Abstract
Phenomenon of tunneling ionization became the subject of many theoretical studies inspired by recent attoclock experiments on strong-field ionization of atoms by few-cycle laser pulses in infrared wavelength region. In particular, the notion of electron tunneling time caused a lot of controversy in various theoretical approaches. Bohmian mechanics seems to be specially suitable for theoretical description of electron tunneling times. We present results of calculations of probability distributions of electron Bohmian tunneling times for the model problem of ionization of 1D atom by a half-cycle laser pulse. Two regimes are studied in details: (a) the case of completely tunneling ionization and (b) the case involving three mechanisms: direct, non-completely and completely tunneling ionization. Probability distributions of tunneling exit positions and exit velocities are also studied. In addition, we discuss the appearance of transient dynamical tunneling due to non-adiabatic switching of external field.
Graphic Abstract
Similar content being viewed by others
Data Availability
This manuscript has no associated data, or the data will not be deposited. [Authors’ comment: This is a theoretical study, and there are no experimental data.]
References
G. Muga, R.S. Mayato, I. Egusquiza (eds.), Time in Quantum Mechanics, vol. 1 (Springer, Berlin Heidelberg, 2009)
G. Muga, A. Ruschhaupt, A. del Campo (eds.), Time in Quantum Mechanics, vol. 2 (Springer, Berlin Heidelberg, 2009)
E.A. Solov’ev, The Foundations of Quantum Physics: New Interpretation and Systematic Application (Lambert Academic Publishing, Saarbrucken, 2017), pp.8–13
C.R. Leavens, Phys. Lett. A 303, 154 (2002)
B. Mielnik, G. Torres-Vega, Univ. J. Phys. Appl. 2, 81 (2005)
D. Bohm, Phys. Rev. 85, 166 (1952)
D. Dürr, S. Teufel, Bohmian Mechanics: The Physics and Mathematics of Quantum Theory (Springer, Berlin, 2009)
C.R. Leavens, Solid State Commun. 76, 253 (1990)
X. Oriols, F. Martín, J. Suñé, Phys. Rev. A 54, 2594 (1996)
S. Das, M. Nöth, D. Dürr, Phys. Rev. A 99, 052124 (2019)
P. Eckle, A.N. Pfeiffer, C. Cirelli, A. Staudte, R. Dörner, H.G. Muller, M. Büttiker, U. Keller, Science 322, 1525 (2008)
A.S. Landsman, M. Weger, J. Maurer, R. Boge, A. Ludwig, S. Heuser, C. Cirelli, L. Gallmann, U. Keller, Optica 1, 343 (2014)
L. Torlina, F. Morales, J. Kaushal, I.A. Ivanov, A. Kheifets, A. Zielinski, A. Scrinzi, H.G. Muller, S. Sukiasyan, M.Y. Ivanov, O. Smirnova, Nat. Phys. 11, 503 (2015)
T. Zimmermann, S. Mishra, B.R. Doran, D.F. Gordon, A.S. Landsman, Phys. Rev. Lett. 116, 233603 (2016)
N. Teeny, E. Yakaboylu, H. Bauke, C.H. Keitel, Phys. Rev. Lett. 116, 063003 (2016)
H. Ni, U. Saalmann, J.M. Rost, Phys. Rev. Lett. 117, 023002 (2016) newpage
N. Camus, E. Yakaboylu, L. Fechner, M. Klaiber, M. Laux, Y. Mi, K.Z. Hatsagortsyan, T. Pfeifer, C.H. Keitel, R. Moshammer, Phys. Rev. Lett. 119, 023201 (2017)
H. Ni, U. Saalmann, J.M. Rost, Phys. Rev. A 97, 013426 (2018)
H. Ni, N. Eicke, C. Ruiz, J. Cai, F. Oppermann, N.I. Shvetsov-Shilovski, L.W. Pi, Phys. Rev. A 98, 013411 (2018)
U. Sainadh, H. Xu, X. Wang, A. Atia-Tul-Noor, W. Wallace, N. Douguet, A. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. Sang, I. Litvinyuk, Nature (London) 568, 75 (2019)
M. Klaiber, Q.Z. Lv, S. Sukiasyan, D. Bakucz Canário, K.Z. Hatsagortsyan, C.H. Keitel, Phys. Rev. Lett. 129, 203201 (2022)
C. Hofmann, A.S. Landsman, U. Keller, J. Mod. Opt. 66, 1052 (2019)
A.S. Kheifets, J. Phys. B: At. Mol. Opt. Phys. 53, 072001 (2020)
C. Hofmann, A. Bray, W. Koch, H. Ni, N.I. Shvetsov-Shilovski, Eur. Phys. J. D 75, 208 (2021)
F. Guo, J. Chen, S. Li, Y. Yang, Chin. Phys. Lett. 32, 073201 (2015)
I.A. Ivanov, C.H. Nam, K.T. Kim, Sci. Rep. 7, 39919 (2017)
N. Douguet, K. Bartschat, Phys. Rev. A 97, 013402 (2018)
W. Xie, M. Li, Y. Zhou, P. Lu, Phys. Rev. A 105, 013119 (2022)
X. Lai, X. Liu, Chin. Phys. B 29, 013205 (2020)
Acknowledgements
This work was supported by Serbia-JINR collaboration program.
Author information
Authors and Affiliations
Contributions
Tasko P. Grozdanov and Evgeni A. Solov’ev have contributed equally to this work.
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Grozdanov, T.P., Solov’ev, E.A. Bohmian tunneling times in strong-field ionization. Eur. Phys. J. D 77, 33 (2023). https://doi.org/10.1140/epjd/s10053-023-00620-w
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjd/s10053-023-00620-w