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Tracing the evolution of molecular coherences can provide a direct, unambiguous probe of nonadiabatic molecular processes, such as the passage through conical intersections of electronic states. Two techniques, attosecond transient absorption spectroscopy (ATAS) and Transient Redistribution of Ultrafast Electronic Coherences in Attosecond Raman Signals (TRUECARS), have been used or proposed for monitoring nonadiabatic molecular dynamics. Both techniques employ the transmission of a weak attosecond extreme-ultraviolet or X-ray probe to interrogate the molecule at controllable time delays with respect to an optical pump, thereby extracting dynamical information from transient spectral features. The connection between these techniques has not been firmly established yet. In this theoretical study, we provide a unified description of both transient transmission techniques, establishing their relationship as limits of the same pump-probe spectroscopy technique for different pulse parameter regimes. We demonstrate this by quantum dynamical simulations of thiophenol photodissociation and show how complementary coherence information can be revealed by the two techniques.

Elementary events that determine photochemical outcomes and molecular functionalities happen on the femtosecond and subfemtosecond timescales. Among the most ubiquitous events are the nonadiabatic dynamics taking place at conical intersections. These facilitate ultrafast, nonradiative transitions between electronic states in molecules that can outcompete slower relaxation mechanisms such as fluorescence. The rise of ultrafast X-ray sources, which provide intense light pulses with ever-shorter durations and larger observation bandwidths, has fundamentally revolutionized our spectroscopic capabilities to detect conical intersections. Recent theoretical studies have demonstrated an entirely new signature emerging once a molecule traverses a conical intersection, giving detailed insights into the coupled nuclear and electronic motions that underlie, facilitate, and ultimately determine the ultrafast molecular dynamics. Following a summary of current sources and experiments, we survey these techniques and provide a unified overview of their capabilities. We discuss their potential to dramatically increase our understanding of ultrafast photochemistry.

We theoretically monitor the photoinduced ππ* → n π* internal conversion process in 4-thiouracil (4TU), triggered by an optical pump. The element-sensitive spectroscopic signatures are recorded by a resonant X-ray probe tuned to the sulfur, oxygen, or nitrogen K-edge. We employ high-level electronic structure methods optimized for core-excited electronic structure calculation combined with quantum nuclear wavepacket dynamics computed on two relevant nuclear modes, fully accounting for their quantum nature of nuclear motions. We critically discuss the capabilities and limitations of the resonant technique. For sulfur and nitrogen, we document a pre-edge spectral window free from ground-state background and rich with ππ* and n π* absorption features. The lowest sulfur K-edge shows strong absorption for both ππ* and n π*. In the lowest nitrogen K-edge window, we resolve a state-specific fingerprint of the ππ* and an approximate timing of the conical intersection via its depletion. A spectral signature of the n π* transition, not accessible by UV-vis spectroscopy, is identified. The oxygen K-edge is not sensitive to molecular deformations and gives steady transient absorption features without spectral dynamics. The ππ*/ n π* coherence information is masked by more intense contributions from populations. Altogether, element-specific time-resolved resonant X-ray spectroscopy provides a detailed picture of the electronic excited-state dynamics and therefore a sensitive window into the photophysics of thiobases.

Time-resolved photoelectron spectroscopy (TRPES) signals that monitor the relaxation of the RNA base uracil upon optical excitation are simulated. Distinguishable signatures of coherence dynamics at conical intersections are identified, with temporal and spectral resolutions determined by the duration of the ionizing probe pulse. The frequency resolution of the technique, either directly provided by the signal or retrieved at the data-processing stage, can magnify the contribution from molecular coherences, enabling the extraction of most valuable information about the nonadiabatic molecular dynamics. The predicted coherence signatures in TRPES could be experimentally observed with existing ultrashort pulses from high-order harmonic generation or free-electron lasers.

We present a novel approach to transient Raman spectroscopy, which combines stochastic probe pulses and a covariance-based detection to measure stimulated Raman signals in alpha-quartz. A coherent broadband pump is used to simultaneously impulsively excite a range of different phonon modes, and the phase, amplitude, and energy of each mode are independently recovered as a function of the pump-probe delay by a noisy-probe and covariance-based analysis. Our experimental results and the associated theoretical description demonstrate the feasibility of 2D-Raman experiments based on the stochastic-probe schemes, with new capabilities not available in equivalent mean-value-based 2D-Raman techniques. This work unlocks the gate for nonlinear spectroscopies to capitalize on the information hidden within the noise and overlooked by a mean-value analysis., (© 2022. The Author(s).)

Direct imaging of the ultrafast quantum motion of valence electrons in molecules is essential for understanding many elementary chemical and physical processes. We present a simulation study of valence-electron dynamics of oxazole. A valence-state electronic wavepacket is prepared with an attosecond soft X-ray pulse through a stimulated resonant X-ray Raman process and then probed with time-resolved off-resonant single-molecule X-ray diffraction. We find that the time dependent diffraction signal originates solely from the electronic coherences and can be detected by existing experimental techniques. We thus provide a feasible way of imaging electron dynamics in molecules. Moreover, the created electronic coherences and subsequent electron dynamics can be manipulated by the resonant X-ray Raman excitation tuned to different core-excited states.

Resonant stimulated X-ray Raman spectroscopy of the bimetallic [Mn III Mn IV (μ-O) 2 (μ-OAC)(tacn) 2 ] 2+ manganese complex is investigated in a simulation study. Essential biological processes, including water oxidation in photosynthesis, involve charge transfer between manganese sites of different oxidation states. We study a prototypical binuclear mixed-valence transition-metal complex with two Mn atoms in different oxidation states surrounded by ligand structures and employ a pump-probe sequence of resonant X-ray Raman excitations to follow the charge transfer occurring in the molecule. This allows us to generate and monitor valence-electron wave packets at selected regions in the molecule by exploiting element-specific core-excited states. A two-color protocol is presented, with pump and probe pulses tuned to the Mn and N K-edges. A natural orbital decomposition allows the visualization of the electron dynamics underlying the signal.

The outcomes and timescales of molecular nonadiabatic dynamics are decisively impacted by the quantum coherences generated at localized molecular regions. In time-resolved X-ray diffraction imaging, these coherences create distinct signatures via inelastic photon scattering, but they are buried under much stronger background elastic features. Here, we exploit the rich dynamical information encoded in the inelastic patterns, which we reveal by frequency-dispersed covariance ultrafast powder X-ray diffraction of stochastic X-ray free-electron laser pulses. This is demonstrated for the photoisomerization of azobenzene involving the passage through a conical intersection, where the nuclear wave packet branches and explores different quantum pathways. Snapshots of the coherence dynamics are obtained at high frequency shifts, not accessible with conventional diffraction measurements. These provide access to the timing and to the confined spatial distribution of the valence electrons directly involved in the conical intersection passage. This study can be extended to full three-dimensional imaging of conical intersections with ultrafast X-ray and electron diffraction., Competing Interests: Competing interest statement: S.M. and H.J.W. are coauthors on a 2018 roadmap article, L. Young et al., Roadmap of ultrafast X-ray atomic and molecular physics, J. Phys. B At. Mol. Opt. Phys. 51, 032003 (2018).

We demonstrate how optical cavities can be exploited to control both valence- and core-excitations in a prototypical model transition metal complex, ferricyanide ([Fe(iii)(CN) 6 ] 3- ), in an aqueous environment. The spectroscopic signatures of hybrid light-matter polariton states are revealed in UV/Vis and X-ray absorption, and stimulated X-ray Raman signals. In an UV/Vis cavity, the absorption spectrum exhibits the single-polariton states arising from the cavity photon mode coupling to both resonant and off-resonant valence-excited states. We further show that nonlinear stimulated X-ray Raman signals can selectively probe the bipolariton states via cavity-modified Fe core-excited states. This unveils the correlation between valence polaritons and dressed core-excitations. In an X-ray cavity, core-polaritons are generated and their correlations with the bare valence-excitations appear in the linear and nonlinear X-ray spectra., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

High-intensity ultrashort pulses at extreme ultraviolet (XUV) and x-ray photon energies, delivered by state-of-the-art free-electron lasers (FELs), are revolutionizing the field of ultrafast spectroscopy. For crossing the next frontiers of research, precise, reliable and practical photonic tools for the spectro-temporal characterization of the pulses are becoming steadily more important. Here, we experimentally demonstrate a technique for the direct measurement of the frequency chirp of extreme-ultraviolet free-electron laser pulses based on fundamental nonlinear optics. It is implemented in XUV-only pump-probe transient-absorption geometry and provides in-situ information on the time-energy structure of FEL pulses. Using a rate-equation model for the time-dependent absorbance changes of an ionized neon target, we show how the frequency chirp can be directly extracted and quantified from measured data. Since the method does not rely on an additional external field, we expect a widespread implementation at FELs benefiting multiple science fields by in-situ on-target measurement and optimization of FEL-pulse properties.

Time-resolved, resonant X-ray sum-frequency generation in aligned selenophene molecules is calculated. A wave packet of valence-excited states, prepared by an extreme-ultraviolet pump pulse, is probed by two 12-keV X-ray probe pulses resonant with the Se core-excited states for variable time delays. At these hard-X-ray frequencies, the angström wavelength of the X-ray probe is comparable to the molecular size. We thus employ a nonlocal description of the light-matter interaction based on the minimal-coupling Hamiltonian. The wavevector-resolved resonant stimulated sum-frequency-generation signal, obtained by varying the propagation direction of hard-X-ray pulses, can thus directly monitor the transition current densities between core and ground/valence states. This is in contrast to off-resonant diffraction, which detects the transition charge densities.

A scheme to infer the temporal coherence of EUV frequency combs generated from intracavity high-order harmonic generation is put forward. The excitation dynamics of highly charged Mg-like ions, which interact with EUV pulse trains featuring different carrier-envelope-phase fluctuations, are simulated. While demonstrating the microscopic origin of the macroscopic equivalence between excitations induced by pulse trains and continuous-wave lasers, we show that the coherence time of the pulse train can be determined from the spectrum of the excitations. The scheme will provide a verification of the comb temporal coherence at timescales several orders of magnitude longer than current state of the art, and at the same time will enable high-precision spectroscopy of EUV transitions with a relative accuracy up to δω/ω∼10^{-17}.

A scheme is put forward to generate fully coherent x-ray lasers based on population inversion in highly charged ions, created by fast inner-shell photoionization using broadband x-ray free-electron-laser (XFEL) pulses in a laser-produced plasma. Numerical simulations based on the Maxwell-Bloch theory show that one can obtain high-intensity, femtosecond x-ray pulses of relative bandwidths Δω/ω = 10 -5 -10 -7 , by orders of magnitude narrower than in x-ray free-electron-laser pulses for discrete wavelengths down to the sub-ångström regime. Such x-ray lasers can be applicable in the study of x-ray quantum optics and metrology, investigating nonlinear interactions between x-rays and matter, or in high-precision spectroscopy studies in laboratory astrophysics.

Resonant X-ray sum-frequency generation is calculated for excitations of the fluorine and the oxygen core K-edge in acetyl fluoride using real-time time-dependent density functional theory. The signal is generated by an extreme-ultraviolet pulse followed by an X-ray pulse with variable delay T . The X-ray pulse is tuned to different element-specific core excitations and used to probe the dynamics of a valence electronic wave packet. A two-dimensional signal is recorded depending on the dispersed X-ray pulse frequency and the frequency conjugated to T , revealing the couplings between core and valence excited states. Molecular orbital decomposition of the signal reveals which regions of the molecule contribute to the X-ray excitation.

We demonstrate time-resolved nonlinear extreme-ultraviolet absorption spectroscopy on multiply charged ions, here applied to the doubly charged neon ion, driven by a phase-locked sequence of two intense free-electron laser pulses. Absorption signatures of resonance lines due to 2p-3d bound-bound transitions between the spin-orbit multiplets ^{3}P_{0,1,2} and ^{3}D_{1,2,3} of the transiently produced doubly charged Ne^{2+} ion are revealed, with time-dependent spectral changes over a time-delay range of (2.4±0.3)  fs. Furthermore, we observe 10-meV-scale spectral shifts of these resonances owing to the ac Stark effect. We use a time-dependent quantum model to explain the observations by an enhanced coupling of the ionic quantum states with the partially coherent free-electron laser radiation when the phase-locked pump and probe pulses precisely overlap in time.

The reconstruction of the full temporal dipole response of a strongly driven time-dependent system from a single absorption spectrum is demonstrated, only requiring that a sufficiently short pulse is employed to initialize the coherent excitation of the system. We apply this finding to the time-domain observation of Rabi cycling between doubly excited atomic states in the few-femtosecond regime. This allows us to pinpoint the breakdown of few-level quantum dynamics at the critical laser intensity near 2  TW/cm^{2} in doubly excited helium. The present approach unlocks single-shot real-time-resolved signal reconstruction across timescales down to attoseconds for nonequilibrium states of matter. In contrast to conventional pump-probe schemes, there is no need for scanning time delays in order to access real-time information. The potential future applications of this technique range from testing fundamental quantum dynamics in strong fields to measuring and controlling ultrafast chemical and biological reaction processes when applied to traditional transient-absorption spectroscopy.

The quantum dynamics of a V-type three-level system, whose two resonances are first excited by a weak probe pulse and subsequently modified by another strong one, is studied. The quantum dynamics of the multi-level system is closely related to the absorption spectrum of the transmitted probe pulse and its modification manifests itself as a modulation of the absorption line shape. Applying the dipole-control model, the modulation induced by the second strong pulse to the system's dynamics is quantified by eight intensity-dependent parameters, describing the self and inter-state contributions. The present study opens the route to control the quantum dynamics of multi-level systems and to quantify the quantum-control process.

The evolution of a V-type three-level system is studied, whose two resonances are coherently excited and coupled by two ultrashort laser pump and probe pulses, separated by a varying time delay. We relate the quantum dynamics of the excited multilevel system to the absorption spectrum of the transmitted probe pulse. In particular, by analyzing the quantum evolution of the system, we interpret how atomic phases are differently encoded in the time-delay-dependent spectral absorption profiles when the pump pulse either precedes or follows the probe pulse. This scheme is experimentally applied to atomic Rb, whose fine-structure-split 5s  (2)S{1/2}→5p(2)P{1/2} and 5s(2)S_{1/2}→5p(2)P{3/2} transitions are driven by the combined action of a pump pulse of variable intensity and a delayed probe pulse. The provided understanding of the relationship between quantum phases and absorption spectra represents an important step towards full time-dependent phase reconstruction (quantum holography) of bound-state wave packets in strong-field light-matter interactions with atoms, molecules, and solids.

Line intensities and oscillator strengths for the controversial 3C and 3D astrophysically relevant lines in neonlike Fe(16+) ions are calculated. A large-scale configuration-interaction calculation of oscillator strengths is performed with the inclusion of higher-order electron-correlation effects, suggesting that these contributions cannot explain existing discrepancies between theory and experiment. Then, we investigate nonlinear dynamical effects, showing that, for strong x-ray sources, the modeling of the spectral lines by a peak with an area proportional to the oscillator strength is not sufficient. The dynamical effects give a possible resolution of discrepancies of theory and experiment found by recent measurements, which motivates the use of light-matter interaction models also valid for strong light fields in the analysis and interpretation of astrophysical and laboratory spectra.