Ionization in a 1-Dimensional Dipole Model

TL;DR

This paper analyzes ionization dynamics in a 1D dipole model atom with a delta potential under periodic radiation, demonstrating complete ionization and constructing explicit resonance expansions.

Contribution

It introduces an explicit resonance expansion for the model, including Gamow vectors, and characterizes the asymptotic behavior of the system.

Findings

Complete ionization occurs with periodic fields.

Resonance expansion explicitly constructed with Gamow vectors.

Asymptotic power series describes long-term behavior.

Abstract

We study the evolution of a one dimensional model atom with $\delta$-function binding potential, subjected to a dipole radiation field $E(t) x$ with $E(t)$ a $2\pi/\omega$-periodic real-valued function. Starting with $\psi(x,t=0)$ an initially localized state and $E(t)$ a trigonometric polynomial, complete ionization occurs; the probability of finding the electron in any fixed region goes to zero. For $\psi(x,0)$ compactly supported and general periodic fields, we construct a resonance expansion. Each resonance is given explicitly as a Gamow vector, and is $2\pi/\omega$ periodic in time and behaves like the exponentially growing Green's function near $x=\pm \infty$. The remainder is given by an asymptotic power series in $t^{-1/2}$ with coefficients varying with $x$.