  Phase-shift differences and amplitude ratios of the outgoing $s$ and $d$
continuum wave packets generated by two-photon ionization of helium atoms are
determined from the photoelectron angular distributions obtained using velocity
map imaging. Helium atoms are ionized with ultrashort extreme-ultraviolet
free-electron laser pulses with a photon energy of 20.3, 21.3, 23.0, and 24.3
eV, produced by the SPring-8 Compact SASE Source test accelerator. The measured
values of the phase-shift differences are distinct from scattering phase-shift
differences when the photon energy is tuned to an excited level or Rydberg
manifold. The difference stems from the competition between resonant and
non-resonant paths in two-photon ionization by ultrashort pulses. Since the
competition can be controlled in principle by the pulse shape, the present
results illustrate a new way to tailor the continuum wave packet.
