Multichannel photoelectron phase lag across atomic barium autoionizing resonances

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 $\omega-2\omega$ 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.