General properties of the RABBITT at parity mixing conditions

Parity mixing in photoionization, i.e. when emitted electrons have different parities but the same energy, causes interference observable only in angle-resolved measurements. The interference typically manifests as a symmetry violation in the photoelectron angular distributions. The traditional, based on HHG, RABBITT scheme with high-order harmonics separated by twice the seed field energy, precludes parity mixing. On the contrary, a free-electron laser provides a possibility to generate even harmonics. Using triple the fundamental frequency as a seed, one obtains a comb of alternating even and odd harmonics, separated by three times the initial frequency [Nature 578, 386-391 (2020)] (2-SB RABBITT). In this setup, there are two sidebands between the main photoelectron lines, versus one in the traditional scheme. In the paper, we examine the general properties of a two-sideband scheme and analyze the symmetry breakdown of photoelectron angular distributions for various polarization geometries of the incident pulse. We found a crucial difference in symmetries between 2-SB RABBITT and other photoionization schemes with parity mixing. Illustrative calculations are carried out for neon with pulse parameters typical for modern facilities. The possibility to reconstruct the temporal profile of the pulse from the angle-resolved measurements is discussed.