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Annals of Physics

Time delay and nonadiabatic calibration of the attoclock. Multiphoton process versus tunneling in strong field interaction

Ossama Kullie, Igor A. Ivanov

Published Mar 24, 2024• 1 citation
Publisher

Abstract

The measurement of the tunneling time delay in attosecond experiments, termed attoclock, sparked a heated debate about tunneling time and the role of time in quantum mechanics. We show a model that explains the experimental result of the attoclock in the nonadiabatic field calibration, where we find good agreement with the experimental data of Hofmann et al. (2019). We confirm our result with the numerical integration of the time-dependent Schrödinger equation. We also found that at a field strength F≤Fa (Fa is the atomic field strength), the model always predicts a time delay with respect to the quantum (lower) limit τa at F=Fa. For an adiabatic tunneling, the saturation at the limit (F=Fa) explains the well-known Hartman effect or Hartman paradox.

DOI
10.1016/j.aop.2024.169648

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The measurement of the tunneling time delay in attosecond experiments, termed attoclock, sparked a heated debate about tunneling time and the role of time in quantum mechanics. We show a model that explains the experimental result of the attoclock in the nonadiabatic field calibration, where we find good agreement with the experimental data of Hofmann et al. (2019). We confirm our result with the numerical integration of the time-dependent Schrödinger equation. We also found that at a field strength F≤Fa (Fa is the atomic field strength), the model always predicts a time delay with respect to the quantum (lower) limit τa at F=Fa. For an adiabatic tunneling, the saturation at the limit (F=Fa) explains the well-known Hartman effect or Hartman paradox.
The measurement of the tunneling time in attosecond experiments, termed attoclock, triggered a hot debate about the tunneling time, the role of time in quantum mechanics, where the interaction with the laser pulse involves two regimes of a different character, the multiphoton and the tunneling (field-) ionization. In the adiabatic field calibration, one of us (O. K.) developed in earlier works a real tunneling time model and showed that the model fits well to the experimental data of Landsmann et al. (Optica {\bf 1}, 343 2014). In the present work, it is shown that the model explains the experimental result in the nonadiabatic field calibration, where one reaches a good agreement with the experimental data of Hofmann et al. (J. of Mod. Opt. {\bf 66}, 1052, 2019). Furthermore, we confirm the result with the numerical integration of the time-dependent Schrödinger equation. The model is appealing because it offers a clear picture of the multiphoton and tunneling field-ionization regimes. In the nonadiabatic case (the nonadiabatic field calibration), the ionization is mainly driven by multiphoton absorption. Surprisingly, at a field strength F≤FaF \le F_aF≤Fa​ (FaF_aFa​ is the atomic field strength) the model always predicts a time delay with respect to the quantum limit τaτ_aτa​ at F=FaF=F_aF=Fa​. For an adiabatic tunneling the saturation at the limit (F=FaF=F_aF=Fa​) explains the well-known Hartman effect or Hartman paradox.
The measurement of the tunneling time-delay is hotly debated and remains controversial. In previous works, we showed that a model that accurately describes the time-delay measured by the attoclock experiment in adiabatic and nonadiabatic field calibrations. In the present work, we show that the tunneling time reveals a universal behavior with disentangled contributions. Even more remarkable is that the barrier tunneling time-delay can be convincingly defined and determined from the difference between the time-delay of adiabatic and nonadiabatic tunnel-ionization, which also show good agreement with experimental results. Furthermore, we illustrate that in the weak measurement limit, the barrier time-delay corresponds to the Larmor-clock time and the interaction time within the barrier.
The measurement of the tunneling time-delay is hotly debated and remains controversial. In previous works, we showed that a model that accurately describes the time-delay measured by the attoclock experiment in adiabatic and nonadiabatic field calibrations. In the present work, we show that the tunneling time reveals a universal behavior with disentangled contributions. Even more remarkable is that the barrier tunneling time-delay can be convincingly defined and determined from the difference between the time-delay of adiabatic and nonadiabatic tunnel-ionization, which also show good agreement with experimental results. Furthermore, we illustrate that in the weak measurement limit, the barrier time-delay corresponds to the Larmor-clock time and the interaction time within the barrier.
Abstract The measurement of the tunneling time-delay is hotly debated and remains controversial. In previous works, we showed that a model that accurately describes the time-delay measured by the attoclock experiment in adiabatic and nonadiabatic field calibrations. In the present work, we show that the tunneling time reveals a universal behavior with disentangled contributions. Even more remarkable is that the barrier tunneling time-delay can be convincingly defined and determined from the difference between the time-delay of adiabatic and nonadiabatic tunnel-ionization, which also show good agreement with experimental results. Furthermore, we illustrate that in the weak measurement limit, the barrier time-delay corresponds to the Larmor-clock time and the interaction time within the barrier.
The quantum tunneling time remains the subject of heated debate, and one of its most curious features is faster-than-light or superluminal tunneling. Our tunnel-ionization model of the time-delay, presented in previous work, shows good agreement with the attoclock measurement in the adiabatic and nonadiabatic field calibrations, which also enables the determination of the barrier time-delay. In the present work, we show that the tunnel-ionization for H-like atoms with large nuclear charge can be superluminal (quantum superluminality), which in principle can be investigated experimentally using the attoclock scheme. We discuss the quantum superluminality in detail for the different regimes of the tunnel-ionization. Our result shows that quantum tunneling faster-than-light is indeed possible, albeit only under somewhat extreme conditions.
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.