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 1snp4pt0ex¹P₁ ($n=3,4,5$) 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 Schr\"odinger equation in the single-active-electron approximation, elucidating the origin and dependences of the observed phenomena.