- Open Access
- Access by Xinjiang University
Sub-barrier recollisions and the three classes of tunneling time delays in strong-field ionization
Phys. Rev. A 107, 053103 – Published 8 May, 2023
DOI: https://doi.org/10.1103/PhysRevA.107.053103
Abstract
Tunneling ionization is characterized by a negative time delay, observed asymptotically as a specific shift of the photoelectron momentum distribution, which is caused by the interference of the sub-barrier recolliding and direct ionization paths. In contrast, a Gedankenexperiment following the peak of the wave function shows a positive tunneling time delay at the tunnel exit, considering only the direct ionization path. In this paper we investigate the effects of sub-barrier recollisions on the time delay pattern at the tunnel exit. We conclude that the interference of the direct and recolliding trajectories decreases the tunneling time delay at the exit by the value equal to the asymptotic time delay, maintaining, however, its sizable positive value. Finally, we discuss the recent experiment [Yu et al., Light Sci. Appl. 11, 215 (2022)] addressing the tunneling time in a modified two-color attoclock setup. The analysis of the experimental findings with our theoretical model indicates the physical necessity to introduce an additional time characteristic for tunneling ionization—the time delay describing the initiation of the tunneling wave packet.
Physics Subject Headings (PhySH)
Article Text
References (79)
- P. B. Corkum and F. Krausz, Attosecond science, Nat. Phys. 3, 381 (2007).
- F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
- C. M. Maharjan, A. S. Alnaser, X. M. Tong, B. Ulrich, P. Ranitovic, S. Ghimire, Z. Chang, I. V. Litvinyuk, and C. L. Cocke, Momentum imaging of doubly charged ions of Ne and Ar in the sequential ionization region, Phys. Rev. A 72, 041403(R) (2005).
- P. Eckle, M. Smolarski, F. Schlup, J. Biegert, A. Staudte, M. Schöffler, H. G. Muller, R. Dörner, and U. Keller, Attosecond angular streaking, Nat. Phys. 4, 565 (2008).
- 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, 1525 (2008).
- A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-samha, L. B. Madsen, and U. Keller, Attoclock reveals natural coordinates of the laser-induced tunnelling current flow in atoms, Nat. Phys. 8, 76 (2012).
- A. S. Landsman, M. Weger, J. Maurer, R. Boge, A. Ludwig, S. Heuser, C. Cirelli, L. Gallmann, and U. Keller, Ultrafast resolution of tunneling delay time, Optica 1, 343 (2014).
- U. S. Sainadh, H. Xu, X. Wang, A. Atia-Tul-Noor, W. C. Wallace, N. Douguet, A. Bray, I. Ivanov, K. Bartschat, A. Kheifets, R. T. Sang, and I. V. Litvinyuk, Attosecond angular streaking and tunnelling time in atomic hydrogen, Nature (London) 568, 75 (2019).
- 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, 023201 (2017).
- N. Teeny, E. Yakaboylu, H. Bauke, and C. H. Keitel, Ionization Time and Exit Momentum in Strong-Field Tunnel Ionization, Phys. Rev. Lett. 116, 063003 (2016).
- N. Teeny, C. H. Keitel, and H. Bauke, Virtual-detector approach to tunnel ionization and tunneling times, Phys. Rev. A 94, 022104 (2016).
- E. Yakaboylu, M. Klaiber, H. Bauke, K. Z. Hatsagortsyan, and C. H. Keitel, Relativistic features and time delay of laser-induced tunnel ionization, Phys. Rev. A 88, 063421 (2013).
- M. Han, P. Ge, Y. Fang, X. Yu, Z. Guo, X. Ma, Y. Deng, Q. Gong, and Y. Liu, Unifying Tunneling Pictures of Strong-Field Ionization with an Improved Attoclock, Phys. Rev. Lett. 123, 073201 (2019).
- G. Orlando, C. R. McDonald, N. H. Protik, G. Vampa, and T. Brabec, Tunnelling time, what does it mean? J. Phys. B 47, 204002 (2014).
- G. Orlando, C. R. McDonald, N. H. Protik, and T. Brabec, Identification of the Keldysh time as a lower limit for the tunneling time, Phys. Rev. A 89, 014102 (2014).
- M. Lein, Streaking analysis of strong-field ionisation, J. Mod. Opt. 58, 1188 (2011).
- A. S. Landsman and U. Keller, Tunnelling time in strong field ionisation, J. Phys. B 47, 204024 (2014).
- 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, 503 (2015).
- H. Ni, U. Saalmann, and J.-M. Rost, Tunneling exit characteristics from classical backpropagation of an ionized electron wave packet, Phys. Rev. A 97, 013426 (2018).
- H. Ni, N. Eicke, C. Ruiz, J. Cai, F. Oppermann, N. I. Shvetsov-Shilovski, and L.-W. Pi, Tunneling criteria and a nonadiabatic term for strong-field ionization, Phys. Rev. A 98, 013411 (2018).
- H. Ni, U. Saalmann, and J.-M. Rost, Tunneling Ionization Time Resolved by Backpropagation, Phys. Rev. Lett. 117, 023002 (2016).
- C. Hofmann, A. Bray, W. Koch, H. Ni, and N. I. Shvetsov-Shilovski, Quantum battles in attoscience: Tunnelling, Eur. Phys. J. D 75, 208 (2021).
- A. S. Landsman and U. Keller, Attosecond science and the tunnelling time problem, Phys. Rep. 547, 1 (2015).
- A. M. Zheltikov, Keldysh parameter, photoionization adiabaticity, and the tunneling time, Phys. Rev. A 94, 043412 (2016).
- T. Zimmermann, S. Mishra, B. R. Doran, D. F. Gordon, and A. S. Landsman, Tunneling Time and Weak Measurement in Strong Field Ionization, Phys. Rev. Lett. 116, 233603 (2016).
- J. Liu, Y. Fu, W. Chen, Z. Lü, J. Zhao, J. Yuan, and Z. Zhao, Offset angles of photocurrents generated in few-cycle circularly polarized laser fields, J. Phys. B 50, 055602 (2017).
- Y. Song, Y. Yang, F. Guo, and S. Li, Revisiting the time-dependent ionization process through the Bohmian-mechanics method, J. Phys. B 50, 095003 (2017).
- M. Yuan, P. Xin, T. Chu, and H. Liu, Exploring tunneling time by instantaneous ionization rate in strong-field ionization, Opt. Express 25, 23493 (2017).
- M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Under-the-Tunneling-Barrier Recollisions in Strong-Field Ionization, Phys. Rev. Lett. 120, 013201 (2018).
- N. Eicke and M. Lein, Trajectory-free ionization times in strong-field ionization, Phys. Rev. A 97, 031402(R) (2018).
- N. Douguet and K. Bartschat, Dynamics of tunneling ionization using bohmian mechanics, Phys. Rev. A 97, 013402 (2018).
- A. W. Bray, S. Eckart, and A. S. Kheifets, Keldysh-Rutherford Model for the Attoclock, Phys. Rev. Lett. 121, 123201 (2018).
- B. Baytaş, M. Bojowald, and S. Crowe, Canonical tunneling time in ionization experiments, Phys. Rev. A 98, 063417 (2018).
- X. Ren, Y. Wu, L. Wang, and Y. Zheng, Entangled trajectories during ionization of an H atom driven by n-cycle laser pulse, Phys. Lett. A 382, 2662 (2018).
- J. Tan, Y. Zhou, M. He, Y. Chen, Q. Ke, J. Liang, X. Zhu, M. Li, and P. Lu, Determination of the Ionization Time Using Attosecond Photoelectron Interferometry, Phys. Rev. Lett. 121, 253203 (2018).
- D. Sokolovski and E. Akhmatskaya, No time at the end of the tunnel, Commun. Phys. 1, 47 (2018).
- W. Quan, V. V. Serov, M. Z. Wei, M. Zhao, Y. Zhou, Y. L. Wang, X. Y. Lai, A. S. Kheifets, and X. J. Liu, Attosecond Molecular Angular Streaking with All-Ionic Fragments Detection, Phys. Rev. Lett. 123, 223204 (2019).
- N. Douguet and K. Bartschat, Attoclock setup with negative ions: A possibility for experimental validation, Phys. Rev. A 99, 023417 (2019).
- C. Hofmann, A. S. Landsman, and U. Keller, Attoclock revisited on electron tunnelling time, J. Mod. Opt. 66, 1052 (2019).
- V. V. Serov, A. W. Bray, and A. S. Kheifets, Numerical attoclock on atomic and molecular hydrogen, Phys. Rev. A 99, 063428 (2019).
- R. Wang, Q. Zhang, D. Li, S. Xu, P. Cao, Y. Zhou, W. Cao, and P. Lu, Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime, Opt. Express 27, 6471 (2019).
- M. Yuan, Direct probing of tunneling time in strong-field ionization processes by time-dependent wave packets, Opt. Express 27, 6502 (2019).
- A. S. Kheifets, The attoclock and the tunneling time debate, J. Phys. B 53, 072001 (2020).
- S. Yusofsani and M. Kolesik, Quantum tunneling time: Insights from an exactly solvable model, Phys. Rev. A 101, 052121 (2020).
- M. Yu, K. Liu, M. Li, J. Yan, C. Cao, J. Tan, J. Liang, K. Guo, W. Cao, P. Lan, Q. Zhang, Y. Zhou, and P. Lu, Full experimental determination of tunneling time with attosecond-scale streaking method, Light Sci. Appl. 11, 215 (2022).
- M. Klaiber, Q. Z. Lv, S. Sukiasyan, D. Bakucz Canário, K. Z. Hatsagortsyan, and C. H. Keitel, Reconciling Conflicting Approaches for the Tunneling Time Delay in Strong Field Ionization, Phys. Rev. Lett. 129, 203201 (2022).
- L. A. MacColl, Note on the transmission and reflection of wave packets by potential barriers, Phys. Rev. 40, 621 (1932).
- L. Eisenbud, The Formal Properties of Nuclear Collisions, Ph.D. thesis, Princeton University, 1948.
- E. P. Wigner and L. Eisenbud, Higher angular momenta and long range interaction in resonance reactions, Phys. Rev. 72, 29 (1947).
- E. P. Wigner, Lower limit for the energy derivative of the scattering phase shift, Phys. Rev. 98, 145 (1955).
- F. T. Smith, Lifetime matrix in collision theory, Phys. Rev. 118, 349 (1960).
- A. I. Baz, Lifetime of intermediate states, Yad. Fiz. 4, 252 (1966) [Sov. J. Nucl. Phys. 4, 182 (1967)].
- M. Büttiker and R. Landauer, Traversal Time for Tunneling, Phys. Rev. Lett. 49, 1739 (1982).
- E. Pollak and W. H. Miller, New Physical Interpretation for Time in Scattering Theory, Phys. Rev. Lett. 53, 115 (1984).
- A. M. Steinberg, How Much Time Does a Tunneling Particle Spend in the Barrier Region? Phys. Rev. Lett. 74, 2405 (1995).
- A. Czirják, R. Kopold, W. Becker, M. Kleber, and W. Schleich, The Wigner function for tunneling in a uniform static electric field, Opt. Commun. 179, 29 (2000).
- A. Peres, Measurement of time by quantum clocks, Am. J. Phys. 48, 552 (1980).
- R. Landauer and T. Martin, Barrier interaction time in tunneling, Rev. Mod. Phys. 66, 217 (1994).
- E. H. Hauge and J. A. Støvneng, Tunneling times: A critical review, Rev. Mod. Phys. 61, 917 (1989).
- Time in Quantum Mechanics, Lecture Notes in Physics No. 72, edited by J. G. Muga, I. L. Egusquiza, and R. S. Mayato (Springer, New York, 2002).
- C. A. A. de Carvalho and H. M. Nussenzveig, Time delay, Phys. Rep. 364, 83 (2002).
- P. C. W. Davies, Quantum tunneling time, Am. J. Phys. 73, 23 (2005).
- R. Ramos, D. Spierings, and I. T. Racicot, Measurement of the time spent by a tunnelling atom within the barrier region, Nature (London) 583, 529 (2020).
- B. Feuerstein and U. Thumm, On the computation of momentum distributions within wavepacket propagation calculations, J. Phys. B 36, 707 (2003).
- X. Wang, J. Tian, and J. H. Eberly, Extended Virtual Detector Theory for Strong-Field Atomic Ionization, Phys. Rev. Lett. 110, 243001 (2013).
- W. Becker, F. Grasbon, R. Kopold, D. B. Milošević, G. G. Paulus, and H. Walther, Above-threshold ionization: From classical features to quantum effects, Adv. Atom. Mol. Opt. Phys. 48, 35 (2002).
- D. B. Canário, M. Klaiber, K. Z. Hatsagortsyan, and C. H. Keitel, Role of reflections in the generation of a time delay in strong-field ionization, Phys. Rev. A 104, 033103 (2021).
- L. V. Keldysh, Ionization in the field of a strong electromagnetic wave, Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].
- F. H. M. Faisal, Multiple absorption of laser photons by atoms, J. Phys. B 6, L89 (1973).
- H. R. Reiss, Effect of an intense electromagnetic field on a weakly bound system, Phys. Rev. A 22, 1786 (1980).
- D. M. Wolkow, Über eine Klasse von Lösungen der Diracschen Gleichung, Z. Phys. 94, 250 (1935).
- D. B. Milošević, Forward- and backward-scattering quantum orbits in above-threshold ionization, Phys. Rev. A 90, 063414 (2014).
- D. B. Milošević and W. Becker, Negative-travel-time quantum orbits in strong-field ionization by an elliptically polarized laser field, Phys. Rev. A 105, L031103 (2022).
- A. Čerkić, E. Hasović, D. B. Milošević, and W. Becker, High-order above-threshold ionization beyond the first-order Born approximation, Phys. Rev. A 79, 033413 (2009).
- D. B. Milošević, Low-frequency approximation for above-threshold ionization by a laser pulse: Low-energy forward rescattering, Phys. Rev. A 90, 063423 (2014).
- M. Klaiber, E. Yakaboylu, H. Bauke, K. Z. Hatsagortsyan, and C. H. Keitel, Under-the-Barrier Dynamics in Laser-Induced Relativistic Tunneling, Phys. Rev. Lett. 110, 153004 (2013).
- A. Lohr, M. Kleber, R. Kopold, and W. Becker, Above-threshold ionization in the tunneling regime, Phys. Rev. A 55, R4003(R) (1997).
- K. Krajewska, J. Z. Kamiński, and K. Wódkiewicz, Zero-range interaction in arbitrary dimensions and in the presence of external forces, Opt. Commun. 283, 843 (2010).
- N. Suárez, A. Chacón, M. F. Ciappina, J. Biegert, and M. Lewenstein, Above-threshold ionization and photoelectron spectra in atomic systems driven by strong laser fields, Phys. Rev. A 92, 063421 (2015).