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Physical Review A

Dynamic extension of the Keldysh-Rutherford model for attoclocks

Vladislav Viktorovich Serov, Anatoli S. Kheifets

Published Jun 17, 2022• 1 citation
Publisher

Abstract

The classical Keldysh-Rutherford (KR) model of the attoclock [A. W. Bray et al., Phys. Rev. Lett. 121, 123201 (2018)] was introduced to interpret attosecond angular streaking on atomic hydrogen in the low laser intensity regime. In this model, the photoelectron acquires its final velocity immediately after exiting the tunnel and then scatters elastically on the Coulomb field of the residual ion. In the present work, we make a dynamic extension of the KR model and consider a gradual acceleration of the photoelectron by the driving laser field. By doing so, we observe and explain a significant displacement of the peaks of the angular distribution of the mean photoelectron momentum and the angular resolved ionization probability. These peaks should be close within the original KR model.

DOI
10.1103/physreva.105.063106

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The classical Keldysh-Rutherford (KR) model of the attoclock [A. W. Bray et al., Phys. Rev. Lett. 121, 123201 (2018)] was introduced to interpret attosecond angular streaking on atomic hydrogen in the low laser intensity regime. In this model, the photoelectron acquires its final velocity immediately after exiting the tunnel and then scatters elastically on the Coulomb field of the residual ion. In the present work, we make a dynamic extension of the KR model and consider a gradual acceleration of the photoelectron by the driving laser field. By doing so, we observe and explain a significant displacement of the peaks of the angular distribution of the mean photoelectron momentum and the angular resolved ionization probability. These peaks should be close within the original KR model.
Attoclock is a promising chronoscopy of the ultrafast dynamics of atoms and molecules in intense laser fields. The attoclock procedure is established based on the one-to-one correspondence between the photoelectron emission angle and the tunneling instant at each photoelectron kinetic energy for ionization of atoms and molecules subject to elliptically polarized strong laser fields. In this work, our joint theoretical and experimental study demonstrates that this correspondence could be broken down for photoelectrons emitted in a direction close to the minimum yield. Two trajectories with different tunneling instants and different initial velocities are found to correspond to a specific final momentum of the photoelectron in this direction, and a multi-peak structure appears in the photoelectron kinetic energy spectrum that can be attributed to interference between these two trajectories. Our work is essential for a deeper understanding and further development of the attoclock scheme.
Attosecond angular streaking (or "attoclock") is an insightful technique for probing the ultrafast electron dynamics in strong laser fields. Up until recently, this technique relied solely on an accurate measurement of the photoelectron momentum distribution and has remained restricted to atomic targets. Here, we propose a novel attosecond angular streaking scheme applicable to molecules, for which the ionic fragments of dissociative ionization are detected in the polarization plane of a close-to-circular polarized laser light. Our ionic attoclock measurements are consistent with theoretical results from a numerical solution of the time-dependent Schrödinger equation and an upper bound of 10 as on the tunneling time from the attoclock readings in the H_{2} molecule has been given, which is significantly smaller than any definitions of tunneling time available in the literatures.
Attosecond time-resolved electron tunneling dynamics have been investigated by using attosecond angular streaking spectroscopy, where a clock reference to the laser field vector is required in atomic strong-field ionization and the situation becomes complicated in molecules. Here we reveal a resonant ionization process via a transient state by developing an electron-tunneling-site-resolved molecular attoclock in Ar-Kr^{+}. Two distinct deflection angles are observed in the photoelectron angular distribution in the molecular frame, corresponding to the direct and resonant ionization pathways. We find the electron is temporally trapped in the Coulomb potential wells of the Ar-Kr^{+} before finally releasing into the continuum when the electron tunnels through the internal barrier. By utilizing the direct tunneling ionization as a self-referenced arm of the attoclock, the time delay of the electron trapped in the resonant state is revealed to be 3.50±0.04 fs. Our results give an impetus to exploring the ultrafast electron dynamics in complex systems and also endow a semiclassical presentation of the electron trapping dynamics in a quantum resonant state.
We theoretically study the infrared (IR)-dressed photoionization of atoms excited by extreme ultraviolet attosecond pulse trains above ionization threshold. The initial state of atoms is treated perturbatively by the IR field, and the continuum states are considered as Coulomb–Volkov (CV) waves. CV waves can much reduce the gauge difference calculated with Volkov waves, and, in general, the contribution of ground-state perturbation to the photoelectron spectrum is negligible. Our calculations show qualitative agreement with the experimental results [Phys. Rev. Lett. 95, 013001 (2005)]. An evident dependence of the photoelectron spectrum on the delay phase between the IR field and the attosecond pulse train is exhibited in both helium and argon. The angular distribution of photoelectrons with various IR polarizations and the corresponding photoelectron spectra are presented. The linearly polarized IR fields are shown to have a higher controlling capability of the spectrum via IR delay phases than the circularly polarized fields. On the other hand, the circularly polarized IR fields have a fruitful angular dependence of photoelectrons with various IR delay phases.
Theoretical models often fail to describe the dynamics due to numerical limitations, and we need to develop better approximate models for the ultrafast dynamics on an atomic scale, where quantum mechanics becomes essential. Novel time-resolved attosecond streaking techniques such as energy streaking and the attoclock (i.e. angular streaking) are currently being applied in an attempt to answer a very fundamental question in quantum mechanics: how fast can light remove a bound electron from an atom or a solid?
A semiclassical model is developed to understand the electronic dynamics in the low-energy attosecond streaking. Under a relatively strong infrared (IR) pulse, the low-energy part of photoelectrons initialized by a single attosecond pulse (SAP) can either rescatter with the ionic core and induce interferences structures in the momentum spectra of the ionized electrons or be recaptured into the Rydberg states. The Coulomb potential plays essential roles in both the electron rescattering and recapturing processes. We find that by changing the time delay between the SAP and the IR pulse, the photoelectrons yield or the population of the Rydberg states can be effectively controlled. The present study demonstrates a fascinating way to steer the electron motion in the continuum.