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

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.