Phase dependence of (N+1)-color (N>1) ir-uv photoionization of atoms with higher harmonics

We discuss, via a numerical calculation, the main properties of atomic photoelectron spectra, as they would be obtained by using a radiation pulse containing N+1 frequencies associated with a ‘‘Dirac comb’’ of N higher harmonics together with the laser which has been used to generate them. We address more precisely the physically relevant situation in which the harmonics have much weaker intensities than the one of the laser. In such (N+1)-color photoionization processes, the atom can simultaneously absorb harmonic uv photons and exchange, i.e., absorb and/or emit, (via stimulated emission) laser ir photons. We have simulated the photoelectron spectra by numerically solving the time-dependent Schrödinger equation for a three-dimensional hydrogen atom in the presence of the radiation pulse. Our results show that, everything else being kept fixed, the magnitudes of the photoelectron peaks are strongly dependent on the difference of phase between successive harmonics. This strong dependence results from interference effects taking place between competing quantum paths leading to a given final state. An interesting feature is that these interferences involve transitions in the continuum states of the atom and do not depend on resonances in the discrete spectrum. Another interesting outcome of our study is to show that such effects should be observable with currently developed harmonic sources.