Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Multiphoton absorption above ionization threshold by atoms in strong laser fields

Zhifang Deng, Joseph H. Eberly

Published Mar 1, 1985• 143 citations
Publisher

Abstract

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.

DOI
10.1364/josab.2.000486

Related papers

Strong-field high-frequency approximation to the multiphoton ionization of hydrogen

Fabio Trombetta, S. Basile, G. Ferrante

The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.

Journal of the Optical Society of America B•Apr 1, 1990•6 citations

Beyond ATI: Strong Field Quantum Control

P. H. Bucksbaum, David J. Wineland, Carl Wieman +1 more

Above‐threshold ionization (ATI) is the ionization of atoms by more than the minimum number photons necessary to overcome the Coulomb binding energy. Although ATI is contrary to the predictions of minimum‐order perturbation theory, it is the dominant mode of ionization whenever the light field becomes comparable to the static fields in the atom. We have learned a great deal by studying ATI over the past several years. We now know that by controlling these high intensity optical fields, we can control atomic and molecular processes such as ionization and dissociation. We can even engineer wave‐functions.

AIP conference proceedings•Jan 1, 1994•8 citations

ABOVE-THRESHOLD-IONIZATION BY MULTIPHOTON ABSORPTION OF ATOM UNDER SHORT LASER PULSE

Wenqing Zhang, TAN WEI-HAN, 中国科学院上海光学精密机械研究所,上海,201800

The Above-threshold-ionization(ATI) Spectrum of electrons produced by multiphoton absorption of atom has been obtained with spatial Gauss and temporal Sech shape of the incident laser pulse. It is found that our model can explain many phenomena such as peak suppression and switching. In addition, what is more important is that we can explain the red shift of the peaks decreases to zero gradually, as the pulse width changes from short to long pulse regime.

Acta Physica Sinica•Jan 1, 1991•0 citations

Multiphoton ionization in strong fields

Harm Geert Muller, A. Tip

The photoionization of atoms in a strong electromagnetic field leads to the effect of "above-threshold" ionization, displaying a number of peaks in the energy spectrum of the photoelectrons. In the case of a one-electron model atom in a circularly polarized field, we derive expressions that describe the position as well as the intensity of those peaks as a function of the field parameters by means of a nonperturbative method. It is immediately clear from our formulas that the lowest-energy peaks in general disappear with increasing field intensity, for Coulomb-like as well as shortrange potentials. For a zero-range potential, a numerical evaluation is easily performed, leading to results that are in every respect qualitatively similar to the experimental results obtained thus far on these kinds of processes.

Physical Review A•Dec 1, 1984•89 citations

Model study of above threshold multiphoton ionisation in strong fields

M Edwards, Laura L. Pan, L Armstrong

In a recent experiment involving multiphoton ionisation of Xe it was found that the photoelectron spectrum contained peaks which corresponded to absorption of more than the minimum number of photons required ionise. The effective orders of nonlinearity, furthermore, showed a striking uniformity. The authors investigated these effects with a model approximation consisting of a single bound state and m continua. Simple analytic expressions are obtained for the quantity measured in the experiment and the limit m to infinity is obtained. The results show good qualitative agreement with experiment.

Journal of Physics B Atomic and Molecular Physics•May 28, 1985•45 citations

Laser-Atom Interaction at High Intensities

Thomas J. Mcilrath, C. W. Clark

A general program has been developed to calculate multiphoton processes in atomic hydrogen to arbitrarily high order in perturbation theory. This program can be used to calculate quantities in intense field multiphoton processes, such as the generalized cross section of multiphoton absorption, the a.c. Stark effect (shift and the broadening of the level due to the field interaction), and the parameters in nonlinear optics such as the nonlinear index of refraction and the nonlinear susceptibility. Effective parametrization of high-order susceptibilities has been achieved over a wide range of frequencies, utilizing concepts from quantum defect theory to express the results of lengthy calculations in a compact form that also permits extrapolation across thresholds and resonance poles. Significant progress has been made in direct numerical solution of the time-dependent Schroedinger equation. In addition, contributions have been made in: understanding the role of spatial dimensionality in the solution of model systems (e.G., the one-dimensional delta-function potential); the development of a general R-matrix code for perturbative computations of multiphoton processes in many-electron atoms; and multiphoton ionization with two commensurate laser frequencies.

•May 20, 1991•0 citations
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.
The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.
Above‐threshold ionization (ATI) is the ionization of atoms by more than the minimum number photons necessary to overcome the Coulomb binding energy. Although ATI is contrary to the predictions of minimum‐order perturbation theory, it is the dominant mode of ionization whenever the light field becomes comparable to the static fields in the atom. We have learned a great deal by studying ATI over the past several years. We now know that by controlling these high intensity optical fields, we can control atomic and molecular processes such as ionization and dissociation. We can even engineer wave‐functions.
The photoionization of atoms in a strong electromagnetic field leads to the effect of "above-threshold" ionization, displaying a number of peaks in the energy spectrum of the photoelectrons. In the case of a one-electron model atom in a circularly polarized field, we derive expressions that describe the position as well as the intensity of those peaks as a function of the field parameters by means of a nonperturbative method. It is immediately clear from our formulas that the lowest-energy peaks in general disappear with increasing field intensity, for Coulomb-like as well as shortrange potentials. For a zero-range potential, a numerical evaluation is easily performed, leading to results that are in every respect qualitatively similar to the experimental results obtained thus far on these kinds of processes.
In a recent experiment involving multiphoton ionisation of Xe it was found that the photoelectron spectrum contained peaks which corresponded to absorption of more than the minimum number of photons required ionise. The effective orders of nonlinearity, furthermore, showed a striking uniformity. The authors investigated these effects with a model approximation consisting of a single bound state and m continua. Simple analytic expressions are obtained for the quantity measured in the experiment and the limit m to infinity is obtained. The results show good qualitative agreement with experiment.
A general program has been developed to calculate multiphoton processes in atomic hydrogen to arbitrarily high order in perturbation theory. This program can be used to calculate quantities in intense field multiphoton processes, such as the generalized cross section of multiphoton absorption, the a.c. Stark effect (shift and the broadening of the level due to the field interaction), and the parameters in nonlinear optics such as the nonlinear index of refraction and the nonlinear susceptibility. Effective parametrization of high-order susceptibilities has been achieved over a wide range of frequencies, utilizing concepts from quantum defect theory to express the results of lengthy calculations in a compact form that also permits extrapolation across thresholds and resonance poles. Significant progress has been made in direct numerical solution of the time-dependent Schroedinger equation. In addition, contributions have been made in: understanding the role of spatial dimensionality in the solution of model systems (e.G., the one-dimensional delta-function potential); the development of a general R-matrix code for perturbative computations of multiphoton processes in many-electron atoms; and multiphoton ionization with two commensurate laser frequencies.