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Physical Review Letters

Line Broadening in Multiphoton Processes with a Resonant Intermediate Transition

Charles C. Wang, John V. James, Jing-fang Xia

Published Jul 18, 1983• 9 citations
Publisher

Abstract

The linewidth of the excitation spectrum for multiphoton ionization is found to be broadened much more severely than the cascade fluorescence originating from the resonant intermediate level. These results are due to the mutual effects of the ionizing and resonating transitions, which are not properly accounted for in perturbative treatments.

DOI
10.1103/physrevlett.51.184

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The linewidth of the excitation spectrum for multiphoton ionization is found to be broadened much more severely than the cascade fluorescence originating from the resonant intermediate level. These results are due to the mutual effects of the ionizing and resonating transitions, which are not properly accounted for in perturbative treatments.
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.
Even in the frame of first-order perturbation theory a molecule can be excited by off-resonance photons if it is subjected to a line-broadening mechanism. The case of collision-broadening is considered here. When a beam of coherent monochromatic off-resonance photons is passed through a gas, the competing processes of excitation and de-excitation lead to an equilibrium concentration of excited molecules, which is proportional to the beam intensity. This concentration is computed through the successive use of a classical and of a semi-quantum-mechanical treatment. Ionization is considered as a special case of excitation. The probability of ionization deduced from this theory in the case of medium pressures, is larger than that of multiphoton ionization.
Within the framework of a three-level model, the process of three-photon ionization with one-photon resonance between two excited levels (with the lower one being initially unpopulated) is considered using the density matrix method. It is shown that such resonance can result in the appearance of a maximum in the three-photon ionization spectrum when detuning between the resonance wavenumber and the wavenumber of the transition responsible for the lower excited level being populated exceeds the laser radiation linewidth by more than three orders of magnitude.
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.