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arXiv:2301.02802 · Physical Review A

Coherent-control phase lag across doubly excited atomic strontium resonances in an ω−2ω interference scheme

Yimeng Wang, Chris H. Greene

Published Mar 7, 2023• 1 citation
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Abstract

Accurate calculations of phase lag associated with coherent control where an excited system decays into more than one product channel have recently been reported for atomic barium in Wang and Greene [Y. Wang and C. H. Greene, Phys. Rev. A 105, 013113 (2022)]. The present study extends the calculations to make predictions of that observable for another alkaline-earth-metal atom, strontium, with a discussion of its spectrum and phase lag for energies between the ${\mathrm{Sr}}^{+}\phantom{\rule{4pt}{0ex}}4{d}_{3/2}$ and $4{d}_{5/2}$ thresholds. We explore the physics influenced by the electron correlations of strontium and the long-range Coulomb potential. The behavior of the phase lag cannot be simply addressed by a time-delay analysis, although the latter is often used to address the prominent channel of resonance decay of doubly excited states.

DOI
10.1103/physreva.107.032804

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Accurate calculations of phase lag associated with coherent control where an excited system decays into more than one product channel have recently been reported for atomic barium in Wang and Greene [Y. Wang and C. H. Greene, Phys. Rev. A 105, 013113 (2022)]. The present study extends the calculations to make predictions of that observable for another alkaline-earth-metal atom, strontium, with a discussion of its spectrum and phase lag for energies between the Sr+4d3/2{\mathrm{Sr}}^{+}\phantom{\rule{4pt}{0ex}}4{d}_{3/2}Sr+4d3/2​ and 4d5/24{d}_{5/2}4d5/2​ thresholds. We explore the physics influenced by the electron correlations of strontium and the long-range Coulomb potential. The behavior of the phase lag cannot be simply addressed by a time-delay analysis, although the latter is often used to address the prominent channel of resonance decay of doubly excited states.
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.
We present the results of our study on coherent control of photoionization of atomic barium. Our study focused on the understanding of the controllability, especially due to the effect of the coherent interaction between the atomic system and the laser field. The first half of the study investigates the mechanisms of the control behind the previously observed laser phase-insensitive product state control. The controllability of this excitation scheme, two-color two-photon resonantly enhanced excitation, was analyzed from two aspects, the role of ac Stark shift introduced by the strong laser field and the multi-pathway quantum mechanical interferences. We have analyzed the excitation scheme from the analysis of the photoelectron angular distribution measured using the excitation scheme and the monitoring of the intermediate state population. Analysis of the data as well as the numerical simulation showed clear understanding of the role of two mechanisms in the product state control reported. We also investigated the control of the phase lag during the product state control. We conducted the control of the phase lag in the study of asymmetric photoelectron angular distribution, which arises from the concurrent even-odd parity outgoing electron wave excitation. The phase lag was controlled in full range, 2π, and the results were analyzed in terms of the role of autoionizing resonance structures as well as the nature of outgoing electron waves at different locations of the autoionizing resonances.
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.
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.
Coherent short-pulse laser excitation has been used to control the approximate energy and relative proximity of two valence electrons within the same alkaline-earth atom, thereby providing insight into the dynamical evolution of a three-body Coulomb system. Our time-domain experiments enable direct experimental study of the electron dynamics at the classical limit of a two-electron atom. As an example, we look at the mechanism of autoionization for one two-electron configuration class and find that the doubly excited atom decays through a single violent electron-electron collision rather than a gradual exchange of energy between the electrons.
Rydberg blockade at $n\ensuremath{\sim}300$, is examined using strontium n1F3n\phantom{\rule{0.16em}{0ex}}^{1}F_{3}n1F3​ Rydberg atoms excited in an atomic beam in a small volume defined by two tightly focused crossed laser beams. The observation of blockade for such states is challenging due to their extreme sensitivity to stray fields and the many magnetic sublevels associated with FFF states which results in a high local density of states. Nonetheless, with a careful choice of laser polarization to selectively excite only a limited number of these sublevels, sizable blockade effects are observed on an $\ensuremath{\sim}0.1$ mm length scale extending blockade measurements into the near-macroscopic regime and enabling study of the dynamics of strongly coupled many-body high-nnn Rydberg systems under carefully controlled conditions.