High-harmonic generation as a tunneling delay probe

TL;DR

This paper explores how high-harmonic generation can be used as a reliable probe to measure tunneling delays during strong-field ionization, providing a new diagnostic tool that complements existing methods.

Contribution

It introduces a method combining time-frequency analysis of HHG spectra with classical trajectories to extract tunneling delays across different atoms and laser parameters.

Findings

Tunneling delay depends on instantaneous field strength and barrier width.

Delay scales with the inverse square root of laser intensity, consistent with theoretical models.

HHG-based diagnostics align with attoclock observations and show universal trends across species.

Abstract

We investigate the feasibility of using high-harmonic generation (HHG) as a complementary probe of tunneling delay in strong-field ionization. By combining time--frequency analysis of HHG spectra obtained from full time-dependent Schr\"odinger equation (TDSE) simulations with classical three-step-model (TSM) trajectories, we extract an effective tunneling delay associated with electron motion through the laser-suppressed Coulomb barrier. The analysis is carried out for Hydrogen, Helium, and Argon atoms over a range of laser wavelengths and peak intensities within the tunneling regime. The extracted delay exhibits a systematic dependence on the instantaneous field strength and barrier width at the ionization time, and follows the expected $\tau_d \propto 1/\sqrt{I_0}$ scaling consistent with Keldysh--Rutherford-type models and attoclock observations. When recast in terms of the Keldysh parameter, the tunneling delay collapses onto a near-universal trend across different atomic species. While HHG does not provide a direct measurement of tunneling time, the present results demonstrate that it can serve as a robust, internally consistent diagnostic of tunneling dynamics, offering an independent and complementary perspective to established attoclock techniques.