Ghost-imaging-enhanced noninvasive spectral characterization of stochastic x-ray free-electron-laser pulses

ARTICLE https://doi.org/10.1038/s42005-022-00962-8 OPEN Ghost-imaging-enhanced noninvasive spectral characterization of stochastic x-ray free-electronlaser pulses 1234567890():,; Kai Li 1,2 ✉, Joakim Laksman3, Tommaso Mazza3, Gilles Doumy 2, Dimitris Koulentianos 2, Alessandra Picchiotti4, Svitozar Serkez 3, Nina Rohringer 5,6, Markus Ilchen7, Michael Meyer Linda Young 1,2,8 ✉ 3 & High-intensity ultrashort X-ray free-electron laser (XFEL) pulses are revolutionizing the study of fundamental nonlinear x-ray matter interactions and coupled electronic and nuclear dynamics. To fully exploit the potential of this powerful tool for advanced x-ray spectroscopies, a noninvasive spectral characterization of incident stochastic XFEL pulses with high resolution is a key requirement. Here we present a methodology that combines highacceptance angle-resolved photoelectron time-of-flight spectroscopy and ghost imaging to enhance the quality of spectral characterization of x-ray free-electron laser pulses. Implementation of this noninvasive high-resolution x-ray diagnostic can greatly benefit the ultrafast x-ray spectroscopy community by functioning as a transparent beamsplitter for applications such as transient absorption spectroscopy in averaging mode as well as covariance-based xray nonlinear spectroscopies in single-shot mode where the shot-to-shot fluctuations inherent to a self-amplified spontaneous emission (SASE) XFEL pulse are a powerful asset. 1 Department of Physics, The University of Chicago, Chicago, IL 60637, USA. 2 Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL 60439, USA. 3 European XFEL, Holzkoppel 4, 22869 Schenefeld, Germany. 4 The Hamburg Centre for Ultrafast Imaging, Hamburg University, Luruper Chaussee 149, 22761 Hamburg, Germany. 5 Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany. 6 Department of Physics, Universität Hamburg, 20355 Hamburg, Germany. 7 Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany. 8 James Franck Institute, The University of Chicago, Chicago, IL 60637, USA. ✉email: ; COMMUNICATIONS PHYSICS | (2022)5:191 | https://doi.org/10.1038/s42005-022-00962-8 | www.nature.com/commsphys 1 ARTICLE X COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-022-00962-8 -ray free-electron lasers, with brilliance ten orders of magnitude higher than synchrotrons, continuous tunability over the soft and hard x-ray regimes and subfemtosecond pulse duration1, have emerged as a powerful tool both to explore fundamental nonlinear x-ray interactions in isolated atomic and molecular systems2–7 and, to follow photoinduced electronic and nuclear dynamics on their intrinsic femtosecond timescales via pump/probe techniques8,9. For the latter objective, core-level x-ray transient absorption (XTAS) with ultrafast x-ray pulses has become a workhorse - it projects core electronic states onto unoccupied valence/Rydberg states, thereby capturing the evolution of valence electronic motion following an excitation pulse. However, the realization of XTAS is challenging at x-ray free-electron lasers (XFELs) where the x-ray pulses with bandwidth ΔE/E ~ 1%, typically produced by self-amplified spontaneous emission (SASE), have spiky temporal and spectral profiles that vary stochastically on a shot-by-shot basis10–14. The traditional approach for XTAS with XFELs is to monochromatize the SASE beam15,16 and scan the monochromatic beam (ΔE/E ~0.01%) across the desired spectral range. This makes inefficient use of the full XFEL beam, imposes limits on-time resolution via the uncertainty principle, and, by reducing the pulse intensities, hampers the realization of nonlinear x-ray spectroscopies. An alternative approach is to monitor the incident and transmitted intensity to obtain an absorption spectrum, IT(ω)/I0(ω), across the entire SASE bandwidth. With this approach, one may realize experimental techniques employing correlation analysis that take advantage of the intrinsic stochastic nature of XFELs pulses17–20. By using pulses with uncorrelated fluctuations one can leverage the noise such that each repetition of the experiment, i.e., each XFEL shot, represents a new measurement under different conditions. As an example, spectral ghost imaging has been applied to obtain an absorption spectrum with an energy resolution better than the averaged SASE bandwidth21,22. In general, the characterization of the incident pulses is essential to this class of covariance spectroscopies as previously demonstrated in the UV regime23. Several diagnostic tools have demonstrated well-resolved spectral measurements on a single-shot basis without compromising the quality of the x-ray beam. A commonality is the use of optical elements to split the incident x-ray beam into reference and sample beams. Beamsplitters for hard x-rays use crystal Bragg diffraction24,25 while diffraction gratings are used for soft x-rays26,27. An alternative is to use photoionization of dilute target gas and measure the kinetic energy of ejected photoelectrons to retrieve the incident photon spectrum via the photoelectric effect28–30. Indeed, the use of an array of 16 electron timeof-flight spectrometers (eTOFs) radially distributed about the propagating x-ray beam and hereafter referred to as the photoelectron spectrometer array, (PES array) has enabled the measurement of the position, polarization, and central energy of an x-ray photon beam as demonstrated at the PETRA-P04 beamline28. At XFELs, while it is straightforward to measure the central photon energy with the PES array29 as has been demonstrated for two-color x-ray pulses31 and to obtain simultaneously polarization diagnostics32,33, it is more challenging to obtain single-shot spectra with an energy resolution comparable to a grating spectrometer. Here we use a ghost-imaging algorithm to improve the energy resolution of the raw PES array measurements. Thousands of SASE spectra were measured simultaneously by the PES array and a grating spectrometer and ghost imaging was applied to compute the response matrix of the PES array. The response matrix was then used to reconstruct the x-ray spectrum with energy resolution improved from ~1 to 0.5 eV at central energy of 910 eV for a resolution of ΔE/E ~1/2000 under the present conditions. This 2 response matrix derived from ghost imaging also provides predictive power for the spectral profile of yet-to-be-measured XFEL pulses. Results Spectral ghost imaging. Ghost imaging is an experimental technique, which uses statistical fluctuations of an incident beam to extract information about an object using a beam replica that has not physically interacted with the object34. It can be used in the spatial35–37, temporal18, and spectral21,22 domains. Traditional ghost imaging requires a beamsplitter to separate the incident beam into two replicas, the object beam and the reference beam. The object (...truncated)