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

Physical Review A

Equivalence of Reiss's Semiclassical Method of Multiphoton Transitions in Intense Radiation Fields with the Ordinary Perturbation Theory

Surya P. Tewari

Published Nov 1, 1973• 7 citations
Publisher

Abstract

Reiss's zeroth-order term is obtained directly from the ordinary perturbation theory in terms of the interaction Hamiltonian ${H}^{\ensuremath{'}}=\ensuremath{-}(\frac{e}{\mathrm{mc}})\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}+\frac{{e}^{2}{A}^{2}}{2m{c}^{2}}$.

DOI
10.1103/physreva.8.2727

Related papers

Multiphoton Ionization of Hydrogen Atoms in the Semiclassical Treatment of an Intense Radiation Field

Surya P. Tewari

The transition probability for the multiphoton ionization of the ground-state hydrogen atom by an intense electromagnetic field has been calculated following a nonperturbative method developed by Reiss. One distinctive feature of the calculation is a minor reduction in the power-law dependence of the interaction parameter in the transition probability.

Physical Review A•Nov 1, 1972•3 citations

Reiss Approximation at Moderate Intensities

S. N. Haque

In this paper we show that for an intensity parameter much less than unity, the Reiss approximation for the multiphoton ionization of atoms is equivalent to the neglect of the mean-frequency term in the treatment of Bebb and Gold. We have also improved upon the result of Reiss by including a first-order term. As an example of the above result, numerical values for many-photon $1s\ensuremath{\rightarrow}2s$ transitions in hydrogen atoms are presented and are compared with the exact values of Gontier and Trahin.

Physical Review A•Aug 1, 1973•1 citation

APPLICATION OF PERTURBATION THEORY FOR DESCRIBING MULTIPHOTON PROCESSES IN THE IONIZATION OF ATOMS.

G. A. Delone, Nikolai B. Delone, Nikolai L. Manakov +1 more

•Jan 1, 1971•0 citations

On the inadequacy of the momentum-translation approximation: multiphoton ionization of atomic hydrogen

A. Rachman, G Laplanche

The cross section for multiphoton ionization of hydrogen is computed using the momentum translation method (MTA) in the cases of linearly and circularly polarized light, alternatively. Extended numerical comparison is made with well-established results obtained from the Nth-order time-dependent perturbation theory in the weak intensity limit. The MTA does not reproduce the values given by perturbation theory and considerable differences are observed. Higher order iterations than the lower one are introduced and an analysis of the leading terms of the development is made: at weak intensities the zeroth-order term that defines the MTA cancels with higher order terms and the final result obtained after making (N-1 iterations is none other than the well-known transition amplitude deduced from standard perturbation theory, defined by the remaining terms of the last iteration after mutual cancellation with lower-order ones. According to the results obtained in this work, it is not possible to affirm that the MTA is adequate to calculate atomic multiphoton ionization cross sections.

Journal of Physics B Atomic and Molecular Physics•Apr 21, 1975•2 citations

PERTURBATION THEORY OF MULTIPHOTON IONIZATION OF ATOMS.

B. A. Zon, Nikolai L. Manakov, Л. П. Рапопорт

Journal of Experimental and Theoretical Physics•Jan 1, 1971•3 citations

Interaction of a three-level atom Lambda, V, lader with a two-mode field beyond rotating wave approximation: Intermixed intensity-dependent coupling

N. Asili Firouzabadi, Mohammad Kazem Tavassoly

Recalling that the rotating wave approximation (RWA) is only valid in the weak coupling regimes, the purpose of this paper is to study the Hamiltonian dynamics describing the full quantum mechanical approach of the interaction between various configurations of three-level atoms Lambda, V and ladder distinctly with a two-mode radiation field, while the RWA is not considered; the counter-rotating terms (CRTs) are taken into account. Generally, the presence of CRTs in the Hamiltonian prevents one to achieve an analytical solution. Moreover, as we will show in the present work, using the perturbation theory, analytical solvable Hamiltonians can be successfully obtained. According to our calculations, the contribution of CRTs within the ordinary Hamiltonian is equivalent to the replacement of the constant detuning with a specific intensity dependent detuning in the first order, and the constant atom field coupling with a particular intensity dependent (f deformed) coupling in the second order of the associated perturbation parameter. Moreover, noticing that according to the initial expression of the Hamiltonian, each mode of the field interacts only with a specific pair of the allowed transitions of each type of the three-level atom, it is surprisingly observed that via applying the mentioned approach, the obtained intensity dependent coupling functions depend on both modes of the field, f(na,nb). In this way, it is seen that the CRTs are removed with the price of arriving at some intermixed intensity dependent atom field coupling functions of the two modes of the field. In this way, the obtained final Hamiltonians are analytically solvable. At last, by determining the time evolution of the atom field wave function, we study the effects of CRTs on a few nonclassical properties of the state of the system, including the atomic population inversion and photon statistics.

arXiv:2108.06372•Aug 13, 2021•0 citations
Reiss's zeroth-order term is obtained directly from the ordinary perturbation theory in terms of the interaction Hamiltonian H\ensuremath′=\ensuremath−(emc)A\ensuremath→\ifmmode⋅\else\textperiodcentered\fip\ensuremath→+e2A22mc2{H}^{\ensuremath{'}}=\ensuremath{-}(\frac{e}{\mathrm{mc}})\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}+\frac{{e}^{2}{A}^{2}}{2m{c}^{2}}H\ensuremath′=\ensuremath−(mce​)A\ensuremath→​\ifmmode⋅\else\textperiodcentered\fip\ensuremath→​+2mc2e2A2​.
In this paper we show that for an intensity parameter much less than unity, the Reiss approximation for the multiphoton ionization of atoms is equivalent to the neglect of the mean-frequency term in the treatment of Bebb and Gold. We have also improved upon the result of Reiss by including a first-order term. As an example of the above result, numerical values for many-photon $1s\ensuremath{\rightarrow}2s$ transitions in hydrogen atoms are presented and are compared with the exact values of Gontier and Trahin.
The cross section for multiphoton ionization of hydrogen is computed using the momentum translation method (MTA) in the cases of linearly and circularly polarized light, alternatively. Extended numerical comparison is made with well-established results obtained from the Nth-order time-dependent perturbation theory in the weak intensity limit. The MTA does not reproduce the values given by perturbation theory and considerable differences are observed. Higher order iterations than the lower one are introduced and an analysis of the leading terms of the development is made: at weak intensities the zeroth-order term that defines the MTA cancels with higher order terms and the final result obtained after making (N-1 iterations is none other than the well-known transition amplitude deduced from standard perturbation theory, defined by the remaining terms of the last iteration after mutual cancellation with lower-order ones. According to the results obtained in this work, it is not possible to affirm that the MTA is adequate to calculate atomic multiphoton ionization cross sections.
Recalling that the rotating wave approximation (RWA) is only valid in the weak coupling regimes, the purpose of this paper is to study the Hamiltonian dynamics describing the full quantum mechanical approach of the interaction between various configurations of three-level atoms Lambda, V and ladder distinctly with a two-mode radiation field, while the RWA is not considered; the counter-rotating terms (CRTs) are taken into account. Generally, the presence of CRTs in the Hamiltonian prevents one to achieve an analytical solution. Moreover, as we will show in the present work, using the perturbation theory, analytical solvable Hamiltonians can be successfully obtained. According to our calculations, the contribution of CRTs within the ordinary Hamiltonian is equivalent to the replacement of the constant detuning with a specific intensity dependent detuning in the first order, and the constant atom field coupling with a particular intensity dependent (f deformed) coupling in the second order of the associated perturbation parameter. Moreover, noticing that according to the initial expression of the Hamiltonian, each mode of the field interacts only with a specific pair of the allowed transitions of each type of the three-level atom, it is surprisingly observed that via applying the mentioned approach, the obtained intensity dependent coupling functions depend on both modes of the field, f(na,nb). In this way, it is seen that the CRTs are removed with the price of arriving at some intermixed intensity dependent atom field coupling functions of the two modes of the field. In this way, the obtained final Hamiltonians are analytically solvable. At last, by determining the time evolution of the atom field wave function, we study the effects of CRTs on a few nonclassical properties of the state of the system, including the atomic population inversion and photon statistics.