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The Journal of Chemical Physics

Rotational effects in the study of the phase lag in the coherent control of HI

Hélène Lefebvre-Brion

Published Sep 8, 2002• 1 citation
Publisher

Abstract

A method which introduces the rotation in the calculation of both the dissociation and the autoionization cross sections by the unified multichannel quantum theory is developed. This is applied to the study of the ionization and dissociation phases observed in the coherent control of the 5sσ resonance of HI and DI. It is shown that the absolute value of the dissociation phase is maximum in the vicinity of this resonance.

DOI
10.1063/1.1497631

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A method which introduces the rotation in the calculation of both the dissociation and the autoionization cross sections by the unified multichannel quantum theory is developed. This is applied to the study of the ionization and dissociation phases observed in the coherent control of the 5sσ resonance of HI and DI. It is shown that the absolute value of the dissociation phase is maximum in the vicinity of this resonance.
The phase lag between the ionization and dissociation products of HI and DI molecules obtained by one- and three-photon excitation was measured as a function of excitation energy in the vicinity of a molecular resonance. The phase lag was observed to have an asymmetric profile with a deep minimum near the center of the resonance. A strong isotope effect was also observed. A theoretical analysis, using projection operators to partition the Lippmann-Schwinger equation, showed that a molecular phase is responsible for the energy dependence of the phase lag.
The phase lag associated with coherent control by two-pathway excitation in the presence of autoionizing and/or predissociating resonances is studied experimentally and theoretically. For a mixture of HI and DI, the phase lag $\ensuremath{\Delta}\ensuremath{\delta}$ between the two-parent ion signals vanishes to within experimental accuracy, whereas for an HI/H2S\mathrm{HI}/{\mathrm{H}}_{2}\mathrm{S}HI/H2​S mixture, $|\ensuremath{\Delta}\ensuremath{\delta}|$ reaches a maximum in the vicinity of the HI $5s\ensuremath{\sigma}$ resonance. These and previous observations are all explained within a single theoretical model which clarifies the origins of the phase lag in different atomic and molecular systems.
Phase lag associated with coherent control where an excited system decays into more than one product channel has been subjected to numerous investigations. Although previous theoretical studies have treated the phase lag across resonances in model calculations, quantitative agreement has never been achieved between the theoretical model and an experimental measurement of the phase lag from the $\ensuremath{\omega}\ensuremath{-}2\ensuremath{\omega}$ ionization of atomic barium. Yamazaki and Elliot, Phys. Rev. Lett. 98, 053001 (2007); Phys. Rev. A 76, 053401 (2007), suggesting that a toy model with phenomenological parameters is inadequate to describe the observed phase lag behavior. Here the phase lag is treated quantitatively in a multichannel coupling formulation, and our calculation based on a multichannel quantum defect and RRR-matrix treatment achieves good agreement with the experimental observations. Our treatment also develops formulas to describe the effects of hyperfine depolarization on multiphoton ionization processes. Moreover, we identify resonances between Ba+5d3/2{\text{Ba}}^{+}\phantom{\rule{4pt}{0ex}}5{d}_{3/2}Ba+5d3/2​ and 5d5/25{d}_{5/2}5d5/2​ thresholds that have apparently never been experimentally observed and classified.
An ab initio investigation of the excitation of an H(2) resonance, coupled to ionization and dissociation continua, was performed. The excitation occurs via a one- and a three-photon path where both fields have a variable but well-defined phase relation. While both continuum yields show an oscillatory behavior as the phase is varied, a pronounced phase lag between the two oscillations is observed, if the excitation energy is detuned from the resonant transition. The results are discussed in connection to a recent series of experiments performed on HI and the subsequent discussion on the possible origin of the observed phase lag.
Active control of the distribution of products of a chemical reaction was demonstrated by using a method based on the principle of quantum mechanical interference. Hydrogen iodide (HI) molecules were simultaneously excited above their ionization threshold by two competing pathways. These paths were absorption of three ultraviolet photons of frequency ω 1 and one vacuum ultraviolet photon of frequency ω 3 = 3ω 1 . The HI + and I + signals were modulated as the phase between the lasers was varied, with the HI + signal lagging by 150° ± 15°. A mechanism consisting of autoionization and predissociation is proposed.
Molecular phases are computed near the resonances in the (ω1,ω3) coherent control scheme for excitations to predissociating final states. We show that the phase factors for the one- and three-photon transition amplitudes are identical, giving a vanishing molecular phase, when the intermediate manifolds consist only of discrete states and when the final continuum states do not interact. The phase lag between the dissociation products identically vanishes across the resonance in this case. On the other hand, when there is contribution of the intermediate continuum states, the imaginary part of the three-photon transition operator can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of the molecular phase in (ω1,ω3) coherent control. It is also shown that couplings between the final continuum states can give different molecular phase for different product channels in the absence of the effects of the intermediate continuum states, exhibiting the phase lag of the products near resonances. We demonstrate that the phase lag may show minimum near the top of the resonance, as was observed in Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on the phase lag in HI coherent control experiments, indicating that the observed phase lag is due to the effects of the molecular phase.