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arXiv:2609.30282

Attosecond topological interference beyond Floquet-Volkov paths

Hyosub Park, J. D. Lee

quant-phSubmitted Aug 31, 2026• Announced Sep 1, 2026
arXivHTMLPDF

Abstract

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.

Comments
45 pages, 15 figures

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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.
Reconstruction of attosecond beating by interference of two-photon transitions is a cornerstone technique of attosecond chronoscopy, routinely used to extract photoemission delays from the phase of sideband oscillations. Here, we theoretically investigate the reconstruction of attosecond beating by interference of two-photon transitions protocol driven by quantum light and demonstrate that it is intrinsically sensitive to the quantum nature of the driving field. When the probe field is prepared in a nonclassical state, its photon statistics are imprinted onto photoelectrons via continuum-continuum transitions, giving rise to an additional time delay of several tens of attoseconds. We trace this delay to the phase associated with the second-order anomalous moment ⟨a[over ^]^{2}⟩ of the probe field. Extending the framework to a three-sideband configuration, which enables retrieval of the fourth-order anomalous moment ⟨a[over ^]^{4}⟩, we show that the interferometer exhibits significantly enhanced sensitivity to quantum fluctuations. Our work illustrates quantum attosecond photoelectron interferometry as a phase-sensitive probe of quantum light, offering a promising route for time-resolved quantum metrology at the attosecond scale.
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.
Attosecond chronoscopy enables the exploration of correlated electron dynamics in real time. One key observable of attosecond physics is the determination of "time zero" of photoionization, the time delay with which the wave packet of the ionized electron departs from the ionic core. This observable has become accessible by experimental advances in attosecond streaking and reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) techniques. In this Letter, we explore photoionization time delays by strong extreme ultraviolet fields beyond the linear-response limit. We identify novel signatures in time delays signifying strong coupling between atoms and light fields and the light-field dressing of the ion. As a prototypical case, we study the interelectronic coherence and entanglement in helium driven by a strong extreme ultraviolet field. By the numerical solution of the time-dependent Schrödinger equation in its full dimensionality, we show that the time delay of the photoionized electron allows one to monitor the ultrafast variations of coherence dynamics and entanglement in real time.
Photoionization is one of the most fundamental processes in light-matter interaction. Advanced attosecond photoelectron spectroscopy provides the possibility to characterize the ultrafast photoemission process in an extremely short attosecond time scale. Following scattering symmetry rules, residual ions encode ultrafast photoionization prints at the instant of electron removal forming an alternative electron emission chronoscope. Here, we experimentally illustrate the attosecond ion reconstruction of attosecond beating by interference of two-photon transition (RABBIT)-like interferometry through the development of high-resolution ion momentum detection in atomic photoionization processes. Our ion interferometry presents identical momentum- and time-dependent scattering phase shift, as we observed in photoelectron spectroscopy, and thus demonstrates that ion interferometry can be a possible alternative attosecond approach to resolve the photoionization process, without the electron homogeneity limitation.
We present a general theoretical framework for multiphoton processes driven by quantum light fields, establishing a direct link between photon statistics and photoelectron observables. Our results show that the autocorrelation and cross-correlation functions, which quantify the underlying photon statistics, are directly mapped onto the resulting photoelectron spectra. Although our framework is broadly applicable, we demonstrate specifically in the example of reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) the influence of the light statistical properties. In this approach, the amplitude, contrast and phase of the oscillations of the sideband signal as a function of pump-probe delay reveal the quantum nature of light. We analyze these observables across several quantum configurations, including correlated infrared and harmonic modes, as well as the uncorrelated case with non-classical harmonic statistics, thereby establishing a general framework for quantum-light RABBIT spectroscopy. We compare the analytical theory with numerical simulations for the case of classical harmonics and an infrared field in a squeezed coherent state, obtaining excellent agreement. Our results reveal how the interplay between classical and quantum correlations dictates the coherence of the photoemission process, providing a new window into the quantum-optical foundations of attosecond science.
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.