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Physical Review A

Higher-order effects in multiphoton transitions

Bhaskar J. Choudhury

Published Dec 1, 1974• 0 citations
Publisher

Abstract

I have obtained a general analytic result for calculating any higher-order correction to the transition amplitude for $N$-photon absorption by writing the time-dependent perturbation theory in the $S$-matrix form. In obtaining this result, I have made use of the concept of average energy as has been defined by Bebb and Gold. A formal expression has been obtained for the upper bound of the higher-order correction and the results are discussed for the case of the hydrogen atom.

DOI
10.1103/physreva.10.2070

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I have obtained a general analytic result for calculating any higher-order correction to the transition amplitude for NNN-photon absorption by writing the time-dependent perturbation theory in the SSS-matrix form. In obtaining this result, I have made use of the concept of average energy as has been defined by Bebb and Gold. A formal expression has been obtained for the upper bound of the higher-order correction and the results are discussed for the case of the hydrogen atom.
The multiphoton transitions in the hydrogen atom are investigated by taking into account the higher-order terms arising from the SSS-operator expansion. These higher-order effects originate induced shifts and induced breadths on the virtual-atomic-energy levels. It is shown that these perturbations play an important role for resonant multiphoton processes. In this case, the theory predicts a particular flux dependence of the transition rates. Furthermore, the well-known dispersion curves are strongly modified in the neighborhood of any resonance. Thus the transition rates can exhibit several peaks. Numerical results are given for a three-photon bound-free transition from the 2S2S2S state of hydrogen.
The infinite summations over the complete set of unperturbed atomic states appearing in the NNNth-order perturbation theory for multiphoton ionization are performed using the Dalgarno-Lewis method. The relevant transition matrix elements are written in a closed integral form exhibiting all the analytic properties of the amplitude as a function of incident photon energy. The cross sections for two- and three-photon ionization for atomic hydrogen are calculated for both linearly and circularly polarized light with a wide range of photon energy spectrum including the near resonance, and numerical comparison is made with the values obtained by different methods.
Within the framework of time-dependent perturbation theory, general expressions are derived for the cross section of multiphoton processes induced by radiation acting on a hydrogen atom. Bound-bound transitions involving emission of a single quantum and bound-free transitions are calculated for a wide range of photon energies. In the case of resonance, the transition probability is also discussed. The procedure used to evaluate the sums over intermediate states is described. The numerical computation allows one to compare the results obtained for various competing processes.
A general analytical result has been obtained for the calculation of higher-order corrections to the momentum-translation approximation. Explicit analytical results are given for the calculation of higher-order corrections for bound-bound and bound-free transitions for hydrogenic atoms. Numerical results are given for 1S1S1S to 2S2S2S transitions in hydrogen.
The summation of all the higher-order contributions to multiphoton absorption in atoms is presented. The nonperturbative expressions for the transition amplitudes are expressed in terms of continued fractions. They account for the whole perturbation originated by the radiation field on the atom but do not exhibit explicit expression for the level shift. In the case of radiation fields of high intensity the only reliable determination of the level shift involves a careful location of the poles of the resolvent operator. The theory has been tested in considering a two-level atom. An extremely rapid convergence of the continued fractions has been observed, and accurate results concerning high-order resonance shifts have been obtained. The expressions for the transition amplitudes being nonperturbative with regard to the field strength, they can be considered as analytic continuations of the perturbation series. This provides a useful approach to the problem of ultraintense fields.