Super-resolution stimulated X-ray Raman spectroscopy

Propagation of intense X-ray pulses through dense media has led to the observation of phenomena such as atomic X-ray lasing^1,2, self-induced transparency³ and stimulated X-ray Raman scattering (SXRS)⁴. SXRS has been long predicted as a means to launch and probe valence-electron wavepackets and as a building block for nonlinear X-ray spectroscopies^5,6. However, experimental observations of SXRS to date^4,7,8 have not provided spectroscopic information, and theoretical modelling has largely implemented hard-to-realize phase-coherent attosecond pulses. Here we demonstrate SXRS with spectroscopic precision, that is, detection of valence-excited states in neon with a near Fourier-limited joint energy-time resolution of 0.1 eV-40 fs. We used a new covariance analysis between statistically spiky broadband incident X-ray and scattered X-ray Raman pulses. Using 18,000 single shots, we beat not only the incident (about 8 eV) bandwidth but also the  approximately 0.2 eV instrumental energy resolution, thus creating super-resolution conditions, in analogy to super-resolved fluorescence microscopy⁹. Our experimental results, supported by ab initio propagation simulations, reveal the competition between lasing in the ion and stimulated Raman scattering in the neutral. We demonstrate enhanced signal collection efficiency and a broad excitation window, surpassing spontaneous Raman efficiencies by orders of magnitude. This stochastic SXRS approach represents a first step towards tracking elementary events that determine chemical outcomes¹⁰.