Single-shot sorting of Mössbauer time-domain data at X-ray free-electron lasers

Abstract

Mössbauer spectroscopy is widely used to study structure and dynamics of matter with remarkably high energy resolution, provided by the narrow nuclear resonance line widths. However, the narrow width implies low count rates, such that experiments commonly average over extended measurement times or many x-ray pulses (``shots''). This averaging impedes the study of non-equilibrium phenomena. It has been suggested that X-ray free-electron lasers (XFELs) could enable Mössbauer single-shot measurements without averaging, and a proof-of-principle demonstration has been reported. However, so far, only a tiny fraction of all shots resulted in signal-photon numbers which are sufficiently high for a single-shot analysis. Here, we demonstrate coherent nuclear-forward-scattering of self-seeded XFEL radiation, with up to 900 signal-photons per shot. We develop a sorting approach which allows us to include all data on a single-shot level, independent of the signal content of the individual shots. It utilizes the presence of different dynamics classes, i.e. different nuclear evolutions after each excitation. Each shot is assigned to one of the classes, which can then be analyzed separately. Our approach determines the classes from the data without requiring theory modeling nor prior knowledge on the dynamics, making it also applicable to unknown phenomena. We envision that our approach opens up new grounds for Mössbauer science, enabling the study of out-of-equilibrium transient dynamics of the nuclei or their environment.

Figures (13)

• Figure 1: (a) Single-shot sorting. We consider a generic experiment in which Mössbauer nuclei may undergo different dynamics following an x-ray excitation. Two dynamics classes "A" and "B" are indicated in red and blue as examples. The information on the dynamics is typically lost for most shots during the measurement (gray squares). Our data-driven approach identifies different dynamics classes, and subsequently sorts all shots according to the identified classes. This way, the classes can be analyzed separately, avoiding an averaging over different dynamics. (b) Schematic experimental setup at European XFEL. The self-seeded x-rays pass through a double-crystal monochromator (DCM), which removes the off-resonant SASE background, and are then reflected from a thin-film waveguide containing ${}^{57}$Fe nuclei. The nuclear-resonant signal and the off-resonant background are separated using a polarization analyzer. The time-dependent intensity of the x-rays scattered by the nuclei is then recorded using avalanche photo diodes (APD). The two dynamics classes are deterministically implemented using slightly different scattering geometries, as explained in the main text. (c) Average intensities as a function of time after x-ray excitation for dynamics classes A (red) and B (blue) separately, as well as their average (black). Only the latter signal is accessible without per-shot information on the dynamics. The 1-sigma uncertainty band of the measurements falls mostly within the width of the plotted lines (see Appendix \ref{['detection']}).
• Figure 2: Example raw data with high signal content. Out of the full dataset, the time-dependent intensities of the 50 shots with highest signal content are shown in gray. The lines are plotted semi-transparent. This way, for example, the individual single-photon detection events at late times can be distinguished from the overlapping data at early times via the plot density. The black dashed line displays the corresponding time-dependent intensity averaged over the full dataset. The green dotted line indicates the average APD signal amplitude for individual recorded signal photons. The orange shaded area indicates the analysis ROI between 3 ns and 10 ns identified by the data-driven algorithm.
• Figure 3: Overview of the clustering and sorting. First, all shots are sorted by their signal content. Second, the $N_\textrm{hs}$ shots with highest signal content are used
• Figure 4: Histogram of signal contents. A histogram of the signal content of all recorded individual shots. Estimates on the corresponding photon numbers and their uncertainties are indicated by the green bars on the top axis. For details on the photon number estimate see Appendix \ref{['content']}. In addition, the purple dashed lines indicate low (10% of the traces), medium (50% of the traces) and high (50 highest traces) signal content and examples for those regimes are shown in Fig. \ref{['fig:exampleHighNTraces']}. The inset shows a magnification of the highest signal-content region.
• Figure 5: Overall clustering quality $\mathcal{S}$ as function of the analysis region of interest start and end times. Results are shown for the subset of $N_\textrm{hs}=50$ shots with highest signal content. A moving Gaussian average filter of width $\sigma=1$ns was applied to the data to reduce the influence of outliers and to favor stable analysis parameter regions. The lighter the color, the better the clustering quality $\mathcal{S}$, with the optimum found for the analysis ROI of (3 ns, 10 ns) and marked by the red cross. In gray invalid regions are marked.