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arXiv:2506.07445 · Physical Review Letters

Circular RABBITT Goes under Threshold: A Sensitive Probe of Discrete Excitations in Noble Gas Atoms

Vladislav Viktorovich Serov, Jia-Bao Ji, Meng Han, Kiyoshi Ueda, Hans Jakob Wörner, Anatoli S. Kheifets

Published Feb 2, 2026• 4 citations
arXivHTMLPDF

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 Letter establishes cuRABBITT as a powerful attosecond metrology technique, opening the way to polarization-resolved studies of resonant dynamics in atoms and molecules.

DOI
10.1103/z3k5-wqg9

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Abstract We study theoretically the single ionization of noble gas atoms by the combined action of an attosecond pulse train with linear polarization and an assistant laser field with circular polarization. We employ a non-perturbative model that under certain approximations gives closed-form expressions for the angular distributions of photoelectrons. Interestingly, our model allow us to interpret these angular distributions as two-centre interferences where the orientation and the modulus of the separation vector between the virtual emitters is governed by the assistant laser field. Additionally, we show that such a configuration of light fields is similar to the polarization control technique, where both the attosecond pulse train and the assistant laser field have linear polarizations whose relative orientation may be controlled. Moreover, in order to compare our results with the available experimental data, we obtain analytical expressions for the cross sections integrated over the photoelectron emission angles. By means of these expressions, we define the ‘magic time’ as the delay for which the total cross sections for atomic targets exhibit the same functional form as the one of the monochromatic photoionization of diatomic molecular targets.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 14, 2017•6 citations
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 Letter establishes cuRABBITT as a powerful attosecond metrology technique, opening the way to polarization-resolved studies of resonant dynamics in atoms and molecules.
Abstract The process of reconstruction of attosecond bursts by beating of two-photon transitions (RABBITT) can involve a transition from under the ionization threshold. Such an under-threshold RABBITT (or uRABBITT) was demonstrated experimentally and analyzed theoretically in He and Ne. In the present work, we explore an analogous process in the argon atom. The uRABBITT in Ar reveals the familiar physical effects: a phase transition across the threshold and the symmetry modification of the photoelectron momentum distribution. It can also be used for mapping the electronic structure of the target atom bound states.
We utilize the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) technique to study the phase of a Rabi-cycling atom using circularly polarized extreme ultraviolet and infrared fields, where the infrared field induces Rabi oscillations between the 2s2s2s and 2p2p2p states of lithium. Autler-Townes splittings are observed in sidebands of the photoelectron spectra and the relative phases of outgoing electron wave packets are retrieved from the azimuthal angle. In this RABBITT scheme, more ionization pathways beyond the usual two-photon pathways are required. Our results show that the polar-angle-integrated and polar-angle-resolved RABBITT phases have different behaviors when the extreme ultraviolet and infrared fields have co- and counter-rotating circular polarizations, which are traced back to the different ionization channels according to the selection rules in these two cases and their competition relying on the propensity rule in laser-assisted photoionization.
Attosecond pulse trains interacting with a resonantly dressed atom generate a pronounced intra-sideband phase structure that remains hidden in conventional spectrally integrated RABBITT measurements. Using \textit{ab initio} time-dependent Schrödinger equation calculations for lithium near the resonant 2s→2p2s\to2p2s→2p transition, we show that the phase extracted within a single sideband can vary by nearly πππ across its spectral width. The resulting intra-sideband phase dispersion exhibits a characteristic dependence on the IR detuning, pulse duration, intensity, and sideband order. Most strikingly, exact resonant Rabi flopping flattens the intra-sideband phase dispersion, whereas a small detuning generates a pronounced phase modulation despite weaker population transfer. This counterintuitive behavior demonstrates that rainbow RABBITT probes the dynamical phase accumulated by a Rabi-dressed wave packet rather than the instantaneous populations of the participating states. A simple analytical model captures the principal features of the numerical calculations and provides physical insight into the emergence of the intra-sideband phase structure. These results establish intra-sideband phase dispersion as a new interferometric observable for mapping coherent Rabi dynamics.
Abstract The mutual angle formed by the non-collinear polarization axes of two laser pulses is used to control two-photon extreme ultraviolet and infrared ionization of noble gas atoms in the process of reconstruction of attosecond bursts by beating of two-photon transitions (RABBITT). The magnitude and the phase of this beating can be controlled very efficiently by the mutual polarization angle. The mechanism of this control can be understood within the lowest order perturbation theory and the soft photon approximation. We offer a very sensitive test on the polarization control of the angular dependent RABBITT process which validates our numerical simulations. We apply this test to the recent theoretical and experimental results of polarization controlled RABBITT on hydrogen and helium by Boll et al (2023 Phys. Rev. A 107 043113) and heavier noble gases by Jiang et al (2022 Nat. Commun. 13 5072).
The reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) method is a leading technique for time-resolved investigation of photoionization processes. Interpretation of RABBITT spectra is limited to a lowest-order description, while new variants of the technique necessitate higher intensity infrared fields where this description breaks down. Here, we present an extension of RABBITT theory which can account for higher-order processes (RABBITT-HOP), and demonstrate RABBITT-HOP's ability to predict and describe higher-order processes through simulation of a RABBITT experiment targeting the high-lying 1 s n p Rydberg series of helium. We demonstrate that the signature line shape imparted by the resonances in the 2 ω phase of the lowest sideband can also be observed in the 2 ω phase of the next mainband, as well as in the 4 ω phases of the next sideband and mainband—each with additional phase shifts predicted under RABBITT-HOP. Repeating this analysis for a range of infrared intensities, we determine the lower limits of intensities required for these higher-order processes to become observable and upper limits beyond which nonperturbative effects begin to dominate. This new theoretical framework forms a much-needed basis for accurate interpretation of RABBITT spectra in experiments involving more intense fields, and paves the way for the development of new RABBITT-like techniques which take advantage of this new understanding of how atomic resonance effects may be propagated beyond their nearest sideband.
Abstract We study theoretically the single ionization of noble gas atoms by the combined action of an attosecond pulse train with linear polarization and an assistant laser field with circular polarization. We employ a non-perturbative model that under certain approximations gives closed-form expressions for the angular distributions of photoelectrons. Interestingly, our model allow us to interpret these angular distributions as two-centre interferences where the orientation and the modulus of the separation vector between the virtual emitters is governed by the assistant laser field. Additionally, we show that such a configuration of light fields is similar to the polarization control technique, where both the attosecond pulse train and the assistant laser field have linear polarizations whose relative orientation may be controlled. Moreover, in order to compare our results with the available experimental data, we obtain analytical expressions for the cross sections integrated over the photoelectron emission angles. By means of these expressions, we define the ‘magic time’ as the delay for which the total cross sections for atomic targets exhibit the same functional form as the one of the monochromatic photoionization of diatomic molecular targets.