Circular RABBITT goes under threshold

Abstract

We introduce circular under-threshold RABBITT (cuRABBITT) as a new interferometric method to probe discrete electronic excitations in atoms with attosecond resolution. By combining circularly polarized attosecond pulses with broadband (``rainbow'') spectral analysis, we directly access two-photon ionization amplitudes and their relative phases. Time-dependent Schrödinger simulations, supported by Green's function theory, reveal strong resonances in helium and argon and a Cooper-like minimum in xenon. These results demonstrate that cuRABBITT provides continuous spectral mapping of bound-state resonances and extends Fano's propensity rule into the under-threshold regime. Our work establishes cuRABBITT as a powerful attosecond metrology technique, opening the way to polarization-resolved studies of resonant dynamics in atoms and molecules.

Figures (3)

• Figure 1: Schematic of RABBITT processes. (a) Standard case: IR absorption/emission couples adjacent odd XUV harmonics, forming sidebands at $2q\omega$. (b) Under-threshold RABBITT (uRABBITT): one harmonic lies below threshold and couples via discrete Rydberg states. (c) Continuous rainbow RABBITT: a single attosecond pulse yields broadband spectra for extended analysis. The CO and CR cases of circular XUV (blue) and IR (red) polarization are illustrated in the right panel.
• Figure 2: Moduli ratios $\left|T^{\pm}_{\ell-1}/T^{\pm}_{\ell+1}\right|$ (top) and phase differences and phase differences $\arg\!\left[T^{\pm}_{\ell-1}/T^{\pm}_{\ell+1}\right]$ (bottom) for He $1s$, Ar $3p$, and Xe $4d$. The crossing of the "Fano's line" ($R=1$) marks deviations from Fano's propensity rule. Resonant oscillations appear in He and Ar, while Xe shows a Cooper-like minimum with weak resonance structure.
• Figure 3: Individual two-photon amplitudes. Left: $\lvert T^{+}_{0}\rvert$ and $\lvert T^{+}_{2}\rvert$ for He $1s$. Right: $\lvert T^{+}_{1}\rvert$ and $\lvert T^{+}_{3}\rvert$ for Ar $3p$. Resonant peaks align across channels, but displaced anti-resonances (troughs) generate the oscillatory ratios of Fig. \ref{['Fig2']}.