Exact Results for Ionization of Model Atomic Systems

TL;DR

This paper rigorously analyzes quantum atomic systems under periodic fields, deriving exact results on ionization, resonant states, and conditions for bound states, with implications for understanding atomic ionization dynamics.

Contribution

It provides the first rigorous derivation of the structure of wave functions and quasi-energies for atomic systems in time-periodic fields, including conditions for ionization and bound states.

Findings

Wave functions are sums of time-periodic resonant states with complex quasi-energies.

Imaginary parts of resonances are generally negative, indicating ionization.

Examples of zero ionization rate imply existence of Floquet bound states.

Abstract

We present rigorous results for quantum systems with both bound and continuum states subjected to an arbitrary strength time-periodic field. We prove that the wave function takes the form of a sum of time-periodic resonant states with complex quasi-energies and dispersive part of the the solution given by a power series in t^{-1/2}. Generally, the imaginary part of each resonance is negative, leading to ionization of the atom, but we also give examples where the ionization rate is zero implying the existence of a time-periodic Floquet bound state. The complex quasi-energy has a convergent perturbation expansion for small field strengths.