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Physical Review A

Reconstruction of attosecond beating by interference of two-photon transitions with higher-order processes

L. Roantree, H. W. van der Hart, A. C. Brown

Published Jul 14, 2025• 3 citations

Abstract

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.

DOI: 10.1103/bksn-wgkm

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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.

Reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) is a technique that can be used to determine the phases of atomic transition elements in photoionization processes. In the traditional RABBITT scheme, the so-called asymptotic approximation considers the measured phase as a sum of the Wigner phase linked to a single-photon ionization process and the continuum-continuum phase associated with further single-photon transitions in the continuum. In this paper, we extend the asymptotic approximation to multi-sideband RABBITT schemes. The predictions from this approximation are then compared with results obtained by an ab initio calculation based on solving the time-dependent Schr\"odinger equation for atomic hydrogen.

Following up on a previous paper on two-color photoionization of Ar(3p) [D. Bharti , ], we present measurements and calculations for a modified three-sideband (3-SB) version of the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) configuration applied to He(1s) . The 3-SB RABBITT approach allows us to explore interference effects between pathways involving different orders of transitions within the continuum. The relative differences in the retrieved oscillation phases of the three sidebands provide insights into the continuum-continuum transitions. The ground state of helium has zero orbital angular momentum, which simplifies the analysis of oscillation phases and their angle dependence within the three sidebands. We find qualitative agreement between our experimental results and the theoretical predictions for many cases but also observe some significant quantitative discrepancies. Published by the American Physical Society 2024

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

2s

and

2p

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.

In the paper we theoretically investigate the features of RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) spectroscopy under conditions when transitions through discrete spectrum states play a significant role. Two approaches are applied in the article: the numerical solution of rate equations with continuum discretization and the perturbation theory up to the third order in amplitude. Both approaches use transition matrix elements and photoionization amplitudes obtained by the high-precision R-matrix method. Within the framework of these approaches, photoelectron spectra, the amplitude and phase of RABBITT oscillations were obtained, and the effect of the seed optical field intensity and detuning from a resonance upon excitation of discrete states was studied.

In the paper we theoretically investigate the features of RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) spectroscopy under conditions when transitions through discrete spectrum states play a significant role. Two approaches are applied in the article: the numerical solution of rate equations with continuum discretization and the perturbation theory up to the third order in amplitude. Both approaches use transition matrix elements and photoionization amplitudes obtained by the high-precision R-matrix method. Within the framework of these approaches, photoelectron spectra, the amplitude and phase of RABBITT oscillations were obtained, and the effect of the seed optical field intensity and detuning from a resonance upon excitation of discrete states was studied.

Combining attosecond science with semiconductor physics provides a promising interdisciplinary platform for the attosecond control of semiconducting properties. In each field, the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) and the time-resolved and angle-resolved photoemission spectroscopy (tr-ARPES) have been central experimental techniques for probing microscopic dynamics of electrons. However, the integration of the two techniques, bridging the two fields, has been missing so far although they have many technical similarities. Here, we develop a theoretical framework that integrates the two techniques based on the second-order time-dependent perturbation theory. Within this framework, we investigate the RABBIT spectroscopy in semiconductors focusing on the recent hallmark of tr-ARPES, namely quantum path interference between Floquet and Volkov states. Moreover, we theoretically identify a novel quantum path incorporating the virtual excitation, which substantially interferes with the Floquet and Volkov states in both the RABBIT spectroscopy and tr-ARPES of semiconductors. Importantly, we find that such virtual excitation channel induces an attosecond topological interference with the Floquet-Volkov paths, encoding topological quantities such as the local Berry curvature into the time shift of RABBIT sidebands, which is directly related to the photoelectron emission delay. Our findings establish a theoretical framework connecting attosecond spectroscopy to tr-ARPES, paving the way for future applications of attosecond science in semiconductors.