Determination of atomic multiphoton ionization phases by trichromatic multichannel wave packet interferometry

We present a multichannel photoelectron interferometry technique based on trichromatic pulse shaping for unambiguous determination of quantum phases in multiphoton ionization (MPI) of potassium atoms. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the $3d$-state resulting in a (2+1) resonance-enhanced MPI (REMPI), a (1+2) REMPI occurs via the non-resonant intermediate $4p$-state with an initial green or blue pulse. We show that ionization via a non-resonant intermediate state lifts the degeneracy of photoelectron interferograms from pathways consisting of permutations of the colors. The analysis of the interferograms reveals a phase shift of $\pm \pi/2$ depending on the sign of the detunings in the (1+2) REMPI pathways. In addition, we demonstrate that the photoionization time delay in the resonant (2+1) REMPI pathway gives rise to a linear spectral phase in the photoelectron spectra. Insights into the underlying MPI processes are gained through an analytic perturbative description and numerical simulations of a trichromatic driven three level system coupled to the continuum.