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The question of how long it takes for a particle to tunnel through a barrier, which was first put forward by MacColl (Phys. Rev. 40 621 (1932)), belongs to the fundamental process of quantum physics and has been the subject of intense debate since then. Many efforts have been devoted to addressing this question about how to define, explain and measure this tunneling time, but widespread controversies still exist in theories and experiments. Attosecond physics offers insights into ultrafast electron dynamics in atoms and moleculars on the attosecond (10-18 s) timescales, and therefore, ionization of atoms or moleculars in a strong laser filed allows for tackling this question in an experimentally and conceptually well-defined manner. The tunneling ionization dynamics of electrons plays an extremely important role in the field, since tunneling is the first crucial step in strong field ionizations of atoms and molecules and underlies virtually all present experiments in attosecond science. In the present paper, the tunneling ionization time of a single-active electron tunneling through a He atom subjected to a step static electric field, defined as a nonvanishing positive time delay between the instant of switch-on of the step static electric field and the one of ionization, is obtained from the numerical solution of the time-dependent Schrdinger equation in one dimension. The results show that the time delay between the instant of maximum probability current at the potential barrier exit and the one of switch-on of the step static electric field and the time delay needed by the ground wave function evolving to the continuum, which can be expressed as the transition element of the incident and transmitted parts of the wave function, are both very close to the Keldysh time explained as the time it takes for the bound electron having velocity = iIp/2 to cross the tunneling barrier. Compared with the definition of tunneling time delay in other literature, the one of the ground wave function evolution to the continuous state is much consistent with the actual ionization process. The reason why the electron tunneling time cannot be defined as the time delay between the maximum ionization rate and the instant of the laser peak field is that the wave function could penetrate the tunneling barrier earlier if a few-cycle optical field is adopted in experiment. According to the analysis in this article, an experimental method of measuring the actual electron tunneling ionization time using the optical field synthesis technique is proposed. The results of this paper will be helpful in tackling the problem of tunneling time in strong ionization.
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Keywords:
- tunnel ionization /
- attosecond physics /
- tunnel time delay /
- synthesis of light transients
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[2] Keldysh L {1965 Sov. Phys. JETP 20 1307
[3] Perelomov A, Popov V, Terent'ev M {1966 Sov. Phys. JETP 23 924
[4] Bttiker M, Landauer R {1985 Phys. Scr. 49 711
[5] Landauer R, Martin T 1994 Rev. Mod. Phys. 66 217
[6] Yamada N 2004 Phys. Rev. Lett. 93 170401
[7] Eckle P, Pfeiffer A, Cirelli C, Staudte A, Drner R, Muller H, Bttiker M, Keller U 2008 Science 322 1525
[8] Pfeiffer A N, Cirelli C, Smolarski M, Dimitrovski D, Abu-Samha M, Madsen L B, Keller U 2011 Nature Phys. 8 76
[9] Shafir D, Soifer H, Bruner B D, Dagan M, Mairesse Y, Patchkovskii S, Ivanov M Y, Smirnova O, Dudovich N. 2012 Nature 485 343
[10] Mcdonald C R, Orlando G, Vampa G, Brabec T 2013 Phys. Rev. Lett. 111 090405
[11] Hassan M T, Luu T, Moulet A, Raskazovskaya O, Zhokhov P, Garg M, Karpowicz N, Zheltikov A, Pervak V, Krausz F 2016 Nature 530 66
[12] Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
[13] Corkum P B 2011 Phys. Today 64 36
[14] Luo X Y, Liu H F, Ben S, Liu X S 2016 Acta Phys. Sin. 65 123201 (in Chinese) [罗香怡, 刘海凤, 贲帅, 刘学深 2016 物理学报 65 123201]
[15] Liu Y, Jia C, Guo F M, Yang Y J 2016 Acta Phys. Sin. 65 033201 (in Chinese) [刘艳, 贾成, 郭福明, 杨玉军 2016 物理学报 65 033201]
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[18] Gallmann L, Landsman A, Weger M, Maurer J, Boge R, Ludwig A, Heuser S, Cirelli C, Keller U 2013 Conference on and International Quantum Electronics Conference San Jose, Califonia, United States, June 9-14, 2013 p1
[19] Landsman A S, Keller U 2015 Phys. Rep. 547 1
[20] Zhao J, Lein M 2013 Phys. Rev. Lett. 111 043901
[21] Su Q, Eberly J H 1991 Phys. Rev. A 44 5997
[22] Lehtovaara L, Toivanen J, Eloranta J 2007 J. Comput. Phys. 221 148
[23] Zhang G T 2011 Ph. D. Dissertation (Jilin: Jilin University) (in Chinese) [张刚台 2011 博士学位论文 (吉林: 吉林大学)]
[24] Feit M, Fleck J, Steiger A 1982 J. Comput. Phys. 47 412
[25] Teeny N, Yakaboylu E, Bauke H, Keitel C H 2016 Phys. Rev. Lett. 116 063003
[26] Feynman R P, Hibbs A R (Translated by Zhang B G) 1986 Quantum Mechanics and Path Integrals (Beijing: Science Press) pp171-178 (in Chinese) [费曼, 希布斯 著 (张邦固 译) 1986 量子力学与路径积分 (北京: 科学出版社) 第171-178页]
[27] Landsman A S, Keller U 2014 J. Phys. B: At. Mol. Opt. Phys. 47 204024
[28] Yudin G L, Ivanov M Y {2001 Phys. Rev. A 64 289
[29] Orlando G, Mcdonald C R, Protik N H, Vampa G, Brabec T {2014 J. Phys. B: At., Mol. Opt. Phys. 47 44
[30] Pfeiffer A N, Cirelli C, Smolarski M, Keller U 2013 Chem. Phys. 414 84
[31] Wirth A, Hassan M T, Grgura I, Gagnon J, Moulet A, Luu T, Pabst S, Santra R, Alahmed Z, Azzeer A 2011 Science 334 195
[32] Hassan M T, Wirth A, Grguras I, Moulet A, Luu T, Gagnon J, Pervak V, Goulielmakis E 2012 Rev. Sci. Instrum. 83 111301
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[1] Maccoll L A 1932 Phys. Rev. 40 621
[2] Keldysh L {1965 Sov. Phys. JETP 20 1307
[3] Perelomov A, Popov V, Terent'ev M {1966 Sov. Phys. JETP 23 924
[4] Bttiker M, Landauer R {1985 Phys. Scr. 49 711
[5] Landauer R, Martin T 1994 Rev. Mod. Phys. 66 217
[6] Yamada N 2004 Phys. Rev. Lett. 93 170401
[7] Eckle P, Pfeiffer A, Cirelli C, Staudte A, Drner R, Muller H, Bttiker M, Keller U 2008 Science 322 1525
[8] Pfeiffer A N, Cirelli C, Smolarski M, Dimitrovski D, Abu-Samha M, Madsen L B, Keller U 2011 Nature Phys. 8 76
[9] Shafir D, Soifer H, Bruner B D, Dagan M, Mairesse Y, Patchkovskii S, Ivanov M Y, Smirnova O, Dudovich N. 2012 Nature 485 343
[10] Mcdonald C R, Orlando G, Vampa G, Brabec T 2013 Phys. Rev. Lett. 111 090405
[11] Hassan M T, Luu T, Moulet A, Raskazovskaya O, Zhokhov P, Garg M, Karpowicz N, Zheltikov A, Pervak V, Krausz F 2016 Nature 530 66
[12] Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163
[13] Corkum P B 2011 Phys. Today 64 36
[14] Luo X Y, Liu H F, Ben S, Liu X S 2016 Acta Phys. Sin. 65 123201 (in Chinese) [罗香怡, 刘海凤, 贲帅, 刘学深 2016 物理学报 65 123201]
[15] Liu Y, Jia C, Guo F M, Yang Y J 2016 Acta Phys. Sin. 65 033201 (in Chinese) [刘艳, 贾成, 郭福明, 杨玉军 2016 物理学报 65 033201]
[16] Schultze M, Fie M, Karpowicz N, Gagnon J, Korbman M, Hofstetter M, Neppl S, Cavalieri A L, Komninos Y, Mercouris T 2010 Science 328 1658
[17] Goulielmakis E, Loh Z H, Wirth A, Santra R, Rohringer N, Yakovlev V S, Zherebtsov S, Pfeifer T, Azzeer A M, Kling M F 2010 Nature 466 739
[18] Gallmann L, Landsman A, Weger M, Maurer J, Boge R, Ludwig A, Heuser S, Cirelli C, Keller U 2013 Conference on and International Quantum Electronics Conference San Jose, Califonia, United States, June 9-14, 2013 p1
[19] Landsman A S, Keller U 2015 Phys. Rep. 547 1
[20] Zhao J, Lein M 2013 Phys. Rev. Lett. 111 043901
[21] Su Q, Eberly J H 1991 Phys. Rev. A 44 5997
[22] Lehtovaara L, Toivanen J, Eloranta J 2007 J. Comput. Phys. 221 148
[23] Zhang G T 2011 Ph. D. Dissertation (Jilin: Jilin University) (in Chinese) [张刚台 2011 博士学位论文 (吉林: 吉林大学)]
[24] Feit M, Fleck J, Steiger A 1982 J. Comput. Phys. 47 412
[25] Teeny N, Yakaboylu E, Bauke H, Keitel C H 2016 Phys. Rev. Lett. 116 063003
[26] Feynman R P, Hibbs A R (Translated by Zhang B G) 1986 Quantum Mechanics and Path Integrals (Beijing: Science Press) pp171-178 (in Chinese) [费曼, 希布斯 著 (张邦固 译) 1986 量子力学与路径积分 (北京: 科学出版社) 第171-178页]
[27] Landsman A S, Keller U 2014 J. Phys. B: At. Mol. Opt. Phys. 47 204024
[28] Yudin G L, Ivanov M Y {2001 Phys. Rev. A 64 289
[29] Orlando G, Mcdonald C R, Protik N H, Vampa G, Brabec T {2014 J. Phys. B: At., Mol. Opt. Phys. 47 44
[30] Pfeiffer A N, Cirelli C, Smolarski M, Keller U 2013 Chem. Phys. 414 84
[31] Wirth A, Hassan M T, Grgura I, Gagnon J, Moulet A, Luu T, Pabst S, Santra R, Alahmed Z, Azzeer A 2011 Science 334 195
[32] Hassan M T, Wirth A, Grguras I, Moulet A, Luu T, Gagnon J, Pervak V, Goulielmakis E 2012 Rev. Sci. Instrum. 83 111301
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