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Abstract

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.