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Physical Review A

Multiphoton Transition in Hydrogen between 1S and 2P Levels

N. K. Rahman, Howard R. Reiss

Published Sep 1, 1972• 7 citations
Publisher

Abstract

$1S\ensuremath{-}2P$ multiphoton transition amplitudes are calculated for hydrogen atoms in the presence of an intense electromagnetic field. Nonlinear behavior of the transition amplitudes appears as in the case of $1S\ensuremath{-}2S$ transitions considered earlier.

DOI
10.1103/physreva.6.1252

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Atomic Transitions in Intense Fields and the Breakdown of Perturbation Calculations

Howard R. Reiss

Results valid for arbitrarily high intensity of electromagnetic field are presented for induced emission from an excited state of an atom. Comparison with perturbation theory shows that perturbative calculations fail quantitatively and qualitatively at lower intensity than had been expected. Distinctive intense-field features are discussed such as vanishing of the transition probability for certain intensities and photon multiplicities, and appearance of two extrema of the transition amplitude for multiphoton processes at very high intensities.

Physical Review Letters•Oct 26, 1970•65 citations
1S\ensuremath−2P1S\ensuremath{-}2P1S\ensuremath−2P multiphoton transition amplitudes are calculated for hydrogen atoms in the presence of an intense electromagnetic field. Nonlinear behavior of the transition amplitudes appears as in the case of 1S\ensuremath−2S1S\ensuremath{-}2S1S\ensuremath−2S transitions considered earlier.
Transition amplitudes corresponding to bound-bound multiphoton transitions with the emission or absorption of one and two Raman photons in the hydrogen atom have been evaluated following a recent method of Reiss. Results show that the transition probability varies smoothly for low values of NNN, where NNN is the number of intense photons absorbed or emitted during the transition. For larger values of NNN the amplitude, however, has oscillatory behavior. A particular feature of the present method of calculation is that we find the "reduced" transition amplitude for induced emission of two Raman photons is enhanced compared with single-Raman-photon emission. Another distinctive feature is the appearance of many more extrema in the transition amplitude for higher transitions for multiphoton processes at high intensity.
Analyses of the resonant multiphoton ionization of atoms require knowledge of ac Stark energy shifts and of multiphoton, bound-to-bound state, transition amplitudes. In this paper, we consider the three-photon photoionization of hydrogen atoms at frequencies that are at and surrounding the two-photon 1s to 2s resonance. AC energy shift sums of both the 1s and 2s states are calculated as a function of the laser frequency along with two-photon 1s ? 2s resonant transition amplitude sums. These quantities are calculated using an extended version of a method, which has often been employed in a variety of ways, of calculating these sums by expressing them in terms of solutions to a variety of differential equations that are derived from the different sums being evaluated. We demonstrate how exact solutions are obtained to these differential equations, which lead to exact evaluations of the corresponding sums. A variety of different cases are analysed, some involving analytic continuation, some involving real number analysis and some involving complex number analysis. A dc Stark sum calculation of the 2s state is carried out to illustrate the case where analytic continuation, pole isolation and pole subtraction are required and where the calculation can be carried out analytically; the 2s state, ac Stark shift sum calculations involve a case where no analytic continuation is required, but where the solution to the differential equation produces complex numbers owing to the finite photoionization lifetime of the 2s state. Results from these calculations are then used to calculate three-photon ionization probabilities of relevance to an analysis of the multiphoton ionization data published by Kyrala and Nichols (1991 Phys. Rev. A 44, R1450).
Results valid for arbitrarily high intensity of electromagnetic field are presented for induced emission from an excited state of an atom. Comparison with perturbation theory shows that perturbative calculations fail quantitatively and qualitatively at lower intensity than had been expected. Distinctive intense-field features are discussed such as vanishing of the transition probability for certain intensities and photon multiplicities, and appearance of two extrema of the transition amplitude for multiphoton processes at very high intensities.