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The Journal of Chemical Physics

Study of the origin of the phase lag between signals in coherent laser control

Hélène Lefebvre-Brion

Published Feb 8, 1997• 25 citations
Publisher

Abstract

It is shown that the origin of the phase lag between signals corresponding to photoionization and photodissociation of Rydberg levels of HI observed in a recent coherent control experiment [Zhu et al., Science 270, 77 (1995)] is not the difference in the molecular phase of the two processes.
DOI
10.1063/1.473158

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The Journal of Chemical Physics•Mar 8, 1998•15 citations
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.
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.
Systematic analysis is carried out for molecular phase in (ω1,ω3) coherent control scheme. Two mechanisms for nonzero molecular phase are proposed. It is shown that the imaginary part of the three-photon transition operator, which is due to the contribution of the intermediate continuua, can give different phase factors for the one- and three-photon transition amplitudes, yielding very important effects of molecular phase in (ω1,ω3) coherent control. We also show that the interactions between the final continuum states can result in nonzero molecular phase, when the intermediate states are discrete. These findings are discussed in relation to Gordon and co-workers’ recent observations [Zhu et al., Science 270, 77 (1995)] on phase lag.
In coherent control experiments the product signal intensity is modulated by interference between two excitation paths. This modulation is produced by varying the relative phase of the electromagnetic fields used to excited the target. It is observed that the modulated signals for different channels may be out of phase with respect to each other. The phase lag between different channels is energy dependent and contains information about the dynamics of the system. This paper explores different mechanisms that produce such phase lags and assesses what may be learned from them.
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.
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.