Smirnova O, Mouritzen A S, Patchkovskii S, Ivanov M Y 2007J. Phys. B:Atomic, Molecular and Optical Physics 40 F197
[32]	Brabec T, Ivanov M Y, Corkum P B 1996Phys. Rev. A 54 R2551
[33]	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, D Bauer, Popruzhenko S V, Vrakking M J J 2011Science 331 61
[34]	Song X, Lin C, Sheng Z, Liu P, Chen Z, Yang W, Hu S, Lin C D, Chen J 2016Sci. Reports 6 28392
[35]	Smirnova O, Spanner M, Ivanov M 2008Phys. Rev. A 77 033407
[36]	Popov V S 1999Physics-Uspekhi 42 733
[37]	Perelomov A M, Popov V S, Terent'ev M V 1966JETP 23 924
[38]	Popruzhenko S V, Mur V D, Popov V S, Bauer D 2008Phys. Rev. Lett. 101 193003
[39]	Kästner A, Saalmann U, Rost J M 2012Phys. Rev. Lett. 108 033201
[40]	Kästner A, Saalmann U, Rost J M 2012J. Phys. B:Atomic, Molecular and Optical Physics 45 074011
[41]	Nubbemeyer T, Gorling K, Saenz A, Eichmann U, Sandner W 2008Phys. Rev. Lett. 101 233001
[42]	Landsman A S, Pfeiffer A N, Hofmann C, Smolarski M, Cirelli C, Keller U 2013New J. Phys. 15 013001

Cited By

[1]	Blaga C I, Catoire F, Colosimo P, Paulus G G, Muller H G, Agostini P, DiMauro L F 2008Nat. Phys. 5 335
[2]	Quan W, Lin Z, Wu M, Kang H, Liu H, Liu X, Chen J, Liu J, He X T, Chen S G, Xiong H, Guo L, Xu H, Fu Y, Cheng Y, Xu Z Z 2009Phys. Rev. Lett. 103 093001
[3]	Liu C, Hatsagortsyan K Z 2010Phys. Rev. Lett. 105 113003
[4]	Liu C, Hatsagortsyan K Z 2011J. Phys. B:Atomic, Molecular and Optical Physics 44 095402
[5]	Liu C, Hatsagortsyan K Z 2012Phys. Rev. A 85 023413
[6]	Paulus G G, Becker W, Nicklich W, Walther H 1994J. Phys. B:Atomic, Molecular and Optical Physics 27 L703
[7]	Becker W, Grasbon F, Kopold R, Milošević D, Paulus G, Walther H 2002In Advances in Atomic, Molecular, and Optical Physics (edited by Walther B B A H) (Vol. 48) (Waltham:Academic Press) pp35-98
[8]	Miloševic D B, Ehlotzky F 1998J. Phys. B:Atomic, Molecular and Optical Physics 31 4149
[9]	Popruzhenko S, Bauer D 2008J. Mod. Opt. 55 2573
[10]	Yan T M, Popruzhenko S V, Vrakking M J J, Bauer D 2010Phys. Rev. Lett. 105 253002
[11]	Yan T M, Bauer D 2012Phys. Rev. A 86 053403
[12]	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, Chen J 2012Phys. Rev. Lett. 109 043001
[13]	Dura J, Camus N, Thai A, Britz A, Hemmer M, Baudisch M, Senftleben A, Schröter C D, Ullrich J, Moshammer R, Biegert J 2013Sci. Reports 3 2675
[14]	Pullen M G, Dura J, Wolter B, Baudisch M, Hemmer M, Camus N, Arne Senftleben, Schroeter C D, Moshammer R, Ullrich J, Biegert J 2014J. Phys. B:Atomic, Molecular and Optical Physics 47 204010
[15]	Wolter B, Lemell C, Baudisch M, Pullen M G, Tong X M, Hemmer M, Senftleben A, Schröter C D, Ullrich J, Moshammer R, Biegert J, Burgdörfer J 2014Phys. Rev. A 90 063424
[16]	Torlina L, Smirnova O 2012Phys. Rev. A 86 043408
[17]	Torlina L, Ivanov M, Walters Z B, Smirnova O 2012Phys. Rev. A 86 043409
[18]	Pisanty E, Ivanov M 2016Phys. Rev. A 93 043408
[19]	Kaushal J, Smirnova O 2013Phys. Rev. A 88 013421
[20]	Torlina L, Kaushal J, Smirnova O 2013Phys. Rev. A 88 053403
[21]	Smirnova O, Spanner M, Ivanov M 2006J. Phys. B:Atomic, Molecular and Optical Physics 39 S307
[22]	Walters Z B, Smirnova O 2010J. Phys. B:Atomic, Molecular and Optical Physics 43 161002
[23]	Caillat J, Zanghellini J, Kitzler M, Koch O, Kreuzer W, Scrinzi A 2005Phys. Rev. A 71 012712
[24]	Scrinzi A 2010Phys. Rev. A 81 053845
[25]	Tao L, Scrinzi A 2012New J. Phys. 14 013021
[26]	Kuchiev M Y 1987JETP Lett. 45 404
[27]	Corkum P B 1993Phys. Rev. Lett. 71 1994
[28]	Yudin G L, Ivanov M Y 2001Phys. Rev. A 63 033404
[29]	Chen Z, Le A T, Morishita T, Lin C D 2009Phys. Rev. A 79 033409
[30]	Le A T, Lucchese R R, Tonzani S, Morishita T, Lin C D 2009Phys. Rev. A 80 013401
[31]	Smirnova O, Mouritzen A S, Patchkovskii S, Ivanov M Y 2007J. Phys. B:Atomic, Molecular and Optical Physics 40 F197
[32]	Brabec T, Ivanov M Y, Corkum P B 1996Phys. Rev. A 54 R2551
[33]	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, D Bauer, Popruzhenko S V, Vrakking M J J 2011Science 331 61
[34]	Song X, Lin C, Sheng Z, Liu P, Chen Z, Yang W, Hu S, Lin C D, Chen J 2016Sci. Reports 6 28392
[35]	Smirnova O, Spanner M, Ivanov M 2008Phys. Rev. A 77 033407
[36]	Popov V S 1999Physics-Uspekhi 42 733
[37]	Perelomov A M, Popov V S, Terent'ev M V 1966JETP 23 924
[38]	Popruzhenko S V, Mur V D, Popov V S, Bauer D 2008Phys. Rev. Lett. 101 193003
[39]	Kästner A, Saalmann U, Rost J M 2012Phys. Rev. Lett. 108 033201
[40]	Kästner A, Saalmann U, Rost J M 2012J. Phys. B:Atomic, Molecular and Optical Physics 45 074011
[41]	Nubbemeyer T, Gorling K, Saenz A, Eichmann U, Sandner W 2008Phys. Rev. Lett. 101 233001
[42]	Landsman A S, Pfeiffer A N, Hofmann C, Smolarski M, Cirelli C, Keller U 2013New J. Phys. 15 013001

[1]	Xiao Zhi-Lei, Quan Wei, Xu Song-Po, Liu Xiao-Jun, Wei Zheng-Rong, Chen Jing. Low energy structure of above-threshold ionization spectra produced by mid-infrared laser pulses. Acta Physica Sinica, 2022, 71(23): 233208. doi: 10.7498/aps.71.20221609
[2]	Zhu Bing, Feng Hao. Electron scattering studies of NO2 radical using R-matrix method. Acta Physica Sinica, 2017, 66(24): 243401. doi: 10.7498/aps.66.243401
[3]	Du Wen-Liao, Tao Jian-Feng, Gong Xiao-Yun, Gong Liang, Liu Cheng-Liang. Dual-tree complex wavelet transform based multifractal detrended fluctuation analysis for nonstationary time series. Acta Physica Sinica, 2016, 65(9): 090502. doi: 10.7498/aps.65.090502
[4]	Xiao Xiang-Ru, Wang Mu-Xue, Li Min, Geng Ji-Wei, Liu Yun-Quan, Peng Liang-You. Semiclassical methods for strong field ionization of atoms. Acta Physica Sinica, 2016, 65(22): 220203. doi: 10.7498/aps.65.220203
[5]	Guo Li, Han Shen-Sheng, Chen Jing. Study of above-threshold ionization by Wigner-distribution-like function method. Acta Physica Sinica, 2016, 65(22): 223203. doi: 10.7498/aps.65.223203
[6]	Wang Pin-Yi, Jia Xin-Yan, Fan Dai-He, Chen Jing. Resonance-like enhancement in high-order above-threshold ionzation of argon at different wavelengths. Acta Physica Sinica, 2015, 64(14): 143201. doi: 10.7498/aps.64.143201
[7]	Xu Feng, Zheng Yu-Jun. Dynamics of entangled trajectories in quantum phase space. Acta Physica Sinica, 2013, 62(21): 213401. doi: 10.7498/aps.62.213401
[8]	Tian Yuan-Ye, Guo Fu-Ming, Zeng Si-Liang, Yang Yu-Jun. Investigation of photoionization of excited atom irradiated by the high-frequency intense laser. Acta Physica Sinica, 2013, 62(11): 113201. doi: 10.7498/aps.62.113201
[9]	Tian Yuan-Ye, Wei Shan-Shan, Guo Fu-Ming, Li Su-Yu, Yang Yu-Jun. Effect of carrier envelope phase on the above threshold ionization under resonant condition. Acta Physica Sinica, 2013, 62(15): 153202. doi: 10.7498/aps.62.153202
[10]	Tian Yuan-Ye, Guo Fu-Ming, Yang Yu-Jun. The effect of atomic potential on the above threshold ionization. Acta Physica Sinica, 2013, 62(7): 073202. doi: 10.7498/aps.62.073202
[11]	Deng Shan-Hong, Gao Song, Li Yong-Ping, Pei Yun-Chang, Lin Sheng-Lu. A semiclassical analyses on the auto-ionization of lithium atom in parallel electric and magnetic fields. Acta Physica Sinica, 2010, 59(2): 826-831. doi: 10.7498/aps.59.826
[12]	Wang Mo-Ge, Lu Qi-Sheng, Xu Xiao-Jun, Guo Shao-Feng. The theoretical model of broad band dye laser and experimental validation. Acta Physica Sinica, 2008, 57(3): 1857-1861. doi: 10.7498/aps.57.1857
[13]	He Zhi-Hong, Yao Jian-Quan, Shi Hua-Feng, Huang Xiao, Luo Xi-Zhang, Jiang Shao-Ji, Li Jian-Rong, Wang Peng. Effect of pump laser intensity on optically pumped D2O gas terahertz laser. Acta Physica Sinica, 2007, 56(11): 6451-6456. doi: 10.7498/aps.56.6451
[14]	He Zhi-Hong, Yao Jian-Quan, Shi Hua-Feng, Huang Xiao, Luo Xi-Zhang, Jiang Shao-Ji, Wang Peng. Semiclassical theory of optically pumped D2O gas tera-Hz laser. Acta Physica Sinica, 2007, 56(10): 5802-5807. doi: 10.7498/aps.56.5802
[15]	Oyang Shi-Gen, Guan Yi, She Wei-Long. . Acta Physica Sinica, 2002, 51(7): 1596-1599. doi: 10.7498/aps.51.1596
[16]	TONG XIAO-MIN, LI JIA-MING. THEORY OF ABOVE THRESHOLD IONIZATION PHENOMENA IN INTENSE LASER FIELDS. Acta Physica Sinica, 1991, 40(2): 190-197. doi: 10.7498/aps.40.190
[17]	CHEN BAO-ZHEN. ANGULAR DISTRIBUTION OF ABOVE-THRESHOLD IONIZATION OF H ATOM. Acta Physica Sinica, 1990, 39(1): 40-45. doi: 10.7498/aps.39.40
[18]	LI GUO-QIANG, XU GONG-OU. THE PROPERTITIES OF GIANT RESONANCED ON HOT NUC-LEI STUDIED BY FINITE TEMPERATURE SELFCO-NSISTENT SEMICLASSICAL APPROACH. Acta Physica Sinica, 1989, 38(9): 1413-1421. doi: 10.7498/aps.38.1413
[19]	PAN SHAO-HUA, HAN QUAN-SHENG. SEMICLASSICAL THEORY OF DISTRIBUTED FEEDBACK DYE LASERS. Acta Physica Sinica, 1982, 31(3): 318-327. doi: 10.7498/aps.31.318
[20]	PAN SHAO-HUA. A SEMICLASSICAL THEORY OF MODE COUPLING IN DYE LASERS. Acta Physica Sinica, 1981, 30(8): 1067-1076. doi: 10.7498/aps.30.1067

Catalog

Vol. 65, Issue 22 - 2016-11-20

Metrics

Abstract views: 4488
PDF Downloads: 334
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板