Interference effects in one- and two-photon ionization by femtosecond VUV pulses

Investigations of coherent control of atomic and molecular processes have rapidly developed since the advent of coherent light sources such as X-ray free electron lasers (XFELs) and achievements in high harmonic generation. In practice, radiation from XFELs contains a small fraction of the second harmonic, which is difficult to filter out but can strongly influence experimental data on the two-photon ionization process, such as the angular distribution. Specifically, the direct first-order second-harmonic ionization process may interfere with, and possibly even dominate a second-order two-photon process caused by the fundamental. While this interference has been investigated in the optical regime with many-cycle pulses, possible effects due to short pulses, as well as a physical intermediate resonance state that may serve as a stepping stone for the second-order process, need a careful study for particular experimental conditions. Here we consider the photo\-ionization of atomic hydrogen for photon energies near the excitation energy of the 2p state (0.375~a.u.\ or 121.6 nm). We compare results obtained from a direct numerical solution of the time-dependent Schr\"odinger equation and second-order perturbation theory.