  Young's archetypal double-slit experiment forms the basis for modern
diffraction techniques: the elastic scattering of waves yields an interference
pattern that captures the real-space structure. Here, we report on an inelastic
incarnation of Young's experiment and demonstrate that resonant inelastic x-ray
scattering (RIXS) measures interference patterns which reveal the symmetry and
character of electronic excited states in the same way as elastic scattering
does for the ground state. A prototypical example is provided by the
quasi-molecular electronic structure of insulating Ba3CeIr2O9 with structural
Ir dimers and strong spin-orbit coupling. The double 'slits' in this resonant
experiment are the highly localized core levels of the two Ir atoms within a
dimer. The clear double-slit-type sinusoidal interference patterns that we
observe allow us to characterize the electronic excitations, demonstrating the
power of RIXS interferometry to unravel the electronic structure of solids
containing, e.g., dimers, trimers, ladders, or other superstructures.
