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.

The chaotic nature of x-ray free-electron-laser pulses is a major bottleneck that has limited the joint temporal and spectral resolution of spectroscopic measurements. We show how to use the stochastic x-ray field statistics to overcome this difficulty through correlation signals averaged over independent pulse realizations. No control is required over the spectral phase of the pulse, enabling immediate application of existing, noisy x-ray free-electron-laser pulses. The proposed stimulated Raman technique provides the combined broad observation bandwidth and high time-frequency resolution needed for the observation of elementary molecular events. A model is used to simulate chaotic free-electron-laser pulses and calculate their correlation properties. The resulting joint temporal and spectral resolution is exemplified for a molecular model system with time-dependent frequencies and for the RNA base uracil passing through a conical intersection. Ultrafast coherences, which constitute a direct signature of the nonadiabatic dynamics, are resolved. The detail and depth of physical information accessed by the proposed stochastic signal are virtually identical to those obtained by phase-controlled pulses.

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.

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.

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.