Ionization in damped time-harmonic fields

TL;DR

This paper analyzes the long-term ionization probability in a one-dimensional quantum model with a time-dependent delta potential, revealing singular behaviors and differences from abrupt transition models.

Contribution

It provides an explicit asymptotic analysis of ionization probabilities for a damped time-harmonic potential, highlighting novel singular effects and scaling laws.

Findings

Ionization probability approaches a constant times rac{1}{3} ext{ power of } \

rac{1}{3} ext{ power law for survival probability at } \

The long pulse limit exhibits singular behavior, especially at } \

Abstract

We study the asymptotic behavior of the wave function in a simple one dimensional model of ionization by pulses, in which the time-dependent potential is of the form $V(x,t)=-2\delta(x)(1-e^{-\lambda t} \cos\omega t)$, where $\delta$ is the Dirac distribution. We find the ionization probability in the limit $t\to\infty$ for all $\lambda$ and $\omega$. The long pulse limit is very singular, and, for $\omega=0$, the survival probability is $const \lambda^{1/3}$, much larger than $O(\lambda)$, the one in the abrupt transition counterpart, $V(x,t)=\delta(x)\mathbf{1}_{\{t\ge 1/\lambda\}}$ where $\mathbf{1}$ is the Heaviside function.