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Journal of the Optical Society of America B

Nonperturbative treatments of nonresonant multiphoton ionization of the hydrogen atom: weak-field limit

Fabio Trombetta, G. Ferrante, S. Basile

Published Apr 1, 1989• 15 citations

Abstract

A nonperturbative treatment of the multiphoton ionization of the hydrogen atom based on the S matrix and devised for nonresonant strong-field situations is analyzed in the weak-field limit. Comparisons are presented with other S matrices as well as other nonperturbative approaches. Our treatment is found to perform generally better than similar S-matrix treatments. The usual perturbative results are recovered provided that the photon wavelengths are sufficiently short and are off resonance with the atomic transitions. Important indications are obtained as to the role of the atomic structure, the relevance of the gauge consistency, and the reliability and improvement of the present nonperturbative treatment. The results represent a significant step toward an assessment of the S-matrix-based treatments of multiphoton ionization.

DOI: 10.1364/josab.6.000554

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A nonperturbative treatment of the multiphoton ionization of the hydrogen atom based on the S matrix and devised for nonresonant strong-field situations is analyzed in the weak-field limit. Comparisons are presented with other S matrices as well as other nonperturbative approaches. Our treatment is found to perform generally better than similar S-matrix treatments. The usual perturbative results are recovered provided that the photon wavelengths are sufficiently short and are off resonance with the atomic transitions. Important indications are obtained as to the role of the atomic structure, the relevance of the gauge consistency, and the reliability and improvement of the present nonperturbative treatment. The results represent a significant step toward an assessment of the S-matrix-based treatments of multiphoton ionization.

The infinite summations over the complete set of unperturbed atomic states appearing in the

N

th-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.

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.

The general theory of multiphoton ionization of hydrogen atoms by simultaneous absorption of several photons is discussed. In the nonrelativistic dipole approximation, the calculations lead to a recursion relationship concerning angular functions and involve radial matrix elements containing many summations over intermediate states. A general method for exactly evaluating several sums is described in detail and applied to the photo-ionization of atomic hydrogen in the ground state. Numerical results are presented as dispersion curves of the transition rate $\frac{{\ensuremath{\sigma}}_{n}}{{I}^{N\ensuremath{-}1}}$ for a range of wavelengths from 1000 up to 7200 \AA{}.

Multiphoton ionization of hydrogen atoms by a strong multimode field when several final continuum states are populated is treated theoretically within a model based on the S-matrix formalism. The field is taken in dipole approximation, with zero bandwidth. Field-dressed Coulomb wave functions are used for the electron final states. Ionization rates are calculated for different numbers of photons absorbed in excess of the minimum number required to go into the continuum. In general, the calculated quantities are in good qualitative agreement with the corresponding experimental observations.

An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.