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Physical Review A

Double resonance via continuum states: Ionization quantum beats

Munir Hasan Nayfeh, Wallace L. Glab

Published Mar 1, 1982• 5 citations
Publisher

Abstract

The two-photon process with continuum intermediate states is investigated. The line shape is found to be a singlet rather than a doublet as in the case of discrete intermediates (Autler-Townes doublet). The ionization line shape is a doublet and exhibits oscillations as a result of the coherence and the interference between the yields from the initial and final states.

DOI
10.1103/physreva.25.1619

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The two-photon process with continuum intermediate states is investigated. The line shape is found to be a singlet rather than a doublet as in the case of discrete intermediates (Autler-Townes doublet). The ionization line shape is a doublet and exhibits oscillations as a result of the coherence and the interference between the yields from the initial and final states.
Abstract We study the three-photon ionization of atomic lithium by intense, short light pulses, via numerically solving the time-dependent Schrödinger equation. Two-photon Rabi oscillations are induced between the 2s and 4s states, which are damped due to single-photon ionization to the p continuum. Developing a minimal three-level model, we analyze the spectral features of the Autler–Townes (AT) doublet that is formed upon the resonant coupling with the laser pulse. Furthermore, we show that this 2 s →→ 4 s → p c o n t i n u u m pathway is the dominant process, if the duration of the laser pulse exceeds a certain value. For shorter pulses, ionization through the 2p state ( 2 s → 2 p → 4 d → f c o n t i n u u m ) gradually becomes the dominant process, provided that the pulse is strong enough to induce several Rabi floppings. Here, we trace the competition of these ionization pathways by observing the structural changes in the shape of the AT doublet.
The author presents a theory for NNN-photon ionization in which two intermediate states can be in resonance with the ground state over a narrow range of photon frequencies. The theory is applied to the three-photon 6F6F6F resonance-state spin-orbit doublet in the four-photon ionization of Cs. The amplitude for the process is the sum of two components, each containing a complex line-shape function. In the limit of zero splitting, the previously studied isolated resonance result, in which the line shape is Lorentzian is recovered. For the splitting in Cs (6F6F6F), the absorption profile is studied as a function of the splitting parameters of the state, the $6S\ensuremath{\rightarrow}6F$ three-photon Rabi rate, and the field-induced shift and width for the $6S\ensuremath{\rightarrow}6F$ transition. This profile depends in a complicated way on the relative magnitudes of the shift and the spacing between the fine-structure levels.
Resonant photoionization in the intense high-frequency regime can exhibit extremely asymmetric Autler-Townes doublets whose origin remains debated. It has been attributed either to interference between perturbative ionization pathways or to a nonperturbative dressing of the continuum. Here, we show that these interpretations arise from a common effective Hamiltonian framework, in which dressed-state stabilization is governed by the coherent interplay of resonant and nonresonant pathways. We demonstrate that further simplification, using the strong-field approximation, obscures this mechanism. In contrast, our time-dependent essential-state model, where electrons are rigorously coupled to the continuum, achieves excellent agreement with simulations of the time-dependent Schrödinger equation for helium.
Photoelectron energy spectra resulting from two-photon ionization of calcium atoms by 180 fs pulses have been studied as a function of wavelength (380--405 nm) and intensity ( $9\ensuremath{-}900\phantom{\rule{0ex}{0ex}}\mathrm{GW}/{\mathrm{cm}}^{2}$). When the wavelength is tuned near the $4s\ensuremath{\rightarrow}4p$ or $4s\ensuremath{\rightarrow}5s$ ionic core transition, the photoelectron peaks display a characteristic splitting proportional to the field strength and assignable to a two-electron continuum-continuum Autler-Townes effect. Spectra obtained by an essential-state model involving three coupled continua are compared to the experiment.
We know that the Fano profile is obtained for single-photon absorption to the ionization continuum in the presence of an autoionizing state. We have shown that, in the case of (1+1)-photon absorption to an autoionizing state embedded in the ionization continuum, the absorption profile changes radically to a mirror image of the Fano profile for the value of q=\ifmmode\pm\else\textpm\fi{}1, q being the Fano q parameter. Moreover, for higher values of q, the (1+1)-photon absorption profile exhibits a broad minimum, while a distinct interference pattern is obtained in the profile of single-photon absorption. The absorption line shape has been found to oscillate between the Fano and a modified Fano profile for the autoionization through odd and even number of steps, respectively, via resonances.