Competition of resonant and nonresonant paths in resonance-enhanced two-photon single ionization of He by an ultrashort extreme-ultraviolet pulse

We theoretically study the pulse-width dependence of the photoelectron angular distribution (PAD) from the resonance-enhanced two-photon single ionization of He by femtosecond ($\lesssim 20$ fs) extreme-ultraviolet pulses, based on the time-dependent perturbation theory and simulations with the full time-dependent Schr\"odinger equation. In particular, we focus on the competition between resonant and nonresonant ionization paths, which leads to the relative phase $\delta$ between the $S$ and $D$ wave packets distinct from the corresponding scattering phase shift difference. When the spectrally broadened pulse is resonant with an excited level, the competition varies with pulse width, and, therefore, $\delta$ and the PAD also change with it. On the other hand, when the Rydberg manifold is excited, $\delta$ and the PAD do not much vary with the pulse width, except for the very short pulse regime.