Delay time and Non-Adiabatic Calibration of the Attoclock. Multiphoton process versus tunneling in strong field interaction

TL;DR

This paper extends a real tunneling time model to nonadiabatic conditions, explaining experimental data and clarifying the roles of multiphoton and tunneling ionization regimes in strong field interactions.

Contribution

It demonstrates that the tunneling time model accurately describes nonadiabatic attoclock experiments, bridging the gap between multiphoton and tunneling ionization regimes.

Findings

The model fits experimental data in nonadiabatic calibration.

Ionization is mainly driven by multiphoton absorption at F ≤ F_a.

The model predicts a time delay at the atomic field strength.

Abstract

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 Schr\"odinger 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 $F \le F_a$ ($F_a$ is the atomic field strength) the model always predicts a time delay with respect to the quantum limit $\tau_a$ at $F=F_a$. For an adiabatic tunneling the saturation at the limit ($F=F_a$) explains the well-known Hartman effect or Hartman paradox.