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Nature Communications

Heterodyne analysis of high-order partial waves in attosecond photoionization of helium

Wenyu Jiang, Luke Roantree, Lulu Han, Jia-Bao Ji, Yidan Xu, Zitan Zuo, Hans Jakob Wörner, Kiyoshi Ueda, A. C. Brown, H. W. van der Hart, Xiaochun Gong, Jian Wu

Published Jan 3, 2025• 11 citations
Publisher

Abstract

Abstract Partial wave analysis is key to interpretation of the photoionization of atoms and molecules on the attosecond timescale. Here we propose a heterodyne analysis approach, based on the delay-resolved anisotropy parameters to reveal the role played by high-order partial waves during photoionization. This extends the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions technique into the few-photon regime. We demonstrate that even for moderate ( ~ 1TW/cm2) intensities, near-infrared-assisted photoionization of helium through Rydberg states results in a tiny contribution from the g0 wave, which has a significant impact on the photoelectron angular distributions via interference with the s- and d0-waves. This modulation also causes a substantial deviation in the angular distribution of the recovered spectral phase shift. Our analysis provides an efficient method to resolve isolated partial wave contributions beyond the perturbative regime, and paves the way towards understanding resonance-enhancement of partial waves.

DOI
10.1038/s41467-024-55247-1

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Abstract Partial wave analysis is key to interpretation of the photoionization of atoms and molecules on the attosecond timescale. Here we propose a heterodyne analysis approach, based on the delay-resolved anisotropy parameters to reveal the role played by high-order partial waves during photoionization. This extends the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions technique into the few-photon regime. We demonstrate that even for moderate ( ~ 1TW/cm2) intensities, near-infrared-assisted photoionization of helium through Rydberg states results in a tiny contribution from the g0 wave, which has a significant impact on the photoelectron angular distributions via interference with the s- and d0-waves. This modulation also causes a substantial deviation in the angular distribution of the recovered spectral phase shift. Our analysis provides an efficient method to resolve isolated partial wave contributions beyond the perturbative regime, and paves the way towards understanding resonance-enhancement of partial waves.
Abstract Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics from gas to condensed phase with attosecond temporal resolution. It has, however, not yet been able to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attosecond chronoscopy to reveal their roles from the angle-resolved photoionization phase shifts in rare gas atoms. By scanning the relative polarization angle between an extreme-ultraviolet attosecond pulse train and a phase-locked near-infrared laser field serving as a partial wave meter, we break the cylindrical symmetry and observe an emission direction dependent phase shift in the photoionized electron momenta. The experimental observations are well supported by numerical simulations using the R-matrix with time-dependence method, and by analytical analysis using the soft-photon approximation. Our symmetry-resolved, partial-wave analysis identifies the transition rate and phase shifts of each individual ionization pathway in the attosecond photoelectron emission dynamics. Our findings provide critical insights into the ubiquitous attosecond optical timer and the underlying attosecond photoionization dynamics, thereby offer new perspectives for the control, manipulation, and exploration of ultrafast electron dynamics in complex systems.
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.
Photoionization is one of the most fundamental photoreactions that leads to the ejection of an electron and the formation of an ion. With the help of modern 3D momentum imaging spectrometers, the interplay between the time and frequency domain upon ionization is studied. In this work, single photoionization of helium is investigated in the few-cycle pulse regime of the driving infrared laser pulses with ultrashort attosecond pulses in a dressing infrared field. By varying the carrier-to-envelope phase of the infrared field to modify the spectro-temporal structure of the attosecond pulses, we analyze how the infrared field impacts the measured angularly-resolved photoelectron energy distribution. To this end, a newly built coincidence 3D momentum spectrometer was used. A thorough understanding of the experiment is achieved by using simulations within the strong field approximation. This analysis allows us to separate our observation into two scenarios, one at two attosecond pulses when the carrier-to-envelope phase is π/2\pi/2π/2 and the second one at three attosecond pulses when the carrier-to-envelope phase is 0 or π\piπ. When the dressing infrared field is added, the photoelectron spectrum changes in comparison to photoionization with attosecond pulses only. While two attosecond pulses in the dressing infrared field modify the photoelectron spectrum in a continuous way, we observe sidebands appearing in the spectrum generated by three pulses in the dressing infrared field. Finally, the resolution of the spectrometer is studied before and after an upgrade of the spectrometer was performed in the context of this work. This study allows us to understand the limiting factors of the energy resolution. In particular, it shows that the resolution is essentially limited by the source volume of the emitted particles, while the magnetic field does not limit the resolution as it was expected.
Metastable states are important actors in the ionisation of atoms and molecules. Sub-femtosecond extreme ultraviolet pulses can coherently populate several transiently bound states at once, thus starting the attosecond clocks which are required to monitor and control ultrafast electronic evolution above the ionisation threshold. Here we illustrate, from a theoretical point of view, the effects coherent superpositions of 1 P o doubly excited states in the helium atom have on channel-resolved photoelectron spectra as well as on the transient absorption spectrum of the atom in the extreme ultraviolet region, when they are created by a single-attosecond pulse in the presence of a strong few-cycle near-infrared/visible pulse which acts as a probe. Interference fringes varying rapidly with the pump-probe time delay are visible in both photoelectron and transient absorption spectra. From such fringes, the wave packet itself can conceivably be reconstructed. Conversely, all observables are modulated by the characteristic beating periods of the wave packet, so that control of partial ionisation yields, branching ratios, and light absorption or amplification can be achieved.
We theoretically study the infrared (IR)-dressed photoionization of atoms excited by extreme ultraviolet attosecond pulse trains above ionization threshold. The initial state of atoms is treated perturbatively by the IR field, and the continuum states are considered as Coulomb–Volkov (CV) waves. CV waves can much reduce the gauge difference calculated with Volkov waves, and, in general, the contribution of ground-state perturbation to the photoelectron spectrum is negligible. Our calculations show qualitative agreement with the experimental results [Phys. Rev. Lett. 95, 013001 (2005)]. An evident dependence of the photoelectron spectrum on the delay phase between the IR field and the attosecond pulse train is exhibited in both helium and argon. The angular distribution of photoelectrons with various IR polarizations and the corresponding photoelectron spectra are presented. The linearly polarized IR fields are shown to have a higher controlling capability of the spectrum via IR delay phases than the circularly polarized fields. On the other hand, the circularly polarized IR fields have a fruitful angular dependence of photoelectrons with various IR delay phases.
Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach because of the difficulty of combining attosecond temporal resolution with fine spectral and angular resolutions. Here, we achieve full decoding of the intricate angle-dependent dynamics of a photoemission process in helium, spectrally and anisotropically structured by two-photon transitions through intermediate bound states. Using spectrally and angularly resolved attosecond electron interferometry, we characterize the complex-valued transition probability amplitude toward the photoelectron quantum state. This allows reconstructing in space, time, and energy the complete formation of the photoionized wave packet.