  We study atomic autoionization processes in the time domain. With the
emerging attosecond extreme vacuum ultraviolet and soft x-ray pulses, we first
address how to characterize the time evolution of the decay of a discrete state
into a degenerate continuum. A short pump beam generates a number of resonance
states in a series and the nearby background continuum, and the resultant wave
packet evolves with time until the full decay of the bound states. Taking the
2pns(^1P^o) resonance series embedded in the 2sEp(^1P^o) continuum in beryllium
atom as an example, the time evolution of the autoionizing wave packet in
energy domain and in coordinate space is calculated and analyzed, where Fano
profiles build up in the photoelectron energy during the process. A proposed
pump-probe scheme assumes that the probe beam ionizes the 2s inner electron in
the wave packet. The lifetimes of the resonances and the photoelectron energy
distribution can be obtained from the ionization yield versus the time delay of
the probe.
