Phase dependence of resonant and antiresonant two-photon excitations

Measurements of the phase of two-photon matrix elements are presented for resonant and antiresonant two-color ionization of helium. A tunable, narrow-bandwidth, near-infrared (NIR) laser source is used for extreme ultraviolet (XUV) high-harmonic generation (HHG). The 15th harmonic of the laser is used within (1 + 1') XUV + NIR two-photon ionization and tuned in and out of resonance with members of the 1snp P-1(1) (n = 3, 4, 5) Rydberg series, covering a broad spectral range with high spectral resolution. The technique allows us to observe characteristic rapid changes in the phase of the two-photon matrix elements around the resonances and at the antiresonances between the resonances. Similar effects are observed for (1 +2') XUV + NIR three-photon ionization. The experimental results are compared to a perturbative model and to numerical solutions of the time-dependent Schrodinger equation in the single-active-electron approximation, elucidating the origin and dependences of the observed phenomena.