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Scientific Reports

Simulation of laser-induced tunnel ionization based on a curved waveguide

Arnon Ben levy, Amir Hen, Merav Kahn, Yoad Aharon, Tamar Levin, Noa Mazurski, Uriel Levy, Gilad Marcus

Published Aug 3, 2023• 3 citations
Publisher

Abstract

The problem of tunneling ionization and the associated questions of how long it takes for an electron to tunnel through the barrier, and what the tunneling rate has fascinated scientists for almost a century. In strong field physics, tunnel ionization plays an important role, and accurate knowledge of the time-dependent tunnel rate is of paramount importance. The Keldysh theory and other more advanced related theories are often used, but their accuracy is still controversial. In previous work, we suggested using a curved waveguide as a quantum simulator to simulate the tunnel ionization process. Here we implemented for the first time such a curved waveguide and observed the simulated tunneling ionization process. We compare our results with the theory.

DOI
10.1038/s41598-023-39142-1

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Tunnel-ionization is investigated in the framework of relativistic quantum mechanics. \nFor an arbitrary constant electromagnetic field a gauge invariant energy \noperator is introduced in order to identify the classically forbidden region for \ntunnel-ionization. Furthermore, relativistic features of tunnel-ionization are explored. \nA one-dimensional intuitive picture predicts that the ionized electron wave \npacket in the relativistic regime experiences a momentum shift along the laser’s \npropagation direction. This is shown to be consistent with the well-known strong \nfield approximation. Furthermore, spin dynamics in tunnel-ionization process \nis discussed in the standard as well as in the dressed strong field approximation. \nNext, the tunneling time delay is investigated for tunnel-ionization by extending \nthe definition of the Wigner time delay. Later, this concept is redefined in terms of \nthe phase of the fixed energy propagator. The developed formalism is applied to \nthe deep-tunneling and the near-threshold-tunneling regimes. It is shown that in \nthe latter case signatures of the tunneling time delay can be measurable at remote \ndistance. Finally, the path-dependent formulation of gauge theory is discussed. It \nis demonstrated that this equivalent formulation of gauge theory leads to a canonical \ngauge fixing, in which the Feynman path integral becomes more intuitive and \nthe calculation of the quasiclassical propagator is considerably simplified

•Jan 1, 2014•0 citations
The problem of tunneling ionization and the associated questions of how long it takes for an electron to tunnel through the barrier, and what the tunneling rate has fascinated scientists for almost a century. In strong field physics, tunnel ionization plays an important role, and accurate knowledge of the time-dependent tunnel rate is of paramount importance. The Keldysh theory and other more advanced related theories are often used, but their accuracy is still controversial. In previous work, we suggested using a curved waveguide as a quantum simulator to simulate the tunnel ionization process. Here we implemented for the first time such a curved waveguide and observed the simulated tunneling ionization process. We compare our results with the theory.
Tunneling and tunneling time are hot debated and very interesting issues because of their fundamental role in the quantum mechanics. The measurement of the tunneling time in today's attosecond and strong field (low-frequency) experiments, despite its controversial discussion offers a fruitful opportunity to understand the time measurement and the role of time in quantum mechanics. In previous work Kullie (2015 Phys. Rev. A 92 , 052118), we suggested a model and derived a simple relation to calculate the tunneling time, which showed a good agreement with the experimental result for He-atom. In the present work we analyze and discuss our model considering the experimental result for H-atom, which is obtained recently by Satya Sainadh et al (2017 arXiv: 1707.05445 ). In the tunneling region, we find that our model shows a good agreement with their experimental result (similar to the He-atom in our previous work), and with the accompanied time-dependent Schrödiger equation simulations. However, Sainadh et al use a different picture of the tunneling, in which tunneling time becomes an imaginary quantity. Whereas our model represents a real tunneling time picture, precisely a delay time with respect to the ionization time at the atomic field strength. Moreover, even though the above-threshold-ionization is beyond the tunneling regime, we still see that the actual ionization time is related to our model. However, crucial points arise and keep some questions open especially on the experimental side.
Abstract Quantum tunnelling is a fundamental phenomenon in quantum physics, yet the question of how long it takes for a particle to tunnel through a barrier remains a topic of ongoing debate. Recent advances in attoclock experimental techniques in strong-field physics have renewed interest in this topic. While various definitions of tunneling time have been proposed, a consensus has yet to be reached. In this study, we adopt a definition of tunnelling time based on the ratio of the barrier width to the expected value of the velocity operator within the barrier. This approach reduces to the Büttiker-Landauer time (τBL\tau_{BL}τBL​) in the case of an opaque barrier and offers a clear physical interpretation for very thin barriers, where τBL\tau_{BL}τBL​ may not be well-defined. Additionally, by utilizing a virtual detector at the tunnel exit, we calculate the time delay between the peak of the electric field and the moment of ionization for long wavelengths ($\geq$6 μ\muμm). Our findings indicate that the time delay stabilizes around 190 as, remaining independent of the laser wavelength. Furthermore, through our quantum tunnelling time definition, this time delay can be interpreted as the time required for the electron to tunnel from a point within the barrier to the exit.
The Salecker-Wigner-Peres quantum-clock approach is applied in order to determine the tunneling time of an electron in strong-field tunnel ionization via a time-dependent electric field. Our results show that the ionization of the electron takes a nonvanishing period of time. This tunneling time is of the order of the Keldysh time but strictly larger than the Keldysh time. Comparing the quantum-clock tunneling time to the mean tunneling time as obtained by the virtual-detector approach, one finds that these two complementary methods give very similar results. Due to the asymmetric distribution of the tunneling time, there is a nonnegligible discrepancy between the mean tunneling time and the most probable tunneling time.
The notion of the first passage time is shown to offer a meaningful extension to quantum tunneling, providing a closed-integral-form analytical unification of the tunneling rate and the tunneling passage time. We demonstrate that, in suitable potential settings, the quantum first passage time, found as a solution to the Fokker-Planck and backward Kolmogorov's equations for the quantum probability density, recovers the hallmark results for the Kramers escape rate, the lifetime of tunneling quasi-stationary wave packets, leads to a classical, distance-over-speed passage time for a free-particle wave function, and offers useful insights into Keldysh's intimation on the electron barrier-traversal time in field-induced ionization.
A clear consensus on how long it takes a particle to tunnel through a potential barrier has never been so urgently required, since the electron dynamics in strong-field ionization can be resolved on attosecond time-scale in experiment and the exact nature of the tunneling process is the key to trigger subsequent attosecond techniques. Here a general picture of tunneling time is suggested by introducing a quantum travel time, which is defined as the ratio of the travel distance to the expected value of the velocity operator under the barrier. Specially, if applied to rectangular barrier tunneling, it can retrieve the Büttiker-Landauer time τBLτ_{BL}τBL​ in the case of an opaque barrier, and has a clear physical meaning in the case of a very thin barrier wherein τBLτ_{BL}τBL​ can not be well defined. In the case of strong-field tunneling process, with the help of the newly defined time, the tunneling delay time measured by attoclock experiment can be interpreted as a travel time spent by the electron to tunnel from a point under the barrier to the tunnel exit. In addition, a peculiar oscillation structure in the wavelength dependence of tunneling delay time in deep tunneling regime is observed, which is beyond the scope of adiabatic tunneling picture. This oscillation structure can be attributed to the interference between the ground state tunneling channel and the excited states tunneling channels.
Tunnel-ionization is investigated in the framework of relativistic quantum mechanics. \nFor an arbitrary constant electromagnetic field a gauge invariant energy \noperator is introduced in order to identify the classically forbidden region for \ntunnel-ionization. Furthermore, relativistic features of tunnel-ionization are explored. \nA one-dimensional intuitive picture predicts that the ionized electron wave \npacket in the relativistic regime experiences a momentum shift along the laser’s \npropagation direction. This is shown to be consistent with the well-known strong \nfield approximation. Furthermore, spin dynamics in tunnel-ionization process \nis discussed in the standard as well as in the dressed strong field approximation. \nNext, the tunneling time delay is investigated for tunnel-ionization by extending \nthe definition of the Wigner time delay. Later, this concept is redefined in terms of \nthe phase of the fixed energy propagator. The developed formalism is applied to \nthe deep-tunneling and the near-threshold-tunneling regimes. It is shown that in \nthe latter case signatures of the tunneling time delay can be measurable at remote \ndistance. Finally, the path-dependent formulation of gauge theory is discussed. It \nis demonstrated that this equivalent formulation of gauge theory leads to a canonical \ngauge fixing, in which the Feynman path integral becomes more intuitive and \nthe calculation of the quasiclassical propagator is considerably simplified