Extracting the phase distribution of the electron wave packet ionized by an elliptically polarized laser pulse
Ya-Nan Qin, Min Li, Yudi Feng, Siqiang Luo, Yueming Zhou, Peixiang Lu
Extracting the phase distribution of the electron wave packet ionized by an elliptically polarized laser pulse
We use an interferometic scheme to extract the phase distribution of the electron wave packet from above-threshold ionization in elliptically polarized laser fields. In this scheme, an electron wave packet released from a circularly polarized laser pulse acts as a reference wave and interferes with the electron wave packet ionized by a time-delayed counter-rotating elliptically polarized laser field. The generated vortex-shaped interference pattern in the photoelectron momentum distribution enables us to extract the phase distribution of the electron wave packet in the elliptically polarized laser pulse with high precision. By artificially screening the ionic potential at different ranges when solving the time-dependent Schördinger equation, we find that the angle-dependent phase distribution of the electron wave packet in the elliptically polarized laser field shows an obvious angular shift as compared to the strong-field approximation, whose value is the same as the attoclock shift. We also show that the amplitude of the angle-dependent phase distribution is sensitive to the ellipticity of the laser pulse, providing an alternative way to precisely calibrate the laser ellipticity in the attoclock measurement.
above-threshold ionization / photoelectron interference / vortex structure
[1] |
G. G. Paulus, W. Nicklich, H. Xu, P. Lambropoulos, and H. Walther, Plateau in above threshold ionization spectra, Phys. Rev. Lett. 72(18), 2851 (1994)
CrossRef
ADS
Google scholar
|
[2] |
H. Kang, W. Quan, Y. Wang, Z. Lin, M. Wu, H. Liu, X. Liu, B. B. Wang, H. J. Liu, Y. Q. Gu, X. Y. Jia, J. Liu, J. Chen, and Y. Cheng, Structure effects in angle-resolved high-order above-threshold ionization of molecules, Phys. Rev. Lett. 104(20), 203001 (2010)
CrossRef
ADS
Google scholar
|
[3] |
J. L. Krause, K. J. Schafer, and K. C. Kulander, Highorder harmonic generation from atoms and ions in the high intensity regime, Phys. Rev. Lett. 68(24), 3535 (1992)
CrossRef
ADS
Google scholar
|
[4] |
F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81(1), 163 (2009)
CrossRef
ADS
Google scholar
|
[5] |
B. Walker, B. Sheehy, L. F. DiMauro, P. Agostini, K. J. Schafer, and K. C. Kulander, Precision measurement of strong field double ionization of Helium, Phys. Rev. Lett. 73(9), 1227 (1994)
CrossRef
ADS
Google scholar
|
[6] |
W. Becker, X. Liu, P. J. Ho, and J. H. Eberly, Theories of photoelectron correlation in laser-driven multiple atomic ionization, Rev. Mod. Phys. 84(3), 1011 (2012)
CrossRef
ADS
Google scholar
|
[7] |
G. G. Paulus, F. Zacher, H. Walther, A. Lohr, W. Becker, and M. Kleber, Above-threshold ionization by an elliptically polarized field: Quantum tunneling interferences and classical dodging, Phys. Rev. Lett. 80(3), 484 (1998)
CrossRef
ADS
Google scholar
|
[8] |
S. P. Goreslavski, G. G. Paulus, S. V. Popruzhenko, and N. I. Shvetsov-Shilovski, Coulomb asymmetry in abovethreshold ionization, Phys. Rev. Lett. 93(23), 233002 (2004)
CrossRef
ADS
Google scholar
|
[9] |
X. Wang and J. H. Eberly, Effects of elliptical polarization on strong-field short-pulse double ionization, Phys. Rev. Lett. 103(10), 103007 (2009)
CrossRef
ADS
Google scholar
|
[10] |
C. Liu and K. Z. Hatsagortsyan, Coulomb focusing in above-threshold ionization in elliptically polarized midinfrared strong laser fields, Phys. Rev. A 85(2), 023413 (2012)
CrossRef
ADS
Google scholar
|
[11] |
C. Wang, X. Lai, Z. Hu, Y. Chen, W. Quan, H. Kang, C. Gong, and X. Liu, Strong-field atomic ionization in elliptically polarized laser fields, Phys. Rev. A 90(1), 013422 (2014)
CrossRef
ADS
Google scholar
|
[12] |
P. Eckle, M. Smolarski, P. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, Attosecond angular streaking, Nat. Phys. 4(7), 565 (2008)
CrossRef
ADS
Google scholar
|
[13] |
P. Eckle, A. N. Pfeiffer, C. Cirelli, A. Staudte, R. Dörner, H. G. Muller, M. Büttiker, and U. Keller, Attosecond ionization and tunneling delay time measurements in helium, Science 322(5907), 1525 (2008)
CrossRef
ADS
Google scholar
|
[14] |
J. Liang, Y. Zhou, J. Tan, M. He, Q. Ke, Y. Zhao, M. Li, W. Jiang, and P. Lu, Low-energy photoelectron interference structure in attosecond streaking, Opt. Express 27(26), 37736 (2019)
CrossRef
ADS
Google scholar
|
[15] |
J. Yan, W. Xie, M. Li, K. Liu, S. Luo, C. Cao, K. Guo, W. Cao, P. Lan, Q. Zhang, Y. Zhou, and P. Lu, Photoelectron ionization time of aligned molecules clocked by attosecond angular streaking, Phys. Rev. A 102(1), 013117 (2020)
CrossRef
ADS
Google scholar
|
[16] |
C. Wang, X. Li, X. Xiao, Y. Yang, S. Luo, X. Yu, X. Xu, L. Peng, Q. Gong, and D. Ding, Accurate in situ measurement of ellipticity based on subcycle ionization dynamics, Phys. Rev. Lett. 122(1), 013203 (2019)
CrossRef
ADS
Google scholar
|
[17] |
I. A. Ivanov and A. S. Kheifets, Strong-field ionization of He by elliptically polarized light in attoclock configuration, Phys. Rev. A 89, 021402(R) (2014)
CrossRef
ADS
Google scholar
|
[18] |
L. Torlina, F. Morales, J. Kaushal, I. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H. G. Muller, S. Sukiasyan, M. Ivanov, and O. Smirnova, Interpreting attoclock measurements of tunnelling times, Nat. Phys. 11(6), 503 (2015)
CrossRef
ADS
Google scholar
|
[19] |
N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K. Z. Hatsagortsyan, T. Pfeifer, C. H. Keitel, and R. Moshammer, Experimental evidence for quantum tunneling time, Phys. Rev. Lett. 119(2), 023201 (2017)
CrossRef
ADS
Google scholar
|
[20] |
K. Liu, M. Li, W. Xie, K. Guo, S. Luo, J. Yan, Y. Zhou, and P. Lu, Revealing the effect of atomic orbitals on the phase distribution of an ionizing electron wave packet with circularly polarized two-color laser fields, Opt. Express 28(8), 12439 (2020)
CrossRef
ADS
Google scholar
|
[21] |
D. Pengel, S. Kerbstadt, D. Johannmeyer, L. Englert, T. Bayer, and M. Wollenhaupt, Electron vortices in femtosecond multiphoton ionization, Phys. Rev. Lett. 118(5), 053003 (2017)
CrossRef
ADS
Google scholar
|
[22] |
X. Xiao, M. Wang, H. Liang, Q. Gong, and L. Peng, Proposal for measuring electron displacement induced by a short laser pulse, Phys. Rev. Lett. 122(5), 053201 (2019)
CrossRef
ADS
Google scholar
|
[23] |
N. Ramsey, A molecular beam resonance method with separated oscillating fields, Phys. Rev. 78(6), 695 (1950)
CrossRef
ADS
Google scholar
|
[24] |
J. M. Ngoko Djiokap, S. X. Hu, L. B. Madsen, N. L. Manakov, A. V. Meremianin, and A. F. Starace, Electron vortices in photoionization by circularly polarized attosecond pulses, Phys. Rev. Lett. 115(11), 113004 (2015)
CrossRef
ADS
Google scholar
|
[25] |
J. M. Ngoko Djiokap, A. V. Meremianin, N. L. Manakov, S. X. Hu, L. B. Madsen, and A. F. Starace, Multistart spiral electron vortices in ionization by circularly polarized UV pulses, Phys. Rev. A 94(1), 013408 (2016)
CrossRef
ADS
Google scholar
|
[26] |
J. M. Djiokap, A. V. Meremianin, N. L. Manakov, S. X. Hu, L. B. Madsen, and A. F. Starace, Kinematical vortices in double photoionization of helium by attosecond pulses, Phys. Rev. A 96(1), 013405 (2017)
CrossRef
ADS
Google scholar
|
[27] |
J. M. Ngoko Djiokap, A. V. Meremianin, N. L. Manakov, L. B. Madsen, S. X. Hu, and A. F. Starace, Dynamical electron vortices in attosecond double photoionization of H2, Phys. Rev. A 98(6), 063407 (2018)
CrossRef
ADS
Google scholar
|
[28] |
K. J. Yuan, S. Chelkowski, and A. D. Bandrauk, Photoelectron momentum distributions of molecules in bichromatic circularly polarized attosecond UV laser fields, Phys. Rev. A 93(5), 053425 (2016)
CrossRef
ADS
Google scholar
|
[29] |
K. J. Yuan, H. Lu, and A. D. Bandrauk, Photoionization of triatomic molecular ions H32+ by intense bichromatic circularly polarized attosecond UV laser pulses, J. Phys. At. Mol. Opt. Phys. 50(12), 124004 (2017)
CrossRef
ADS
Google scholar
|
[30] |
J. Chen, X. Zheng, and T. Zhang, Vortex structures in the photoelectron momentum distributions of negative hydrogen ions induced by a short laser pulse, Proc. SPIE 11333, 46 (2019)
CrossRef
ADS
Google scholar
|
[31] |
D. Pengel, S. Kerbstadt, L. Englert, T. Bayer, and M. Wollenhaupt, Control of three-dimensional electron vortices from femtosecond multiphoton ionization, Phys. Rev. A 96(4), 043426 (2017)
CrossRef
ADS
Google scholar
|
[32] |
S. Kerbstadt, K. Eickhoff, T. Bayer, and M. Wollenhaupt, Odd electron wave packets from cycloidal ultrashort laser fields, Nat. Commun. 10(1), 658 (2019)
CrossRef
ADS
Google scholar
|
[33] |
S. Yu, Y. Wang, X. Lai, Y. Huang, W. Quan, and X. Liu, Coulomb effect on photoelectron momentum distributions in orthogonal two-color laser fields, Phys. Rev. A 94(3), 033418 (2016)
CrossRef
ADS
Google scholar
|
[34] |
M. D. Feit, J. A. Jr Fleck, and A. Steiger, Solution of the Schördinger equation by a spectral method, J. Comput. Phys. 47(3), 412 (1982)
CrossRef
ADS
Google scholar
|
[35] |
X. M. Tong, K. Hino, and N. Toshima, Phase-dependent atomic ionization in few-cycle intense laser fields, Phys. Rev. A 74, 031405(R) (2006)
CrossRef
ADS
Google scholar
|
[36] |
M. Protopapas, C. H. Keitel, and P. L. Knight, Atomic physics with super-high intensity lasers, Rep. Prog. Phys. 60(4), 389 (1997)
CrossRef
ADS
Google scholar
|
[37] |
M. Li, J. W. Geng, H. Liu, Y. Deng, C. Wu, L. Y. Peng, Q. Gong, and Y. Liu, Classical-quantum correspondence for above-threshold ionization, Phys. Rev. Lett. 112(11), 113002 (2014)
CrossRef
ADS
Google scholar
|
[38] |
H. Xie, M. Li, S. Luo, Y. Li, Y. Zhou, W. Cao, and P. Lu, Energy-dependent angular shifts in the photoelectron momentum distribution for atoms in elliptically polarized laser pulses, Phys. Rev. A 96(6), 063421 (2017)
CrossRef
ADS
Google scholar
|
[39] |
M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Theory of high-harmonic generation by lowfrequency laser fields, Phys. Rev. A 49(3), 2117 (1994)
CrossRef
ADS
Google scholar
|
[40] |
M. Li, Y. Liu, H. Liu, Q. Ning, L. Fu, J. Liu, Y. Deng, C. Wu, L. Peng, and Q. Gong, Subcycle dynamics of Coulomb asymmetry in strong elliptical laser fields, Phys. Rev. Lett. 111(2), 023006 (2013)
CrossRef
ADS
Google scholar
|
[41] |
A. S. Landsman, C. Hofmann, A. N. Pfeiffer, C. Cirelli, and U. Keller, Unified approach to probing Coulomb effects in tunnel ionization for any ellipticity of laser light, Phys. Rev. Lett. 111(26), 263001 (2013)
CrossRef
ADS
Google scholar
|
[42] |
P. A. Korneev, S. V. Popruzhenko, S. P. Goreslavski, T. M. Yan, D. Bauer, W. Becker, M. Kübel, M. F. Kling, C. Rödel, M. Wünsche, and G. G. Paulus, Interference carpets in above-threshold ionization: From the Coulombfree to the coulomb-dominated regime, Phys. Rev. Lett. 108(22), 223601 (2012)
CrossRef
ADS
Google scholar
|
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