General properties of the RABBITT at parity mixing conditions

TL;DR

The paper analyzes parity mixing in a two-sideband RABBITT scheme fueled by a $3\omega_{ir}$ XFEL seed, enabling alternating even/odd XUV harmonics and two interleaved sidebands. By combining ACE and time-dependent perturbation theory, it derives the full amplitude structure up to third order and reveals how IR-phase control induces parity-violating interference that manifests in angle-resolved photoelectron distributions, particularly at a frequency $3\omega_{ir}$. Through neon simulations and various polarization geometries, the work demonstrates when PADs are axially symmetric or exhibit complex three-lobed patterns, and introduces correlation-based phase-reconstruction methods that do not require equal sideband intensities. The findings provide practical pathways to characterize XUV polarization states and to reconstruct the temporal pulse profile from high-precision angle-resolved measurements, with implications for ultrafast spectroscopy at XFEL sources.

Abstract

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.

Figures (7)

• Figure 1: (a) The scheme of the 2-SB RABBITT for linearly ($E||z$) polarized fields; (b) PAD for different phases of the IR field $\phi$ in PT (note that it oscillates three times faster than the field); (c) the angular anisotropy parameters at $\phi={\pi}/{6}$ approximately corresponding to their maximum values for zero XUV phases $\phi_{N}=0$ and angle integrated photo-electron spectra (does not depend on the phases).
• Figure 2: Scheme '$\uparrow\uparrow$'. (a)--(c) Correlation plots between $\mathcal{P}_{16,17}$ and $\mathcal{P}_{19,21}$ for three different phases of 18th harmonic; (d) The correlation function $\rho_{\rm 16, 17, 19, 20}$ in PT (solid lines) and ACE (dots) compared to a cosine function expected in the ideal conditions.
• Figure 3: (a) Population of states of different magnetic quantum number, solid lines represent right circular polarization, dashed --- left circular polarization; PAD for different phases of the IR field $\phi$ in PT for right circularly polarized XUV pulse and right (b) and left (c) circularly polarized IR pulse.
• Figure 4: (a) The scheme of the 2-SB RABBITT for '$\circlearrowleft\uparrow$'-scheme (b) PAD for different phases of the IR field $\phi$ in PT (note that it oscillates three times faster than the field); (c) angular anisotropy parameters at $\phi={\pi}/{6}$ (near their maximum values for zero XUV phases $\phi_{N}=0$) and integrated photoelectron spectra (does not depend on phases).
• Figure 5: Scheme '$\circlearrowleft\uparrow$'. (a)--(c) Correlation plots between $\mathcal{P}_{16,17}$ and $\mathcal{P}_{19,21}$ for three different phases of 18th harmonic; (d) The correlation function $\rho_{\rm 16, 17, 19, 20}$ in PT (solid lines) and ACE (dots) compared to a cosine function expected in the ideal conditions.