Attosecond transient absorption spectroscopy of molecular nitrogen: Vibrational coherences in the b′ 1Σ+u state

Effects of Autoionizing Resonances on Wave-Packet Dynamics Studied by Time-Resolved Photoelectron Spectroscopy

We report a combined experimental and theoretical study on the effect of autoionizing resonances in time-resolved photoelectron spectroscopy. The coherent excitation of N_{2} by ∼14.15  eV extreme-ultraviolet photons prepares a superposition of three dominant adjacent vibrational levels (v^{'}=14-16) in the valence b^{'} ^{1}Σ_{u}^{+} state, which are probed by the absorption of two or three near-infrared photons (800 nm). The superposition manifests itself as coherent oscillations in the measured photoelectron spectra. A quantum-mechanical simulation confirms that two autoionizing Rydberg states converging to the excited A ^{2}Π_{u} and B ^{2}Σ_{u}^{+} N_{2}^{+} cores are accessed by the resonant absorption of near-infrared photons. We show that these resonances apply different filters to the observation of the vibrational wave packet, which results in different phases and amplitudes of the oscillating photoelectron signal depending on the nature of the autoionizing resonance. This work clarifies the importance of resonances in time-resolved photoelectron spectroscopy and particularly reveals the phase of vibrational quantum beats as a powerful observable for characterizing the properties of such resonances.

Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics

Since the first demonstration of the generation of attosecond pulses (1 as = 10^-18s) in the extreme-ultraviolet spectral region, several measurement techniques have been introduced, at the beginning for the temporal characterization of the pulses, and immediately after for the investigation of electronic and nuclear ultrafast dynamics in atoms, molecules and solids with unprecedented temporal resolution. The attosecond spectroscopic tools established in the last two decades, together with the development of sophisticated theoretical methods for the interpretation of the experimental outcomes, allowed to unravel and investigate physical processes never observed before, such as the delay in photoemission from atoms and solids, the motion of electrons in molecules after prompt ionization which precede any notable nuclear motion, the temporal evolution of the tunneling process in dielectrics, and many others. This review focused on applications of attosecond techniques to the investigation of ultrafast processes in atoms, molecules and solids. Thanks to the introduction and ongoing developments of new spectroscopic techniques, the attosecond science is rapidly moving towards the investigation, understanding and control of coupled electron-nuclear dynamics in increasingly complex systems, with ever more accurate and complete investigation techniques. Here we will review the most common techniques presenting the latest results in atoms, molecules and solids.

Multiphoton Resonance in Attosecond Transient Absorption

We present the theory and simulation of attosecond transient absorption in helium atoms under the single-active-electron approximation. This study investigates the attosecond dynamics of intrinsic atomic states that interact with a field comprising vacuum ultraviolet (VUV) and extreme ultraviolet (XUV) fields. The absorption spectrum of the helium atom is obtained from the response function, which is constructed by numerically solving the three-dimensional time-dependent Schrödinger equation. We observe a fine structure near the intrinsic atomic level, which is modulated with a 0.2 fs period. Based on high-order time-dependent perturbation theory, the frequency-dependent phase of the dipole response induced by the VUV and XUV fields is analytically obtained, and the fine structure is well explained by the phase difference. In addition, the absorption fringes are dependent on the chirp of the VUV field. This study investigates the features of the attosecond transient absorption in the VUV region, which may have valuable applications in the study of ultrafast phenomena in atoms, molecules, and solids.

The density matrix via few dominant observables: The quantum interference in the isotope effect for atto-pumped N2

Atto- and sub-femto-photochemistry enables preparation of molecules in a coherent superposition of several electronic states. Recently [Ajay et al., Proc. Natl. Acad. Sci. U. S. A. 115, 5890-5895 (2018)], we examined an effect of the nuclear mass during the non-adiabatic transfer between strongly coupled Rydberg and valence electronic states in N₂ excited by an ultrafast pulse. Here, we develop and analyze an algebraic description for the density matrix and its logarithm, the surprisal, in such a superposition of states with a focus on the essentially quantum effect of mass. This allows for the identification of a few observables that accurately characterize the density matrix of the system with several coupled electron-nuclear states. We compact the time evolution in terms of time-dependent coefficients of these observables. Using the few observables, we derive an analytical expression for the time-dependent surprisal. This provides a mass-dependent phase factor only in the observables off-diagonal in the electronic index. The isotope effect is shown to be explicitly driven by the shift in the equilibrium position of the valence state potential. It is analytically given as a time-dependent phase factor describing the interference in the overlap of the two wave packets on the coupled electronic states. This phase factorizes as a product of classical and quantal contributions.

Coupled nuclear-electronic decay dynamics of O2 inner valence excited states revealed by attosecond XUV wave-mixing spectroscopy

Multiple Rydberg series converging to the O2+c4Σ-u state, accessed by 20-25 eV extreme ultraviolet (XUV) light, serve as important model systems for the competition between nuclear dissociation and electronic autoionization. The dynamics of the lowest member of these series, the 3sσg state around 21 eV, has been challenging to study owing to its ultra-short lifetime (<10 fs). Here, we apply transient wave-mixing spectroscopy with an attosecond XUV pulse to investigate the decay dynamics of this electronic state. Lifetimes of 5.8 ± 0.5 fs and 4.5 ± 0.7 fs at 95% confidence intervals are obtained for v = 0 and v = 1 vibrational levels of the 3s Rydberg state, respectively. A theoretical treatment of predissociation and electronic autoionization finds that these lifetimes are dominated by electronic autoionization. The strong dependence of the electronic autoionization rate on the internuclear distance because of two ionic decay channels that cross the 3s Rydberg state results in the different lifetimes of the two vibrational levels. The calculated lifetimes are highly sensitive to the location of the 3s potential with respect to the decay channels; by slight adjustment of the location, values of 6.2 and 5.0 fs are obtained computationally for the v = 0 and v = 1 levels, respectively, in good agreement with experiment. Overall, an intriguing picture of the coupled nuclear-electronic dynamics is revealed by attosecond XUV wave-mixing spectroscopy, indicating that the decay dynamics are not a simple competition between isolated autoionization and predissociation processes.

Symmetry of molecular Rydberg states revealed by XUV transient absorption spectroscopy

Transient absorption spectroscopy is utilized extensively for measurements of bound- and quasibound-state dynamics of atoms and molecules. The extension of this technique into the extreme ultraviolet (XUV) region with attosecond pulses has the potential to attain unprecedented time resolution. Here we apply this technique to aligned-in-space molecules. The XUV pulses are much shorter than the time during which the molecules remain aligned, typically \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<$$\end{document}<100 fs. However, transient absorption is not an instantaneous probe, because long-lived coherences re-emit for picoseconds to nanoseconds. Due to dephasing of the rotational wavepacket, it is not clear if these coherences will be evident in the absorption spectrum, and whether the properties of the initial excitations will be preserved. We studied Rydberg states of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}$$\end{document}2 and O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}$$\end{document}2 from 12 to 23 eV. We were able to determine the polarization direction of the electronic transitions, and hence identify the symmetry of the final states.

Transient absorption spectroscopy is used to identify the structural characteristics of the atoms and molecules. Here the authors used extreme ultraviolet transient absorption spectroscopy to identify the Rydberg state symmetry of aligned molecules.

The role of transition dipole phase in atomic attosecond transient absorption from the multi-level model

Based on a multilevel model considering enough bound electronic states of atoms, we theoretically study the role of the transition dipole phase (TDP) in the attosecond transient absorption (ATA) spectrum of helium in intense laser fields. By solving the stationary Schrödinger equation with B-spline basis sets, we first calculate the transition dipole moments with well-defined phases between the bound states. Using the modified multilevel model, we reveal that the TDP plays an important role in determining the spectral structures if two or more paths populate the excited states from the ground state. Our multilevel model with the accurate TDP is convenient to address the origin of atomic ATA spectral structures by freely removing or adding specific electronic states and has been justified by comparing with the ATA spectra via directly solving the time-dependent Schrödinger equation. Hopefully, further incorporating macroscopic propagation into the model will provide indepth physical insights into experimental ATA spectra.

State-Resolved Probing of Attosecond Timescale Molecular Dipoles

We report an experimental study of iodomethane attosecond transient absorption spectroscopy (ATAS) in the region of iodine 4d core-to-valence/Rydberg excitation. Similar to previous atomic experiments, extreme ultraviolet near-infrared (XUV-NIR) delay-dependent absorbance changes reflect a light-induced phase due to an NIR-field driven AC Stark shift of the excited states, as well as pathway interferences arising from couplings between neighboring states. As a novel aspect of molecular ATAS, we observe pronounced differences between the ATAS signatures of valence and Rydberg states. While the core-to-valence transitions carry the majority of the XUV oscillator strength, the core-to-Rydberg transitions are dominantly affected by a moderately strong, nonionizing NIR field. Our experimental findings are corroborated by ab initio calculations and ATAS simulations.

Multidimensional spectroscopy with attosecond extreme ultraviolet and shaped near-infrared pulses

Dynamics following excitation with attosecond extreme ultraviolet (XUV) pulses arise from enormous numbers of accessible excited states, complicating the retrieval of state-specific time evolutions. We develop attosecond XUV multidimensional spectroscopy here to separate interfering pathways on a near-infrared (NIR) energy axis, retrieving single state dynamics in argon atoms in a two-dimensional (2D) XUV-NIR spectrum. In this experiment, we measure four-wave mixing signal arising from the interaction of XUV attosecond pulses centered around 15 eV with two few-cycle NIR pulses. The 2D spectrum is created by measuring the emitted XUV signal field spectrum while applying narrowband amplitude and phase modulations to one of the NIR pulses. Application of such a technique to systems of high dimensionality will provide for the observation of state-resolved pure electronic dynamics, in direct analogy to phenomena unraveled by multidimensional spectroscopies at optical frequencies.

Controlling attosecond transient absorption with tunable, non-commensurate light fields

We demonstrate a transient absorption scheme that uses a fixed-spectrum attosecond pulse train in conjunction with a tunable probe laser to access a wide range of nonlinear light-atom interactions. We exhibit control over the time-dependent Autler-Townes splitting of the 1s4p absorption line in helium, and study its evolution from a resonant doublet to a light-induced sideband with changing probe wavelength. The non-commensurate probe also allows for the background-free study of two-infrared-photon emission processes in a collinear geometry. Using this capability, we observe two different emission pathways with non-trivial delay dependencies, one prompt and the other delayed. We identify the nonlinear processes underlying these emissions by comparing the experimental results to calculations based on the time-dependent Schrödinger equation.

Signatures of a Conical Intersection in Attosecond Transient Absorption Spectroscopy

We characterize attosecond transient absorption spectroscopy (ATAS) in molecules with coupled nuclear and electronic dynamics in the vicinity of a conical intersection between adiabatic potential energy surfaces. With respect to ATAS, the nonadiabatic vibronic coupling strength can be divided into weak, intermediate, and strong, and the characteristics of spectra belonging to each of these domains are discussed. The results can guide the analysis of ATAS experiments in molecules with conical intersections.

Multiple pulse coherent dynamics and wave packet control of the N2 a′′ 1Σ+g dark state by attosecond four-wave mixing

Dark states of molecular nitrogen in the XUV region are spectroscopically investigated using few-femtosecond dynamic wave packet control.