X-ray free-electron lasers (XFELs) provide intense pulses that can generate stimulated X-ray emission, a phenomenon that has been observed and studied in materials ranging from neon to copper. Two schemes have been employed: amplified spontaneous emission (ASE) and seeded stimulated emission (SSE), where a second color XFEL pulse provides the seed. Both phenomena are currently explored for coherent X-ray laser sources and spectroscopy. Here, we report measurements of ASE and SSE of the 5.9 keV Mn Kα₁ fluorescence line from a 3.9 molar NaMnO₄ solution, pumped with 7 femtosecond FWHM XFEL pulses at 6.6 keV. We observed ASE at a pump pulse intensity of 1.7 × 10¹⁹ W/cm², consistent with earlier findings. We observed SSE at dramatically reduced pump pulse intensities down to 1.1 × 10¹⁷ W/cm². These intensities are well within the range of many existing XFEL instruments, which supports the experimental feasibility of SSE as a tool to generate coherent X-ray pulses, spectroscopic studies of transition metal complexes, and other applications.

Coherent nonlinear spectroscopies and imaging in the X-ray domain provide direct insight into the coupled motions of electrons and nuclei with resolution on the electronic length scale and timescale. The experimental realization of such techniques will strongly benefit from access to intense, coherent pairs of femtosecond X-ray pulses. We have observed phase-stable X-ray pulse pairs containing more than 3 × 107 photons at 5.9 keV (2.1 Å) with ∼1 fs duration and 2 to 5 fs separation. The highly directional pulse pairs are manifested by interference fringes in the superfluorescent and seeded stimulated manganese Kα emission induced by an X-ray free-electron laser. The fringes constitute the time-frequency X-ray analog of Young’s double-slit interference, allowing for frequency domain X-ray measurements with attosecond time resolution.

We recently identified two labeling-related mistakes in Optica 10, 513 (2023)OPTIC82334-253610.1364/OPTICA.485989. The first mistake concerns the labeling of the focus used during one scan. The second mistake concerns the labeling of a filter used in some runs to protect the detector. These mistakes do not affect the overall findings and conclusions in our paper, but some numbers, text, and figures are slightly affected by it. These items have been corrected and are listed below. Finally, a missing DOE award number (DE-SC0023270) has been added below.