A general approximator for strong-field ionization rates

TL;DR

This work addresses the challenge of obtaining accurate, time-resolved ionization rates in strong-field physics by introducing GASFIR, a five-parameter ionization-rate functional that reconstructs the rate $\Gamma(t)$ from measured or calculated ionization probabilities via the relation $P_ ext{ion} = 1 - e^{-\int \Gamma(t) dt}$. The method combines a generalized kernel $K(t,T)$ with a flexible $f(t,T)$ that extends beyond the SFA and enforces the correct SFA limit, culminating in an analytical quasistatic limit $\Gamma_\text{QS}(E)$ that agrees with established tunneling rates for H, He, and Ne. Validation on hydrogen demonstrates accurate reproduction of ionization probabilities across a broad parameter range and recovery of SFA rates from probabilities, while the QS limit provides a principled link to tunneling dynamics and Coulomb effects. The framework enables time-domain investigations of strong-field ionization and attosecond metrology, with potential extensions to molecules and solid-state systems for applications in lightwave electronics.

Abstract

We address the long-standing problem of determining accurate, time-resolved ionization rates for atoms in strong laser fields, a quantity that is fundamental to attosecond science. We show that it is possible to retrieve sub-optical-cycle dynamics of strong-field ionization from ionization probabilities obtained for a set of few-cycle laser pulses that covers a sufficiently broad parameter space. To this end, we introduce the General Approximator for Strong-Field Ionization Rates (GASFIR), a retrieval tool that uses a few adjustable parameters to accurately reconstruct ab initio data. By imposing only essential physical constraints, our model provides a versatile framework for time-domain investigations of strong-field ionization and the role of ionization dynamics in attosecond metrology and lightwave electronics.

Figures (4)

• Figure 1: GASFIR reconstruction of ionization probabilities. (a) Strong-field approximation. (b) The numerical solution of the TDSE. For both panels, the probability of ionizing a hydrogen atom with a two-cycle laser pulse was calculated for various combinations of the pulse's central wavelength and peak intensity. The retrieved probabilities (solid lines) are close to both the input data (diamonds) and the validation data (points).
• Figure 2: GASFIR correctly retrieves the SFA ionization rate (blue) from the SFA ionization probabilities. The SFA rate was calculated using Eq. \ref{['eq:K_SFA']} without any adjustable parameters for a hydrogen atom exposed to a 500-nm, single-cycle laser pulse with a peak intensity of $I=10^{14}$ W$\,$cm$^{-2}$ ($E_\mathrm{L}=2.75$ V$\,$Å$^{-1}$). The retrieval process did not use the SFA rates. The shaded area represents the square of the electric field.
• Figure 3: The probability of finding an electron at a distance $r \geq 21$ Å from the ion as a representation of ionization dynamics. Here, we compare the probability obtained from the numerical solution of the TDSE to that evaluated by combining GASFIR's ionization rates with a classical analysis of electron trajectories. The laser parameters were: $\lambda_\mathrm{L}=1000$ nm, $I=10^{14}$ W$\,$cm$^{-2}$ ($E_\mathrm{L}=2.75$ V$\,\text{\AA}^{-1}$), $\tau_\mathrm{FWHM}=3 \times 2\pi/\omega_\mathrm{L} = 10\,\text{fs}$.
• Figure 4: Tunneling (quasistatic) rates. The black crosses indicate the barrier-suppression fields. The other markers represent literature values calculated using the complex-scaling method for the ionization rate in a static electric field for atomic hydrogen (red circles), neon (blue triangles), and helium (green squares). The curves represent the quasistatic limit of GASFIR, Eq. \ref{['eq:QS_kernel']}. The solid curves were obtained by retrieving the model parameters from the data represented by the markers. The corresponding parameters are listed in the last three rows of Table 1. The gray dashed curve was calculated with the model parameters that best describe the ionization of atomic hydrogen by two-cycle laser pulses.