Time-Resolved sub-Ångström Metrology by Temporal Phase Interferometry near X-Ray Resonances of Nuclei.

We introduce an analytical phase-reconstruction principle that retrieves atomic scale motion via time-domain interferometry. The approach is based on a resonant interaction with high-frequency light and does not require temporal resolution on the time scale of the resonance period. It is thus applicable to hard x rays and gamma rays for measurements of extremely small spatial displacements or relative-frequency changes. Here, it is applied to retrieve the temporal phase of a 14.4 keV emission line of an Fe-57 sample, which corresponds to a spatial translation of this sample. The small wavelength of this transition (lambda = 0.86 angstrom) allows for determining the motion of the emitter on sub-angstrom ngstrom length and nanosecond timescales.