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 across resonances in model calculations, quantitative agreement never achieved between and experimental measurements of from $\omega-2\omega$ ionization atomic barium \cite{PhysRevLett.98.053001,PhysRevA.76.053401}, suggesting that a toy phenomenological parameters is inadequate describe observed behavior. Here quantitatively multichannel coupling formulation, our calculations based on quantum defect $R$-matrix treatment achieves good observations. Our also develops formulas effects hyperfine depolarization multiphoton processes, further, identifies $Ba^{+}$ $5d_{3/2}$ $5d_{5/2}$ thresholds apparently experimentally classified.