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Universal behavior of tunneling time and barrier time-delay decoupling in attoclock measurements

Ossama Kullie

Published Feb 11, 2025• 0 citations
Publisher

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.

DOI
10.17170/kobra-2026012611836

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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.

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Communications Physics•Apr 17, 2026•1 citation
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 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 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 tunneling times in strong-field ionization has been the topic of much controversy in recent years, with the attoclock and Larmor clock being two of the main contenders for correctly reproducing these times. By expressing the attoclock as the weak value of temporal delay, we extend its meaning beyond the traditional setup. This allows us to calculate the attoclock time for a static one-dimensional tunneling model consisting of a binding delta potential and a constant electric field. We apply the Steinberg weak-value interpretation of the Larmor clock. Using this definition, we obtain the position-resolved time density during tunnel ionization, yielding a non-zero Larmor tunneling time. Our model allows us to derive the analogue of the position-resolved attoclock tunneling time. While non-zero at the tunnel exit, it vanishes at the detector, far away from the atom. Formally, this means that the attoclock does not measure the "local" Larmor time, but instead a "non-local" time closely related to the phase time.
Abstract The measurement of tunneling times in strong-field ionization has been the topic of much controversy in recent years, with the attoclock and Larmor clock being two of the main contenders for correctly reproducing these times. While the non-zero Larmor tunneling time has been unambiguously detected, the tunneling time measured by the attoclock appears to vanish in tunnel ionization of a hydrogen atom. By expressing the attoclock as the weak value of temporal delay, we extend its meaning beyond the traditional setup and connect it to the weak-value interpretation of the Larmor clock. Our approach allows us to derive the position-resolved attoclock tunneling time. We show how this time, while non-zero at the tunnel exit, vanishes at the detector, far away from the atom. Formally, this means that the attoclock does not measure the “local” Larmor time, but instead a “non-local” time closely related to the phase time.