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A Wigner-distribution-like function is proposed to obtain various distributions of photoelectron emitted from H atoms in few-cycle laser pulses with different frequencies:time-energy distribution, time ionization distribution for linearly polarized laser field and time-emission angle distribution, angular distribution, and time ionization distribution for elliptically polarized laser field. With decreasing frequency, all the distributions clearly show a transition of ionization process from the multi-photon regime to the tunneling regime. For the case of linearly polarized laser pulse, accompanying this transition, the semiclassical relationship between the ionization moment and the final drift energy is becoming more and more close to the time-energy distribution. Meanwhile, the time-energy distribution clearly shows the interference structures in the tunneling regime, which can be attributed to the interference between the electrons with the same energy ejected at different times. For the case of elliptically polarized laser pulse, both the angular offset in the angular distribution and the time offset in the time ionization distribution are obtained by comparing the quantum calculation with the semi-classical result. The results show that the time offset is much smaller than the angular offset. This indicates that the attoclock technique which is based on the correspondence between two offsets is in principle inaccurate. Furthermore, the time offset can be both positive and negative. So this time offset cannot be interpreted as the tunneling time.
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Keywords:
- above-threshold ionization /
- Wigner-distribution-like function /
- time-energy distribution /
- tunneling ionization
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[2] Becker W, Grasbon F, Kopold R, Miloševic D B, Paulus G G, Walther H 2002Adv. At. Mol. Opt. Phys. 48 35
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[7] Corkum P B 1993Phys. Rev. Lett. 71 1994
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[9] Eckle P, Pfeiffer A N, Cirelli C, Staudte A, Doerner R, Muller H G, Buettiker M, Keller U 2008Science 322 1525
[10] Pfeiffer A N, Cirelli C, Smolariski M, Dörner R, Keller U 2011Nat. Phys. 7 428
[11] PfeifferA N, Cirelli C, Smolarski M, Dimitrovski D, Abu-samha M, Madsen L B, Keller U 2012Nat. Phys. 8 76
[12] Boge R, Cirelli C, Landsman A S, Heuser S, Ludwig A, Maurer J, Weger M, Gallmann L, Keller U 2013Phys. Rev. Lett. 111 103003
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[14] Ivanov I A, Kheifets A S 2014Phys. Rev. A 89 021402
[15] Torlina L, Morales F, Kaushal J, Ivanov I, Kheifets A, Zielinski A, Scrinzi A, Muller H G, Sukiasyan S, Ivanov M 2015Nat. Phys. 11 503
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[17] Lee H W 1995Phys. Rep. 259 147
[18] Kim J H, Lee D G, Shin H J, Nam C H 2001Phys. Rev. A 63 063403
[19] Guo L, Han S S, Chen J 2010Opt. Express 18 1240
[20] Guo L, Han S S, Chen J 2012Phys. Rev. A 86 053409
[21] Larochelle S F J, Talebpoury A, Chin S L 1998J. Phys. B 31 1215
[22] Chen J, Liu J, Chen S G 2000Phys. Rev. A 61 033402
[23] Lindner F, Schatzel M G, Walther H, Baltuška A, Goulielmakis E, Krausz F, Miloševi D B, Bauer D, Becker W, Paulus G G 2005Phys. Rev. Lett. 95 040401
[24] Reiss H R 1980Phys. Rev. A 22 1786
[25] Yudin G L, Ivanov M Y 2001Phys. Rev. A 64 013409
[26] Barth I, Smirnova O 2011Phys. Rev. A 84 063415
[27] Wang C L, Lai X Y, Hu Z L, Chen Y J, Quan W, Kang H P, Gong C, Liu X J 2014Phys. Rev. A 90 013422
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[1] Gostini P A, Fabre F, Mainfray G, Petite G, Rahman N K 1979Phys. Rev. Lett. 42 1127
[2] Becker W, Grasbon F, Kopold R, Miloševic D B, Paulus G G, Walther H 2002Adv. At. Mol. Opt. Phys. 48 35
[3] Keldysh L V 1965Sov. Phys. JETP 20 1307
[4] van Linden van den Heuvell H B, Muller H G1988Multiphoton Processes (edited bySmith S J, Knight P L) (Cambridge, UK:Cambridge University Press) p25
[5] Mohideen U, Sher M H, Tom H W K, Aumiller G D, Wood O R, Freeman R R, Bokor J, Bucksbaum P H 1993Phys. Rev. Lett. 71 509
[6] Paulus G G, Nicklich W, Xu H, Lambropoulos P, Walther H 1994Phys. Rev. Lett. 72 2851
[7] Corkum P B 1993Phys. Rev. Lett. 71 1994
[8] Eckle P, Smolarski M, Schlup P, Biegert J, StaudteA, Schöffler M, Muller H G, Dörner R 2008Nat. Phys. 4 565
[9] Eckle P, Pfeiffer A N, Cirelli C, Staudte A, Doerner R, Muller H G, Buettiker M, Keller U 2008Science 322 1525
[10] Pfeiffer A N, Cirelli C, Smolariski M, Dörner R, Keller U 2011Nat. Phys. 7 428
[11] PfeifferA N, Cirelli C, Smolarski M, Dimitrovski D, Abu-samha M, Madsen L B, Keller U 2012Nat. Phys. 8 76
[12] Boge R, Cirelli C, Landsman A S, Heuser S, Ludwig A, Maurer J, Weger M, Gallmann L, Keller U 2013Phys. Rev. Lett. 111 103003
[13] Wu J, Ph L, Schmidt H, Kunitski M, Meckel M, Voss S, Sann H, Kim H, Jahnke T, Czasch A, Dörner R 2012Phys. Rev. Lett. 108 183001
[14] Ivanov I A, Kheifets A S 2014Phys. Rev. A 89 021402
[15] Torlina L, Morales F, Kaushal J, Ivanov I, Kheifets A, Zielinski A, Scrinzi A, Muller H G, Sukiasyan S, Ivanov M 2015Nat. Phys. 11 503
[16] Hillery M, O'Connell R F, Scullyd M O, Wigner E P 1984Phys. Rep. 106 121
[17] Lee H W 1995Phys. Rep. 259 147
[18] Kim J H, Lee D G, Shin H J, Nam C H 2001Phys. Rev. A 63 063403
[19] Guo L, Han S S, Chen J 2010Opt. Express 18 1240
[20] Guo L, Han S S, Chen J 2012Phys. Rev. A 86 053409
[21] Larochelle S F J, Talebpoury A, Chin S L 1998J. Phys. B 31 1215
[22] Chen J, Liu J, Chen S G 2000Phys. Rev. A 61 033402
[23] Lindner F, Schatzel M G, Walther H, Baltuška A, Goulielmakis E, Krausz F, Miloševi D B, Bauer D, Becker W, Paulus G G 2005Phys. Rev. Lett. 95 040401
[24] Reiss H R 1980Phys. Rev. A 22 1786
[25] Yudin G L, Ivanov M Y 2001Phys. Rev. A 64 013409
[26] Barth I, Smirnova O 2011Phys. Rev. A 84 063415
[27] Wang C L, Lai X Y, Hu Z L, Chen Y J, Quan W, Kang H P, Gong C, Liu X J 2014Phys. Rev. A 90 013422
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