ECAMP 15

1. Introduction

The X-ray spectral range can address atomic scale (nm) spatial resolution at ultrafast time (fs) scales, with element specificity and site-selective excitation. Non-linear wave mixing techniques in this range, in particular four-wave mixing (FWM) methods, can thus provide information on the structural and electronic dynamics of atomic and molecular systems with unprecedented resolution. X-ray FWM brings the capability to study the electronic states coupling between spatially localized inner and/or core transitions among different sites of a quantum system or to study transport phenomena at the nanoscale. Whereas mixed XUV/X-ray - optical four-wave mixing and all-EUV have been successfully demonstrated in a transient grating (TG) configuration (see refs. [1-3] and refs. therein), non-linear all-X-ray four-wave mixing spectroscopy has been envisioned and theoretically described [4] but not yet realized experimentally, remaining as a long-awaited goal until now [5].

We demonstrate nonlinear X-ray four-wave mixing (XFWM) will all photons in the soft X-ray range (850-870 eV) using a non-collinear folded ‘Box’ or BoxCARS configuration [6]. In this robust configuration and obeying phase-matching, the X-ray photons generated by three interacting soft X-ray beams are emitted towards the fourth corner of a square, allowing for background-free detection. The signal could thus be clearly discriminated from the incoming beams and detected either by an in-line X-ray grating spectrometer (ΔE≈0.4 eV), allowing for its spectral characterization or by recording the fluorescence from a YAG screen moved into the signal beam path, for its spatial characterization.

2. Results

SASE pulses from the Swiss Free Electron Laser (SwissFEL) are focused by a pair of KB mirrors into an in-vacuum gas-cell filled with a few hundreds mbar of Ne producing a coherent response from core-shell electrons. When scanning the FEL pink beam available at the Maloja end-station around the Ne K-absorption edge at ~870 eV, the YAG fluorescence shows a laser-like signal beam, well isolated from the incoming beams, which shows the maximum signal strength when approaching the pre-edge resonances of Ne. The signal generation efficiency, as defined by the ratio of signal photons that are scattered into the phase-matched direction and the incoming photons is in the order of 0.15 %, demonstrating an efficient signal generation.

The spectrally dispersed XFWM signals provide a rich map, comprising multiple contributions from neutral neon and its ions. The large set of parameters explored, including FEL intensity, gas pressure and pulse duration ranging from 30 fs down to 3 fs (rms), provides key information that allow us to disentangle the different origin of the XFWM signals, including resonantly-enhanced X-ray two-color processes. The measured results are compared to the available literature on stimulated Raman X-ray scattering in Neon [7] and with the results of a dedicated model that accounts for the beam propagation and population changes during the X-ray pulse duration. We discuss in detail the measured and calculated 2D spectral maps, and how the correlation plots reflect the coupling between electronic states of neon, allowing us to distinguish these signals from X-ray lasing processes originated in the ions.

The general feasibility of non-collinear four-wave mixing in the X-ray range is demonstrated. The robustness of the setup, the strength of the signals and the spectral and spatial information achieved from the experiment implies a major breakthrough for the application of nonlinear X-ray wave mixing as a spectroscopic tool in general, and as basis for 2D X-ray correlation spectroscopy. In addition, preliminary time resolved signals and approaches to extend the proposed methodology to the time domain, based on two-colour mode available at the Athos branch of SwissFEL are introduced.

3. References

[1] F. Bencivenga et al., “Four-wave mixing experiments with extreme ultraviolet transient gratings” Nature 520, 205 (2015).
[2] F. Bencivenga, et al. "Nanoscale transient gratings excited and probed by extreme ultraviolet femtosecond pulses." Sci. Adv. 5(7) eaaw5805 (2019).
[3] J.R. Rouxel, D. Fainozzi, R. Mankowsky, B. Rösner, G. Seniutinas, et al. “Hard x-ray transient grating spectroscopy on bismuth germinate” Nat. Photon 15(7), 499–503 (2021)
[4] S. Tanaka and S. Mukamel “X-ray four-wave mixing in molecules” J. Chem. Phys. 116(5), 1877–1891 (2002)
[5] A.S. Morillo-Candas, et al. "Coherent all X-ray four-wave mixing at core shell resonances." arXiv preprint arXiv:2408.11881 (2024), https://doi.org/10.48550/arXiv.2408.11881
[6] Y. Prior, “Three-dimensional phase matching in four-wave mixing” Appl. Opt. 19(11), 1741–11743 (1980)
[7] C. Weninger, M. Purvis, D. Ryan, R.A. London, J.D. Bozek, C. Bostedt, A. Graf, G. Brown, J.J. Rocca, and N. Rohringer, "Stimulated Electronic X-Ray Raman Scattering" PRL 111, 233902 (2013).