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Physical Review A

Interpreting attoclock experiments from the perspective of Bohmian trajectories

Wenhai Xie, Min Li, Yueming Zhou, Peixiang Lu

Published Jan 31, 2022• 12 citations
Publisher

Abstract

We theoretically study the attoclock using the Bohmian trajectory. The Bohmian trajectory includes a nonlocal quantum potential and the Coulomb potential, allowing us to separately study their effects on the attoclock. We show that the quantum potential has a significant effect on the photoelectron momentum spread while it only slightly affects the offset angle in the attoclock. We further show how the Coulomb potential affects the offset angle, revealing that the Coulomb force before the electron reaches the position of the classical tunnel exit has a significant contribution to the offset angle. Thus taking the full Coulomb effect into account during the tunneling ionization is a prerequisite for our understanding of the origin of the offset angle in the attoclock experiment. Our study also implies that there might be an inertia time for the initial wave function in response to the change of the laser electric field.

DOI
10.1103/physreva.105.013119

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We theoretically study the attoclock using the Bohmian trajectory. The Bohmian trajectory includes a nonlocal quantum potential and the Coulomb potential, allowing us to separately study their effects on the attoclock. We show that the quantum potential has a significant effect on the photoelectron momentum spread while it only slightly affects the offset angle in the attoclock. We further show how the Coulomb potential affects the offset angle, revealing that the Coulomb force before the electron reaches the position of the classical tunnel exit has a significant contribution to the offset angle. Thus taking the full Coulomb effect into account during the tunneling ionization is a prerequisite for our understanding of the origin of the offset angle in the attoclock experiment. Our study also implies that there might be an inertia time for the initial wave function in response to the change of the laser electric field.
Recent attoclock experiments and theoretical studies regarding the strong-field ionization of atoms by few-cycle infrared pulses revealed features that have attracted much attention. Here we investigate tunneling ionization and the dynamics of the electron probability using Bohmian mechanics. We consider a one-dimensional problem to illustrate the underlying mechanisms of the ionization process. It is revealed that in the major part of the below-the-barrier ionization regime, in an intense and short infrared pulse, the electron does not tunnel through the entire barrier, but rather starts already from the classically forbidden region. Moreover, we highlight the correspondence between the probability of locating the electron at a particular initial position and its asymptotic momentum. Bohmian mechanics also provides a natural definition of mean tunneling time and exit position, taking account of the time dependence of the barrier. Finally, we find that the electron can exit the barrier with significant kinetic energy, thereby corroborating the results of a recent study [N. Camus et al., Phys. Rev. Lett. 119, 023201 (2017)].
We study the effect of spin flip on tunneling ionization in the attoclock settings. Our study is based on a fully relativistic approach in which we seek a numerical solution of the time-dependent Dirac equation. We find that spin flip during strong field ionization significantly increases the attoclock offset angle, indicating longer tunneling delay relative to electrons with no spin flip. To interpret our numerical findings, we conduct additional modeling within the perturbative Breit-Pauli approach, which allows us to elucidate the role of different relativistic mechanisms. We show that the spin-orbit interaction is mainly responsible for the spin flip, rather than interaction with the magnetic component of the laser field. We further discuss the dynamic mechanisms of the spin-flip effect, suggesting that it takes place while the electron is still bound. Our findings indicate that the attoclock can be used to investigate electron spin-flip dynamics during the tunnel ionization process.
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.
Abstract We investigate how spin polarization of the initial atomic state affects the tunneling delay in the attoclock settings. Using the time dependent Schrödinger equation and the Breit–Pauli Hamiltonian we demonstrate that spin polarization can produce measurable corrections to tunneling delays in attoclock spectroscopy. Our findings indicate that spin–orbit coupling introduces an additional spin-dependent degree of freedom into under-the- barrier motion, suggesting new opportunities for spin-resolved attosecond measurements. We show that the electron’s spin orientation during tunneling produces a contribution to the attoclock offset angle. Our results are interpreted within the framework of the strong field approximation and the imaginary time methods. We show that this approach provides a rare opportunity to get an insight into the details of the sub-barrier electron motion during the tunneling process.
In this paper, Bohmian mechanics is applied to intense laser–atom physics. The motion of an atomic electron in an intense laser field is obtained from the Bohm–Newton equation. We find that the quantum potential that dominates the quantum effect of a physical system becomes negligible as the electron is driven far from the parent ion by the intense laser field, i.e. the behavior of the electron smoothly tends towards classical soon after the electron is ionized. Our numerical calculations present direct positive evidence for semiclassical trajectory methods in intense laser–atom physics where the motion of the ionized electron is treated by classical mechanics, while quantum mechanics is needed before the ionization.