Interferometric characterization of the relative phase between two X-ray free-electron laser pulses using long-lived Mössbauer resonances

Coherence-based spectroscopy methods are powerful tools to explore structure and dynamics of matter. However, towards higher photon energies, the generation of sequences of pulses with well-characterized relative delays and phases remains a challenge. Here, we introduce a method to measure the relative phase $\varphi$ between subsequent transform-limited pulses from high-repetition-rate x-ray free-electron lasers (XFELs). It is based on a Ramsey-type interference measurement, enabled by introducing long-lived M\"ossbauer resonances into the XFEL beam path up- or downstream a primary experiment, which allow one to bridge the temporal gap between the XFEL pulses. The measured phase can be used as additional input for the analysis of the primary experiment.