Multichannel photoelectron phase lag across atomic barium autoionizing resonances

TL;DR

This work presents an ab initio multichannel quantum defect theory (MQDT) combined with an $R$-matrix approach to model the ω-2ω ionization of atomic Ba, capturing the phase lag between competing ionization pathways into two continua. By treating all relevant two-electron configurations within a defined reaction zone, the study achieves quantitative agreement with experimental phase-lag measurements across the $6s_{1/2}$ and $5d_{3/2}$ channels and reveals resonances associated with the $5d_{3/2}$ and $5d_{5/2}$ thresholds. The analysis shows that the phase lag is dominated by specific resonant partial waves (notably $J_f=1$ in the two-photon channel) and that hyperfine depolarization introduces parity-mixing pathways that affect the observed photoelectron angular distributions. These insights highlight the necessity of full multichannel electron-correlation treatments for accurate coherent-control descriptions and identify resonances that refine the Ba photoabsorption spectrum interpretation.

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 experimental measurements of phase lag from the $ω-2ω$ ionization of atomic barium \cite{PhysRevLett.98.053001,PhysRevA.76.053401}, suggesting that a toy model with phenomenological parameters is inadequate to describe the observed phase lag behavior. Here the phase lag is treated quantitatively from a multichannel coupling formulation, and our calculations based on 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, and further, identifies resonances between $Ba^{+}$ $5d_{3/2}$ and $5d_{5/2}$ thresholds that have apparently never been experimentally observed and classified.

Figures (4)

• Figure 1: Energy level diagram for the barium $\omega-2\omega$ interference scheme. Start with a ground state barium $i$, and first use a linearly-polarized pump laser ($\omega_p$) to excite the atom to the $e_1=6s6p$$(^1P_1)$ state. Next, by the concurrent one- and two-photon ionization of that initially excited state (with fundamental frequency $\omega$), the atom reaches the shaded energy region, which can decay into either the continua associated with the $6s_{1/2}$ or the $5d_{3/2}$ ionic state. The relevant threshold energy levels in atomic unit are $E_{6s_{1/2}}=-0.3676$$a.u.$, $E_{5d_{3/2}}=-0.3454$$a.u.$ and $E_{5d_{5/2}}=-0.3418$$a.u.$ (the double ionization threshold is $0$$a.u.$), and their values in $cm^{-1}$ are given in the figure.
• Figure 2: The photoelectron angular distribution parameters $\beta_k^{(a,b)}$ for one- and two-photon ionization process. Without interference effect, the odd-order parameters $\beta_{k_o}=0$. Our calculations (solid curves) are compared to the experimental results (points) from Ref. PhysRevA.76.053401 Fig. 6 and 7. The upper and lower panels are the $\beta$ parameters for two- and one-photon ionizations respectively, and the left and right panels are for channels $(a)$ and $(b)$.
• Figure 3: The angular momenta $J$ and parity $\pi$ allowed by the electron-dipole selection rule (For the single photon $q=1$ pathway, replace $J_{e_2}$ by $J_f$). When the pump and ionization photons are both polarized along z-axis, the red paths are allowed only when the effect from hyperfine depolarization is included in the initially excited $e_1$ state.
• Figure :