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Physical review letters 123(15), 153902 (2019). doi:10.1103/PhysRevLett.123.153902, We introduce an analytical phase-reconstruction principle that retrieves atomic scale motion via timedomaininterferometry. The approach is based on a resonant interaction with high-frequency light and doesnot require temporal resolution on the time scale of the resonance period. It is thus applicable to hard x raysand γ 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 keVemission line of an 57Fe sample, which correspondsto a spatial translation of this sample. The small wavelength of this transition (λ ¼ 0.86 Å) allows fordetermining the motion of the emitter on sub-Ångström length and nanosecond timescales., Published by APS, College Park, Md.

Modern x-ray light sources promise access to structure and dynamics of matter in largely unexplored spectral regions. However, the desired information is encoded in the light intensity and phase, whereas detectors register only the intensity. This phase problem is ubiquitous in crystallography and imaging, and impedes the exploration of quantum effects at x-ray energies. Here, we demonstrate phase-sensitive measurements characterizing the quantum state of a nuclear two-level system at hard x-ray energies. The nuclei are initially prepared in a superposition state. Subsequently, the relative phase of this superposition is interferometrically reconstructed from the emitted x-rays. Our results form a first step towards x-ray quantum state tomography, and provide new avenues for structure determination and precision metrology via x-ray Fano interference., 5 pages, 3 figures, plus supplementary information