Interferometric pump-probe experiments in the extreme ultraviolet (XUV) domain are experimentally very challenging due to the high phase stability required between the XUV pulses. Recently, an efficient phase stabilization scheme was introduced for seeded XUV free electron lasers (FELs) combining shot-to-shot phase modulation with lock-in detection. This method stabilized the seed laser beampath on the fundamental ultraviolet wavelength to a high degree. Here, we extend this scheme including the stabilization of the XUV beampath, incorporating phase fluctuations from the FEL high gain harmonic generation process. Our analysis reveals a clear signal improvement with the new method compared to the previous stabilization scheme.

The autoionization dynamics of superexcited superfluid He nanodroplets doped with Na atoms is studied by extreme-ultraviolet (XUV) time-resolved electron spectroscopy. Following excitation into the higher-lying droplet absorption band, the droplet relaxes into the lowest metastable atomic 1s2s 1,3S states from which interatomic Coulombic decay (ICD) takes place either between two excited He atoms or between an excited He atom and a Na atom attached to the droplet surface. Four main ICD channels are identified, and their decay times are determined by varying the delay between the XUV pulse and a UV pulse that ionizes the initial excited state and thereby quenches ICD. The decay times for the different channels all fall in the range of ∼1 ps, indicating that the ICD dynamics are mainly determined by the droplet environment. A periodic modulation of the transient ICD signals is tentatively attributed to the oscillation of the bubble forming around the localized He excitation.

The relaxation dynamics of superexcited superfluid He nanodroplets is thoroughly investigated by means of extreme-ultraviolet (XUV) femtosecond electron and ion spectroscopy complemented by time-dependent density functional theory (TDDFT). Three main paths leading to the emission of electrons and ions are identified: droplet autoionization, pump-probe photoionization, and autoionization induced by re-excitation of droplets relaxing into levels below the droplet ionization threshold. The most abundant product ions are He2+, generated by droplet autoionization and by photoionization of droplet-bound excited He atoms. He+ appear with some pump-probe delay as a result of the ejection He atoms in their lowest excited states from the droplets. The state-resolved time-dependent photoelectron spectra reveal that intermediate excited states of the droplets are populated in the course of the relaxation, terminating in the lowest-lying metastable singlet and triplet He atomic states. The slightly faster relaxation of the triplet state compared to the singlet state is in agreement with the simulation showing faster formation of a bubble around a He atom in the triplet state.

The recent development of ultrafast extreme ultraviolet (XUV) coherent light sources bears great potential for a better understanding of the structure and dynamics of matter. Promising routes are advanced coherent control and nonlinear spectroscopy schemes in the XUV energy range, yielding unprecedented spatial and temporal resolution. However, their implementation has been hampered by the experimental challenge of generating XUV pulse sequences with precisely controlled timing and phase properties. In particular, direct control and manipulation of the phase of individual pulses within an XUV pulse sequence opens exciting possibilities for coherent control and multidimensional spectroscopy, but has not been accomplished. Here, we overcome these constraints in a highly time-stabilized and phase-modulated XUV-pump, XUV-probe experiment, which directly probes the evolution and dephasing of an inner subshell electronic coherence. This approach, avoiding any XUV optics for direct pulse manipulation, opens up extensive applications of advanced nonlinear optics and spectroscopy at XUV wavelengths.

Collinear double-pulse seeding of the High-Gain Harmonic Generation (HGHG) process in a free-electron laser (FEL) is a promising approach to facilitate various coherent nonlinear spectroscopy schemes in the extreme ultraviolet (XUV) spectral range. However, in collinear arrangements using a single nonlinear medium, temporally overlapping seed pulses may introduce nonlinear mixing signals that compromise the experiment at short time delays. Here, we investigate these effects in detail by extending the analysis described in a recent publication (Wituschek et al., Nat. Commun., 11, 883, 2020). High-order fringe-resolved autocorrelation and wave packet interferometry experiments at photon energies > 23 eV are performed, accompanied by numerical simulations. It turns out that both the autocorrelation and the wave-packet interferometry data are very sensitive to saturation effects and can thus be used to characterize saturation in the HGHG process. Our results further imply that time-resolved spectroscopy experiments are feasible even for time delays smaller than the seed pulse duration.

The effects of high pulse intensity and chirp on two-dimensional electronic spectroscopy signals are experimentally investigated in the highly non-perturbative regime using atomic rubidium vapor as clean model system. Data analysis is performed based on higher-order Feynman diagrams and non-perturbative numerical simulations of the system response. It is shown that higher-order contributions may lead to a fundamental change of the static appearance and beating-maps of the 2D spectra and that chirped pulses enhance or suppress distinct higher-order pathways. We further give an estimate of the threshold intensity beyond which the high-intensity effects become visible for the system under consideration.

Recent work applying multidimentional coherent electronic spectroscopy at dilute samples in the gas phase is reviewed. The development of refined phase cycling approaches with improved sensitivity has opened up new opportunities to probe even dilute gas-phase samples. In this context, first results of two-dimensional spectroscopy performed at doped helium droplets reveal the femtosecond dynamics upon the electronic excitation of cold, weakly-bound molecules, and even the induced dynamics from the interaction with the helium environment. Such experiments, offering well-defined conditions at low temperatures, are potentially enabling the isolation of fundamental processes in the excitation and charge transfer dynamics of molecular structures which so far have been masked in complex bulk environments.

Long-range interparticle interactions are revealed in extremely dilute thermal atomic ensembles using highly sensitive nonlinear femtosecond spectroscopy.

We introduce the concept of phase-synchronous undersampling in nonlinear spectroscopy. The respective theory is presented and validated experimentally in a phase-modulated quantum beat experiment by sampling high phase modulation frequencies with low laser repetition rates. The advantage of undersampling in terms of signal quality and reduced acquisition time is demonstrated and breakdown conditions are identified. The presented method is particularly beneficial for experimental setups with limited signal/detection rates.

Two-dimensional electronic spectroscopy (2DES) is one of the most powerful spectroscopic techniques with unique sensitivity to couplings, coherence properties and real-time dynamics of a quantum system. While successfully applied to a variety of condensed phase samples, high precision experiments on isolated systems in the gas phase have been so far precluded by insufficient sensitivity. However, such experiments are essential for a precise understanding of fundamental mechanisms and to avoid misinterpretations. Here, we solve this issue by extending 2DES to isolated nanosystems in the gas phase prepared by helium nanodroplet isolation in a molecular beam-type experiment. This approach uniquely provides high flexibility in synthesizing tailored, quantum state-selected model systems of single and many-body character. In a model study of weakly-bound Rb 2 and Rb 3 molecules we demonstrate the method’s unique capacity to elucidate interactions and dynamics in tailored quantum systems, thereby also bridging the gap to experiments in ultracold quantum science.

Two dimensional electronic spectroscopy (2DES) is a powerful tool to study coherences and correlations on ultrafast time scales. Until now, 2DES has been limited almost exclusively to condensed phase studies. Our aim is to apply 2DES to controlled isolated systems by using doped helium nanodroplet beams. Helium nanodroplets provide the dopant with a cold environment and minimal perturbation, which are ideal conditions to study the behavior of an individual system in a well-controlled environment. However, the target density in doped helium droplet beams is several orders of magnitude lower than in bulk condensed phase samples. Furthermore, 2DES depends on the third order response of the sample to the incident light. Together, this leads to particularly small signals. We adapt a phase modulation technique combined with lock-in detection to overcome this issue [1]. This technique has already shown significant sensitivity improvements for coherent pump-probe spectroscopy in helium nanodroplets [2]. One advantage of 2D spectroscopy is that in the 2D spectra homogeneous and inhomogeneous broadening mechanisms are readily disentangeled. For this reason, 2D spectroscopy has been used to characterize the dynamics of solvents such as the ultrafast rearrangement dynamics of water [3]. In a similar way, 2DES may be used to get more insights into the helium droplet properties when doped with different species. We currently implement the experimental setup and do initial characterization measurements.

A phase modulation technique to sensitively and selectively isolate multiple-quantum coherences in a femtosecond pump-probe setup is presented. By detecting incoherent observables and incorporating lock-in amplification, even weak signals of highly dilute samples can be acquired. Applying this method, efficient isolation of one- and two-photon quantum beats in a rubidium-doped helium droplet beam experiment is demonstrated and collective resonances are observed in a potassium vapor for the first time up to fourth order. Our approach provides promising perspectives for coherent time-resolved experiments in the deep UV and multidimensional spectroscopy schemes, in particular when mass-selective detection of particles in dilute gas-phase targets is possible.