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Physical Review Letters

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

Rekishu Yamazaki, Daniel S. Elliott

Published Jan 29, 2007• 30 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.98.053001

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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 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 1P16s6p\text{ }{^{1}P}_{1}6s6p 1P1​ intermediate state electron to an energy between the 5d3∕2ϵ5{d}_{3∕2}ϵ5d3∕2​ϵ and the 5d5∕2ϵ5{d}_{5∕2}ϵ5d5∕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, 6s1∕2ϵ6{s}_{1∕2}ϵ6s1∕2​ϵ and 5d3∕2ϵ5{d}_{3∕2}ϵ5d3∕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 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 measure photoion spectra and angular distributions of photoelectrons from the two-color, two-photon resonant ionization of barium atoms in order to probe the effect of the photoionization pathway on autoionization processes. The (6s6p)1{)}^{1})1P${\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}_{1}$ and the (5d6p)1{)}^{1})1P${\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}_{1}$ states are used as intermediates in the photoexcitation of barium to energies in the range of a series of 5dnd autoionizing states. Dramatic differences in the profiles of autoionizing lines are observed for excitation pathways involving different intermediate states. Angular distributions of photoelectrons collected across the range of autoionizing resonances demonstrate strong variations that follow constraints imposed by the angular momentum of the autoionizing peaks and also suggest significant spin-orbit interactions in the photoionization step.
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 1P16s6p\text{ }{^{1}P}_{1}6s6p 1P1​ state of barium in the energy range between the 5d3/25{d}_{3/2}5d3/2​ and 5d5/25{d}_{5/2}5d5/2​ states of Ba+{\text{Ba}}^{+}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 RRR-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.
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.
The role of Rydberg autoionizing states in interfering one- and two-photon ionization paths is theoretically investigated in atomic Ar. The angularly resolved photoionization cross sections for each individual path is provided. By varying the relative optical phase between the two pulses the phase difference between the two interfering paths is extracted. The retrieved phase difference and the photoelectron angular distributions exhibit a strong dependence on the photon energy in the vicinity of the resonant states. In contrast to previous results obtained in atomic Ne, the phase difference features a smooth dependence with photoelectron emission angle.