Coherent control over photoelectron wavepackets, via the use of polarization-shaped laser pulses, can be understood as a time and polarization-multiplexed process. In this work, we investigate this multiplexing via computation of the observable photo
electron angular interferograms resulting from multi-photon atomic ionization with polarization-shaped laser pulses. We consider the polarization sensitivity of both the instantaneous and cumulative continuum wavefunction; the nature of the coherent control over the resultant photoelectron interferogram is thus explored in detail. Based on this understanding, the use of coherent control with polarization-shaped pulses as a methodology for a highly multiplexed coherent quantum metrology is also investigated, and defined in terms of the information content of the observable.
Photoelectron angular distributions (PADs) obtained from ionization of potassium atoms using moderately intense femtosecond IR fields ($sim$10$^{12}$Wcm$^{-2}$) of various polarization states are shown to provide a route to complete photoionization e
xperiments. Ionization occurs by a net 3-photon absorption process, driven via the $4srightarrow4p$ resonance at the 1-photon level. A theoretical treatment incorporating the intra-pulse electronic dynamics allows for a full set of ionization matrix elements to be extracted from 2D imaging data. 3D PADs generated from the extracted matrix elements are also compared to experimental, tomographically reconstructed, 3D photoelectron distributions, providing a sensitive test of their validity. Finally, application of the determined matrix elements to ionization via more complex, polarization-shaped, pulses is demonstrated, illustrating the utility of this methodology towards detailed understanding of complex ionization control schemes and suggesting the utility of such multiplexed intra-pulse processes as powerful tools for measurement.
