Multiple pulse coherent dynamics and wave packet control of the N₂ a'' ¹Σ dark state by attosecond four-wave mixing

Nonlinear multidimensional spectroscopy is ubiquitous in the optical and radio frequency regions as a powerful tool to access structure and dynamics. The extension of this technique into the extreme ultraviolet (XUV) region with attosecond pulses holds promise for probing electronic dynamics and correlations with unprecedented time and spatial resolution. In this work, we use noncollinear four-wave mixing of a weak XUV attosecond pulse train (11-17 eV) and few-femtosecond NIR pulses (800 nm) to spectroscopically and dynamically probe the dipole-forbidden double-well potential of the a'' 1∑+g electronic state of nitrogen. The results demonstrate optical coupling of the inner and outer limits of the initial XUV-prepared vibrational wave packet in the valence character b' 1∑+u state to the inner and outer wells, respectively, of the a'' 1∑+g double well state by 800 nm light. Two four-wave mixing schemes with different pulse timing sequences and noncollinear beam geometries are used (one NIR pulse collinear and one NIR pulse noncollinear versus both NIR pulses noncollinear to the XUV beam) to measure the a'' dark state energetic structure and to control the dynamical preparation and motion of a dark state wave packet by selective population of either the inner Rydberg or outer valence-character potential well. Experimental measurements of the a'' 1∑+g outer well vibrational spacing and anharmonicity closely match the values theoretically predicted for this previously unobserved state.