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Physical Review A

Two-frequency above-threshold ionization with smooth pulses

Kazimierz Rza̧ewski, Li Wang, Joseph W. Haus

Published Sep 1, 1989• 26 citations
Publisher

Abstract

A model of atomic ionization by smooth pulses is solved with bound-continuum and energy-dependent continuum-continuum (C-C) dipole coupling. The rotating-wave approximation for the C-C transitions is avoided. In contrast with the flat continuum result, our ionization rate is independent of the C-C coupling. We also derive the photoelectron energy spectra and show that counterrotating terms make important contributions. Relation to above-threshold ionization experiments with two frequencies is discussed.

DOI
10.1103/physreva.40.3453

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A model of atomic ionization by smooth pulses is solved with bound-continuum and energy-dependent continuum-continuum (C-C) dipole coupling. The rotating-wave approximation for the C-C transitions is avoided. In contrast with the flat continuum result, our ionization rate is independent of the C-C coupling. We also derive the photoelectron energy spectra and show that counterrotating terms make important contributions. Relation to above-threshold ionization experiments with two frequencies is discussed.
We solve a model with one bound state and two continua.1 Two lasers are used to study the above threshold ionization process. The first laser couples the electron in a bound state to a continuum state. The photons are assumed to be energetic enough to promote the electron directly into the continuum far from the threshold; this avoids complications due to the Rydberg levels and the ponderomotive shifts of the threshold. The second laser mixes the electron wavefunction between two continuum states (C—C transitions); since we avoid the rotating wave approximation, multiple transitions between these continua are allowed. We find that the ionization rate is unaffected by the C—C transitions. Our model of hydrogenic atoms allows redistribution among the continua only during the ionization process and the photoelectron spectra exhibits peak suppression; i.e., the population is not the strongest at the energy of the ionization laser.
The dynamics of the bound-state populations and the photoelectron spectra are calculated for model atomic systems irradiated by a pulse with a harmonically modulated frequency. For a system including a single bound state a model is adopted, which takes into account the threshold behavior typical of negative ions and admits continuum-continuum transitions. For a model one-dimensional atom the results are obtained through a numerical integration of the Schr\"odinger equation. The case of a resonant ionization is also considered. The modulation of the frequency results in changing the instantaneous rate of decay of the initial state, in inducing additional population oscillations for multilevel systems, and in additional peaks in the photoelectron spectra.
A nonperturbative method is used to study the two-color multiphoton ionization of atoms by solving the Schr\"odinger equation in momentum space, which facilitates the extraction of the rapidly varying part of the wave function. Our method generalizes the problem for cases where an arbitrary number of ionization photons are absorbed, and also takes into account the threshold shifts due to both the high- and low-frequency fields. The photoelectron energy spectra of the hydrogen atoms are calculated and the dependence on the laser field strengths and frequencies is discussed. \textcopyright{} 1996 The American Physical Society.
We present an atomic model to study above-threshold ionization (ATI). We show that when the laser field is sufficiently intense the usual perturbation theory is not valid. We solve the model dynamics exactly, and several interesting quantities, including the initial-state decay rate and photoelectron spectrum, are calculated. These quantities are related to recent ATI experiments, and qualitatively they agree with these experiments. We specify the strong-field condition for continuum–continuum transitions and explore its physical meaning. Finally some comments on perturbation theory are made.
Model photoionization by a pulse with a modulated frequency is discussed. An approximation generalizing that of Weisskopf-Wigner is proposed, with a pole moving in the rhythm of the modulation. A model taking into account the ionization threshold is adopted, and relatively simple formulas for the nondecay probability and the photoelectron spectrum are obtained. A nonexponential character of the decay curves is demonstrated together with a raising and narrowing of the peaks in the photoelectron spectra.