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arXiv:2606.10272

Rainbow RABBITT as a Probe of Coherent Rabi Dynamics

Vladislav Viktorovich Serov, Anatoli S. Kheifets

Published Jun 9, 2026• 0 citations
arXivHTMLPDF

Abstract

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 $2s\to2p$ transition, we show that the phase extracted within a single sideband can vary by nearly $π$ 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.

DOI
10.48550/arxiv.2606.10272

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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.
We present numerical simulations of the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) on lithium by solving the three-dimensional time-dependent Schr\"odinger equation. In our scheme, the infrared (IR) field couples the 2s2s2s and 2p2p2p states of lithium and leads to the Rabi oscillations of populations between these two states. We analyzed the RABBITT phases of the two peaks in the Rabi-oscillation-induced Autler-Townes splittings. Our results show that the relative phase between these two peaks changes with the photoelectron energy and depends on the intensity of the IR field. Moreover, in the angle-resolved RABBITT measurement, the phases of the two peaks depend differently on the emission angle of photoelectrons. These behaviors are traced back to the different initial phases of the electron wave packets emitted from the dressed 2p2p2p states and the competition among different ionization channels.
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.
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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.
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