# Understanding tunneling ionization of atoms in laser fields with the essence of multiphoton absorption

## TL;DR

This paper investigates the ionization dynamics of atoms in laser fields, comparing quantum and semiclassical models, and reveals how virtual multiphoton absorption processes influence the transition from multiphoton to tunneling regimes.

## Contribution

It introduces a unified quantum framework to understand virtual multiphoton absorption effects beyond traditional tunneling theories.

## Key findings

- Momentum spectra differ between multiphoton and tunneling regimes.
- Virtual multiphoton spectra are continuous in tunneling regime.
- Interference of multiphoton peaks explains complex spectral structures.

## Abstract

The elaborate energy and momentum spectra of ionized electrons from atoms in laser fields suggest that the ionization dynamics described by tunneling theory should be modified. Although many efforts have been done within semiclassical models, there are few discussions describing multiphoton absorption process with quantum framework. In this letter, by comparing the results obtained with the time-dependent Schrodinger equation (TDSE) and Keldysh-Faisal-Reiss (KFR) theory, we have studied the nonperturbative effects of ionization dynamics beyond KFR theory. The difference in momentum spectra between multiphoton and tunneling regimes is understood in a unified picture with virtual multiphoton absorption processes. For the multiphoton regime, the momentum spectra can be obtained by coherent interference of each periodic contribution. However, the interference of multiphoton absorption peaks will result in the complex structure of virtual multiphoton bands in the tunneling regime. It is shown that the virtual spectra will be almost continuous in the tunneling regime instead of the discrete levels in the multiphoton regime. Finally, with a model combining TDSE and KFR theory, we have tried to understand the different effects of virtual multiphoton processes on ionization dynamics.