Two-photon ionization of atoms by ultrashort laser pulses

Based on the direct solution of the time-dependent Schrodinger equation (TDSE), we theoretically study two-photon ionization (TPI) of a hydrogen atom by ultrashort vacuum ultraviolet (VUV) laser pulses with a photon energy close to the ionization threshold and a pulse width from 10 fs down to subfemtoseconds, for which the distinction between stepwise and direct processes becomes subtle. Our analysis on TPI by a double pulse reveals that direct processes are classified into two categories: a purely direct process with no real intermediate levels, and the one via Rydberg or continuum states, which rapidly escape from the nucleus. Our results also show that TPI becomes stepwise for subfemtosecond VUV pulses even for a wavelength corresponding to a direct process in the long pulse limit, since the broad spectrum of the pulse overlaps several discrete bound levels and excites them resonantly. This also leads to a phenomenon peculiar to attosecond pulses, namely, a significant red shift of the photoelectron energy spectrum. The Rydberg wave packet generated by an ultrashort near-threshold laser pulse, containing low-lying levels and the continuum, rapidly disintegrates into several parts. Nevertheless, the bound parts come back to the nucleus in fragments, and each fragment returns in the Kepler orbit time corresponding to its central principal quantum number. The lower-energy part of the double-pulse TPI electron energy spectrum exhibits the effect of the interference between the returning fragments and the wave packet excited by the second pulse.