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

The Journal of Chemical Physics

Theory of multiphoton processes: General formalism

Benjamin Fain, Alex Boeglin, S. H. Lin

Published Jun 15, 1988• 8 citations
Publisher

Abstract

A general framework for description of quantum systems in strong external fields is established. The most important application of the theory is concerned with the multiphoton ionization of atoms and molecules. The adiabatic approximation is developed. The Hamiltonian of the system is diagonalized by a time-dependent unitary transformation, which generates an interaction energy vanishing for very slow fields. A general analysis of the photoionization rates is performed. A specific model is considered: one-dimensional motion in the δ-function potential and external harmonic electric field. This model allows the exact solution for time-dependent eigenvalues and eigenfunctions. These solutions are compared with the conventional free electron approach to the ionization states.

DOI
10.1063/1.454320

Related papers

On the Theory of Multiphoton Ionization of Atoms

A. Szöke

A simple, "exactly solvable" atomic model will be presented that helps to discuss some of the interesting features of multiphoton ionization of atoms. The electromagnetic field is treated non-perturbatively, it can be strong. The atomic electrons are assumed to be non-interacting (Hartree model). They are bound in a harmonic oscillator potential (one- or three-dimensional). At the ionization energy, the potential is cut off and the free electron has no Coulomb attraction. The Schrodinger equation has exact analytic solutions valid in the inner or outer regions. If the field is turned on adiabatically, the exact solution can be found by matching these solutions at the boundary; both of their value and the normal derivative at all times. Thus the machine calculation reduces to repeated application of fast Fourier transforms and to the solution of linear equations (unfortunately a lot of them).

Short Wavelength Coherent Radiation: Generation and Applications•Jan 1, 1986•0 citations

Theory of multiphoton processes for atoms and ions

Bo Gao

In the first part of this thesis, a new variational principle is presented for the calculation of perturbative transition amplitudes of any order but free from any singularities. Applications are made to the multiphoton ionization and harmonic generation for atomic hydrogen. Its formulations in hyperspherical coordinates as well as in Hartree-Fock representation are also presented. In the second part of this thesis, theories for multiphoton detachment in a static electric or magnetic field are developed. They are based on the analytic solutions of an electron in the combined field of a laser and a static electric or magnetic field, and, therefore, are nonperturbative in both the laser intensity and the static electric or magnetic field strength. Heretofore unexpected cyclotron resonances, which are due to the infinite range character of the electron-photon coupling induced by the external magnetic field, are shown to exist under certain conditions.

•Jan 1, 1989•0 citations

Lippmann-Schwinger description of multiphoton ionization

Igor A. Ivanov, Anatoli S. Kheifets

We outline a formalism and develop a computational procedure to treat the process of multiphoton ionization (MPI) of atomic targets in strong laser fields. We treat the MPI process nonperturbatively as a decay phenomenon by solving a coupled set of the integral Lippmann-Schwinger equations. As basic building blocks of the theory, we use a complete set of field-free atomic states, discrete and continuous. This approach should enable us to provide both the total and differential cross sections of MPI of atoms with one and two electrons. As an illustration, we apply the proposed procedure to a simple model of MPI from a square-well potential and to the hydrogen atom.

arXiv:physics/0502016•Physical Review A•Apr 14, 2005•8 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

Multiphoton ionization of an atom with a finite-range binding potential

I. N. Kosarev, Gennady L. Yudin

The authors have formulated a new non-perturbative gauge-invariant analytical approach for solving the multiphoton ionization problem for a one-dimensional atomic system with a finite-range binding potential. Their method is based on the quasistationary state decay picture of ionization. They have applied the general solution to the model potential with the oscillator-like well and carried out the detailed analytical analysis of the ionization process. In the limit of moderately strong low-frequency laser fields and shallow potential wells, the authors' results reduce to those obtained for the case of an atom with the delta -well binding potential. For a finite-range binding potential one can distinguish the following peculiarities: (1) even for the case of non-resonant external field a sufficiently large number of binding states can lead to considerable changes in the multiphoton ionization; (2) in the case when the one-photon channel is open and the laser field is strong enough an atom becomes more stable as the field intensity is increased.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 28, 1992•4 citations

Scattering theory of multiphoton ionization in strong fields

Dong‐Sheng Guo, Teijo Åberg, Bernd Crasemann

Formal time-independent scattering theory is applied to multiphoton ionization of atoms in intense electromagnetic fields. The quantized-field version of the Volkov solution makes this approach possible. With the electron-photon interaction in a monochromatic photon field, it is found that, in the nonrelativistic and large-photon-number limits, the final scattering state exists only in the special case in which the ponderomotive potential per unit photon energy is an integer; otherwise the final state vanishes. In the integer case the corresponding wave function reduces to a single Volkov function, multiplied by an overlap factor. A simple interpretation of this result is given, and some other consequences of this work are discussed.

Physical Review A•Nov 1, 1989•127 citations
A general framework for description of quantum systems in strong external fields is established. The most important application of the theory is concerned with the multiphoton ionization of atoms and molecules. The adiabatic approximation is developed. The Hamiltonian of the system is diagonalized by a time-dependent unitary transformation, which generates an interaction energy vanishing for very slow fields. A general analysis of the photoionization rates is performed. A specific model is considered: one-dimensional motion in the δ-function potential and external harmonic electric field. This model allows the exact solution for time-dependent eigenvalues and eigenfunctions. These solutions are compared with the conventional free electron approach to the ionization states.
A simple, "exactly solvable" atomic model will be presented that helps to discuss some of the interesting features of multiphoton ionization of atoms. The electromagnetic field is treated non-perturbatively, it can be strong. The atomic electrons are assumed to be non-interacting (Hartree model). They are bound in a harmonic oscillator potential (one- or three-dimensional). At the ionization energy, the potential is cut off and the free electron has no Coulomb attraction. The Schrodinger equation has exact analytic solutions valid in the inner or outer regions. If the field is turned on adiabatically, the exact solution can be found by matching these solutions at the boundary; both of their value and the normal derivative at all times. Thus the machine calculation reduces to repeated application of fast Fourier transforms and to the solution of linear equations (unfortunately a lot of them).
In the first part of this thesis, a new variational principle is presented for the calculation of perturbative transition amplitudes of any order but free from any singularities. Applications are made to the multiphoton ionization and harmonic generation for atomic hydrogen. Its formulations in hyperspherical coordinates as well as in Hartree-Fock representation are also presented. In the second part of this thesis, theories for multiphoton detachment in a static electric or magnetic field are developed. They are based on the analytic solutions of an electron in the combined field of a laser and a static electric or magnetic field, and, therefore, are nonperturbative in both the laser intensity and the static electric or magnetic field strength. Heretofore unexpected cyclotron resonances, which are due to the infinite range character of the electron-photon coupling induced by the external magnetic field, are shown to exist under certain conditions.
We outline a formalism and develop a computational procedure to treat the process of multiphoton ionization (MPI) of atomic targets in strong laser fields. We treat the MPI process nonperturbatively as a decay phenomenon by solving a coupled set of the integral Lippmann-Schwinger equations. As basic building blocks of the theory, we use a complete set of field-free atomic states, discrete and continuous. This approach should enable us to provide both the total and differential cross sections of MPI of atoms with one and two electrons. As an illustration, we apply the proposed procedure to a simple model of MPI from a square-well potential and to the hydrogen atom.
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.
The authors have formulated a new non-perturbative gauge-invariant analytical approach for solving the multiphoton ionization problem for a one-dimensional atomic system with a finite-range binding potential. Their method is based on the quasistationary state decay picture of ionization. They have applied the general solution to the model potential with the oscillator-like well and carried out the detailed analytical analysis of the ionization process. In the limit of moderately strong low-frequency laser fields and shallow potential wells, the authors' results reduce to those obtained for the case of an atom with the delta -well binding potential. For a finite-range binding potential one can distinguish the following peculiarities: (1) even for the case of non-resonant external field a sufficiently large number of binding states can lead to considerable changes in the multiphoton ionization; (2) in the case when the one-photon channel is open and the laser field is strong enough an atom becomes more stable as the field intensity is increased.
Formal time-independent scattering theory is applied to multiphoton ionization of atoms in intense electromagnetic fields. The quantized-field version of the Volkov solution makes this approach possible. With the electron-photon interaction in a monochromatic photon field, it is found that, in the nonrelativistic and large-photon-number limits, the final scattering state exists only in the special case in which the ponderomotive potential per unit photon energy is an integer; otherwise the final state vanishes. In the integer case the corresponding wave function reduces to a single Volkov function, multiplied by an overlap factor. A simple interpretation of this result is given, and some other consequences of this work are discussed.