arXiv:2111.06547 · Physical Review A

Multichannel photoelectron phase lag across atomic barium autoionizing resonances

Yimeng Wang, Chris H. Greene

Published Jan 24, 2022• 4 citations

Abstract

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 $R$-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 ${\text{Ba}}^{+}\phantom{\rule{4pt}{0ex}}5{d}_{3/2}$ and $5{d}_{5/2}$ thresholds that have apparently never been experimentally observed and classified.

DOI: 10.1103/physreva.105.013113

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Strong variation of the phase lag in the vicinity of autoionizing resonances

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Observation of the Phase Lag in the Asymmetric Photoelectron Angular Distributions of Atomic Barium

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arXiv:2111.06547 · Physical Review A

Multichannel photoelectron phase lag across atomic barium autoionizing resonances

Yimeng Wang, Chris H. Greene

Published Jan 24, 2022• 4 citations

arXiv HTML PDF

Abstract

\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

R

-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

{\text{Ba}}^{+}\phantom{\rule{4pt}{0ex}}5{d}_{3/2}

and

5{d}_{5/2}

thresholds that have apparently never been experimentally observed and classified.

DOI: 10.1103/physreva.105.013113

Related papers

Strong variation of the phase lag in the vicinity of autoionizing resonances

Rekishu Yamazaki, Daniel S. Elliott

We have observed the phase lag in the sinusoidal variation of the asymmetric photoelectron angular distributions into two ionization channels of atomic barium using an $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ excitation scheme. We excite atomic barium from the $6s6p\text{ }{^{1}P}_{1}$ intermediate state electron to an energy between the $5{d}_{3∕2}ϵ$ and the $5{d}_{5∕2}ϵ$ thresholds with concurrent one-photon and two-photon interactions. The left-right asymmetry of the photoelectron angular distributions for the two energy-resolved product states, $6{s}_{1∕2}ϵ$ and $5{d}_{3∕2}ϵ$ , show sinusoidal modulation as a function of the relative phase of the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ fields. The phase difference between these signals, or phase lag, varies rapidly with the laser frequency when the interaction is nearly resonant with autoionizing resonances in the continuum. An exceptionally large phase lag variation of over $2\ensuremath{\pi}$ was measured.We have observed the phase lag in the sinusoidal variation of the asymmetric photoelectron angular distributions into two ionization channels of atomic barium using an $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ excitation scheme. We excite atomic barium from the $6s6p\text{ }{^{1}P}_{1}$ intermediate state electron to an energy between the $5{d}_{3∕2}ϵ$ and the $5{d}_{5∕2}ϵ$ thresholds with concurrent one-photon and two-photon interactions. The left-right asymmetry of the photoelectron angular distributions for the two energy-resolved product states, $6{s}_{1∕2}ϵ$ and $5{d}_{3∕2}ϵ$, show sinusoidal modulation as a function of the relative phase of the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ fields. The phase difference between these signals, or phase lag, varies rapidly with the laser frequency when the interaction is nearly resonant with autoionizing resonances in the continuum. An exceptionally large phase lag variation of over $2\ensuremath{\pi}$ was measured.

Physical Review ANov 5, 200714 citations

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

Yimeng Wang, Chris H. Greene

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.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.

arXiv:2301.02802Physical Review AMar 7, 20231 citation

Coherent control of photoionization of atomic barium

Rekishu Yamazaki

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.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.

Jan 1, 20060 citations

Observation of the Phase Lag in the Asymmetric Photoelectron Angular Distributions of Atomic Barium

Rekishu Yamazaki, Daniel S. Elliott

We have observed and measured the phase lag in the phase-dependent variation of the asymmetric photoelectron angular distribution of atomic barium. For these measurements, we photoionize the 6s6p(1)P(1) intermediate state of barium with concurrent one-photon and two-photon (omega-2omega) interactions. The laser interactions ionize the atoms in the vicinity of the series of autoionizing states converging upon the 5d(2)D(5/2) threshold. We study the variation of the phase lag as a function of the laser frequency. The variation shows strong correlation to the location of the autoionizing resonances, with full range exceeding 2pi, confirming the critical role of these resonances.We have observed and measured the phase lag in the phase-dependent variation of the asymmetric photoelectron angular distribution of atomic barium. For these measurements, we photoionize the 6s6p(1)P(1) intermediate state of barium with concurrent one-photon and two-photon (omega-2omega) interactions. The laser interactions ionize the atoms in the vicinity of the series of autoionizing states converging upon the 5d(2)D(5/2) threshold. We study the variation of the phase lag as a function of the laser frequency. The variation shows strong correlation to the location of the autoionizing resonances, with full range exceeding 2pi, confirming the critical role of these resonances.

Physical Review LettersJan 29, 200730 citations

One- and two-photon ionization cross sections of the laser-excited 6s6p P11 state of barium

John R. Tolsma, Daniel J. Haxton, Chris H. Greene +2 more

Stimulated by a recent measurement of coherent control in photoionization of atomic barium, we have calculated one- and two-photon ionization cross sections of the aligned $6s6p\text{ }{^{1}P}_{1}$ state of barium in the energy range between the $5{d}_{3/2}$ and $5{d}_{5/2}$ states of ${\text{Ba}}^{+}$ . We have also measured these photoionization spectra in the same energy region, driving the one- or two-photon processes with the second or first harmonic of a tunable dye laser, respectively. Our calculations employ the eigenchannel $R$ -matrix method and multichannel quantum defect theory to calculate the rich array of autoionizing resonances in this energy range. The nonresonant two-photon process is described using lowest-order perturbation theory for the photon-atom interactions, with a discretized intermediate-state one-electron continuum. The calculations provide an absolute normalization for the experiment, and they accurately reproduce the rich resonance structures in both the one- and two-photon cross sections, and confirm other aspects of the experimental observations. These results demonstrate the ability of these computationally inexpensive methods to reproduce experimental observables in one- and two-photon ionization of heavy alkaline earths, and they lay the groundwork for future studies of the phase-controlled interference between one- and two-photon ionization processes.Stimulated by a recent measurement of coherent control in photoionization of atomic barium, we have calculated one- and two-photon ionization cross sections of the aligned $6s6p\text{ }{^{1}P}_{1}$ state of barium in the energy range between the $5{d}_{3/2}$ and $5{d}_{5/2}$ states of ${\text{Ba}}^{+}$. We have also measured these photoionization spectra in the same energy region, driving the one- or two-photon processes with the second or first harmonic of a tunable dye laser, respectively. Our calculations employ the eigenchannel $R$-matrix method and multichannel quantum defect theory to calculate the rich array of autoionizing resonances in this energy range. The nonresonant two-photon process is described using lowest-order perturbation theory for the photon-atom interactions, with a discretized intermediate-state one-electron continuum. The calculations provide an absolute normalization for the experiment, and they accurately reproduce the rich resonance structures in both the one- and two-photon cross sections, and confirm other aspects of the experimental observations. These results demonstrate the ability of these computationally inexpensive methods to reproduce experimental observables in one- and two-photon ionization of heavy alkaline earths, and they lay the groundwork for future studies of the phase-controlled interference between one- and two-photon ionization processes.

arXiv:0906.1638Physical Review ASep 1, 20099 citations

Origin of the Phase Lag in the Coherent Control of Photoionization and Photodissociation

Jeanette A. Fiss, Langchi Zhu, Robert J. Gordon +1 more

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 $\mathrm{HI}/{\mathrm{H}}_{2}\mathrm{S}$ 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 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 $\mathrm{HI}/{\mathrm{H}}_{2}\mathrm{S}$ 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.

Physical Review LettersJan 4, 199941 citations

\ensuremath{\omega}\ensuremath{-}2\ensuremath{\omega}

R

{\text{Ba}}^{+}\phantom{\rule{4pt}{0ex}}5{d}_{3/2}

and

5{d}_{5/2}

thresholds that have apparently never been experimentally observed and classified.

6s6p\text{ }{^{1}P}_{1}

intermediate state electron to an energy between the

5{d}_{3∕2}ϵ

and the

5{d}_{5∕2}ϵ

thresholds with concurrent one-photon and two-photon interactions. The left-right asymmetry of the photoelectron angular distributions for the two energy-resolved product states,

6{s}_{1∕2}ϵ

and

5{d}_{3∕2}ϵ

, show sinusoidal modulation as a function of the relative phase of the $\ensuremath{\omega}\text{\ensuremath{-}}2\ensuremath{\omega}$ fields. The phase difference between these signals, or phase lag, varies rapidly with the laser frequency when the interaction is nearly resonant with autoionizing resonances in the continuum. An exceptionally large phase lag variation of over $2\ensuremath{\pi}$ was measured.

{\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.

Stimulated by a recent measurement of coherent control in photoionization of atomic barium, we have calculated one- and two-photon ionization cross sections of the aligned

6s6p\text{ }{^{1}P}_{1}

state of barium in the energy range between the

5{d}_{3/2}

and

5{d}_{5/2}

states of

{\text{Ba}}^{+}

. We have also measured these photoionization spectra in the same energy region, driving the one- or two-photon processes with the second or first harmonic of a tunable dye laser, respectively. Our calculations employ the eigenchannel

R

-matrix method and multichannel quantum defect theory to calculate the rich array of autoionizing resonances in this energy range. The nonresonant two-photon process is described using lowest-order perturbation theory for the photon-atom interactions, with a discretized intermediate-state one-electron continuum. The calculations provide an absolute normalization for the experiment, and they accurately reproduce the rich resonance structures in both the one- and two-photon cross sections, and confirm other aspects of the experimental observations. These results demonstrate the ability of these computationally inexpensive methods to reproduce experimental observables in one- and two-photon ionization of heavy alkaline earths, and they lay the groundwork for future studies of the phase-controlled interference between one- and two-photon ionization processes.

\mathrm{HI}/{\mathrm{H}}_{2}\mathrm{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.