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Journal de Physique Lettres

Doubly resonant multiphoton ionization

Michele Crance

Published Jan 1, 1978• 2 citations
Publisher

Abstract

We investigate theoretically a particular case of doubly resonant multiphoton ionization. More precisely, we consider two levels quasi-resonant with two successive harmonics of the field frequency. The method used is based on the effective operator formalism first introduced for this problem by Armstrong, Beers and Feneuille. The main result is to show the possibility of observing large interference effects on the width of the resonances. Moreover this treatment allows us to make more precise the connection between effective operator formalism and standard perturbation theory.

DOI
10.1051/jphyslet:0197800390606700

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We investigate theoretically a particular case of doubly resonant multiphoton ionization. More precisely, we consider two levels quasi-resonant with two successive harmonics of the field frequency. The method used is based on the effective operator formalism first introduced for this problem by Armstrong, Beers and Feneuille. The main result is to show the possibility of observing large interference effects on the width of the resonances. Moreover this treatment allows us to make more precise the connection between effective operator formalism and standard perturbation theory.
I present a perturbation theory of multiphoton ionization based on the resolvent operator. The theory is applied to a detailed study of two-photon ionization under near-resonance conditions. It is shown that a distinction must be made between linear level shifts and widths, and resonance shifts and widths which appear in the transition probability. The resonance shifts and widths exhibit saturation effects and their values tend to be much smaller than those of the linear level shifts and widths. Using numerical examples corresponding to tunable dye lasers and alkali-metal atoms, we show that the above shifts can have a dramatic effect on the ionization rate even when the laser is not in exact resonance with the intermediate level. The question of "one-step" vs "two-step" two-photon ionization is also discussed. It is shown that exact resonance does not necessarily imply a two-step process. In fact, in most cases it is quite the opposite. A quantitative criterion for this distinction is established. Finally, a distinction is made between instrumental saturation and saturation of the transition probability. The two are shown to be of different nature. Further extensions of the work are also discussed.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.