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Journal of Physics B Atomic and Molecular Physics

Application of extended two-level model theory to Doppler-, laser- and collision-broadened bound-bound multiphoton absorption

Joseph H. Eberly

Published Oct 28, 1978• 10 citations
Publisher

Abstract

Recent observations allow the first quantitative tests of the ability of theories of multiphoton-resonant processes to deal with Doppler, laser and collisional broadening in bound-bound transitions. The predictions of a certain extended two-level (ETL) model of multiphoton-resonant phenomena are compared with these observations.
DOI
10.1088/0022-3700/11/20/003

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A theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.
The multiphoton absorption processes induced in model two-level systems through their interaction with intense laser and static electric fields are investigated. An analytical treatment of the degenerate system enables one to anticipate the effects of the static field on the multiphoton spectrum, including the influences of collisional damping. Using Floquet theory in the numerical treatment of a nondegenerate system confirms the enhancement of the multiphoton spectrum whose resonances will be more power broadened and will appear at higher frequencies than they would in the absence of the static field.
For pt.I see ibid., vol.8, p.1795 (1975) where the theory of Doppler-free two-photon transitions was discussed for the case of one single laser frequency. Here, the effects of two different frequencies are considered. When the residual Doppler width of the two-photon transition is less than the natural linewidth, the previous results are essentially regained. For large residual Doppler shifts, the absorption profile is a power-broadened Lorentzian if the frequency of the probe field is larger than the frequency of the strong field. In the opposite case, the absorption peak splits because of the AC Stark effect. The high-intensity distortions are minimized when equal frequencies can be used. Power-dependent shifts do not ordinarily occur with a resonantly tuned intermediate level. Some modifications of the spectra are introduced by phase-disturbing collisions.
The review describes atomic transitions where two or more photons are simultaneously absorbed by an atom or a molecule (without any intermediate resonant level). The authors show theoretically and experimentally the possibilities of these transitions for numerous high-resolution spectroscopic studies. The Doppler broadening is suppressed in two-photon transitions if the atoms are irradiated by two laser waves travelling in opposite directions, because the Doppler shift in one wave cancels that in the other. A generalization is made for multiphotonic transitions. A typical experimental set-up with a CW dye laser is described in detail, but the possibilities of other light sources are also discussed.
Results are reported on coherent monochromatic multiphoton excitation in many-level systems, which are representative for some of the basic mechanisms for atomic and molecular multiphoton processes. Numerical solutions are discussed that use the Floquet and quasi-resonant approximations in the framework of the URIMIR program package. The excitation schemes include direct three-photon excitation, two-photon excitation with diagonal coupling, Göppert-Mayer-type two-photon processes, multiphoton excitation with off-resonant inter-mediates, and practically irreversible coherent excitation into dense spectral structures. Several interesting phenomena are observed, such as nonlinear line shifts and broadenings of multi-photon resonances of relevance for multiphoton spectroscopy and almost constant intermediate population inversions, potentially useful for laser design. The accurate numerical results are compared with approximate solutions from perturbation theory, and with simple analytical solutions from Rabi-type formulae.
A model of multiple resonances between groups of discrete and autoionizing levels is proposed for the description of the process of multiphoton ionization. The phenomena of the extremely rapid broadening and growth of amplitudes of the multiphoton resonances, observed experimentally in the yield of Sr+ and Ba+ ions [ J. Phys. B.14, 2253– 2359 ( 1981);Elementary Processes in Laser Radiation Field ( 1988), pp. 122– 153)] are explained on the basis of this model. The strong-coupling method was used in numerical calculations for Sr and Ba atoms in a strong laser field.